TSTP Solution File: KLE044-10 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE044-10 : TPTP v8.1.0. Released v7.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Sep 17 17:23:59 EDT 2022
% Result : Unsatisfiable 69.06s 44.69s
% Output : Proof 69.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 158
% Syntax : Number of formulae : 563 ( 422 unt; 12 typ; 0 def)
% Number of atoms : 712 ( 695 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 245 ( 100 ~; 96 |; 0 &)
% ( 49 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 16 ( 16 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 21 ( 8 >; 13 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-4 aty)
% Number of variables : 551 ( 516 !; 0 ?; 551 :)
% Comments :
%------------------------------------------------------------------------------
tff(tuple_type,type,
tuple: ( $i * $i ) > $i ).
tff(true_type,type,
true: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $i ).
tff(star_type,type,
star: $i > $i ).
tff(addition_type,type,
addition: ( $i * $i ) > $i ).
tff(sK1_goals_X0_type,type,
sK1_goals_X0: $i ).
tff(one_type,type,
one: $i ).
tff(sK2_goals_X0_type,type,
sK2_goals_X0: $i ).
tff(ifeq3_type,type,
ifeq3: ( $i * $i * $i * $i ) > $i ).
tff(multiplication_type,type,
multiplication: ( $i * $i ) > $i ).
tff(ifeq2_type,type,
ifeq2: ( $i * $i * $i * $i ) > $i ).
tff(ifeq_type,type,
ifeq: ( $i * $i * $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( ifeq3(addition(A,B),B,leq(A,B),true) = true )
<=> ( ifeq3(addition(A,B),B,leq(A,B),true) = true ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true )
<=> ! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
tff(5,plain,
! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( ifeq3(addition(A,B),B,leq(A,B),true) = true )
| ( ifeq3(addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true) = true ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
ifeq3(addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true) = true,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
<=> ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
tff(14,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(star(addition(one,sK1_goals_X0)),addition(addition(sK1_goals_X0,one),one)) = addition(multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one)),multiplication(star(addition(one,sK1_goals_X0)),one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
multiplication(star(addition(one,sK1_goals_X0)),addition(addition(sK1_goals_X0,one),one)) = addition(multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one)),multiplication(star(addition(one,sK1_goals_X0)),one)),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one)),multiplication(star(addition(one,sK1_goals_X0)),one)) = multiplication(star(addition(one,sK1_goals_X0)),addition(addition(sK1_goals_X0,one),one)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
^ [A: $i] :
refl(
( ( multiplication(A,one) = A )
<=> ( multiplication(A,one) = A ) )),
inference(bind,[status(th)],]) ).
tff(21,plain,
( ! [A: $i] : ( multiplication(A,one) = A )
<=> ! [A: $i] : ( multiplication(A,one) = A ) ),
inference(quant_intro,[status(thm)],[20]) ).
tff(22,plain,
( ! [A: $i] : ( multiplication(A,one) = A )
<=> ! [A: $i] : ( multiplication(A,one) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
! [A: $i] : ( multiplication(A,one) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
tff(24,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(skolemize,[status(sab)],[24]) ).
tff(26,plain,
! [A: $i] : ( multiplication(A,one) = A ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
( ~ ! [A: $i] : ( multiplication(A,one) = A )
| ( multiplication(star(addition(one,sK1_goals_X0)),one) = star(addition(one,sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(28,plain,
multiplication(star(addition(one,sK1_goals_X0)),one) = star(addition(one,sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[27,26]) ).
tff(29,plain,
^ [B: $i,A: $i] :
refl(
( ( addition(A,B) = addition(B,A) )
<=> ( addition(A,B) = addition(B,A) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
<=> ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
<=> ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
tff(33,plain,
! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ),
inference(skolemize,[status(sab)],[33]) ).
tff(35,plain,
! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[34,30]) ).
tff(36,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,sK1_goals_X0) = addition(sK1_goals_X0,one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(37,plain,
addition(one,sK1_goals_X0) = addition(sK1_goals_X0,one),
inference(unit_resolution,[status(thm)],[36,35]) ).
tff(38,plain,
multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)) = multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one)),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,plain,
multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one)) = multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one)),multiplication(star(addition(one,sK1_goals_X0)),one)) = addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[39,28]) ).
tff(41,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = addition(multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one)),multiplication(star(addition(one,sK1_goals_X0)),one)),
inference(symmetry,[status(thm)],[40]) ).
tff(42,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),
inference(unit_resolution,[status(thm)],[42,35]) ).
tff(44,plain,
addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq2(A,A,B,C) = B )
<=> ( ifeq2(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(46,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[45]) ).
tff(47,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_001) ).
tff(49,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
ifeq2(true,true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[52,51]) ).
tff(54,plain,
^ [A: $i] :
refl(
( ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )
<=> ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )
<=> ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
( ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )
<=> ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(57,axiom,
! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
tff(58,plain,
! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ),
inference(skolemize,[status(sab)],[58]) ).
tff(60,plain,
! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true ),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( ~ ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )
| ( leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = true ) ),
inference(quant_inst,[status(thm)],]) ).
tff(62,plain,
leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = true,
inference(unit_resolution,[status(thm)],[61,60]) ).
tff(63,plain,
ifeq2(leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = ifeq2(true,true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
^ [B: $i,A: $i] :
refl(
( ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
<=> ( ifeq2(leq(A,B),true,addition(A,B),B) = B ) )),
inference(bind,[status(th)],]) ).
tff(65,plain,
( ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
<=> ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ) ),
inference(quant_intro,[status(thm)],[64]) ).
tff(66,plain,
( ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
<=> ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,axiom,
! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order_1) ).
tff(68,plain,
! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ),
inference(skolemize,[status(sab)],[68]) ).
tff(70,plain,
! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B ),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
ifeq2(leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
star(addition(one,sK1_goals_X0)) = ifeq2(leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[72]) ).
tff(74,plain,
star(addition(one,sK1_goals_X0)) = addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[73,63,53,44]) ).
tff(75,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[74]) ).
tff(76,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0)))) = addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
<=> ( addition(A,addition(B,C)) = addition(addition(A,B),C) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
( ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(80,axiom,
! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
tff(81,plain,
! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,plain,
! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(skolemize,[status(sab)],[81]) ).
tff(83,plain,
! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(modus_ponens,[status(thm)],[82,78]) ).
tff(84,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(85,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[84,83]) ).
tff(86,plain,
addition(addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))) = addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[85]) ).
tff(87,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
<=> ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ) )),
inference(bind,[status(th)],]) ).
tff(88,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(90,axiom,
! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
tff(91,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
inference(modus_ponens,[status(thm)],[92,88]) ).
tff(94,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))) = addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(95,plain,
multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))) = addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[94,93]) ).
tff(96,plain,
addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))) = multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[95]) ).
tff(97,plain,
^ [A: $i] :
refl(
( ( multiplication(one,A) = A )
<=> ( multiplication(one,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [A: $i] : ( multiplication(one,A) = A )
<=> ! [A: $i] : ( multiplication(one,A) = A ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [A: $i] : ( multiplication(one,A) = A )
<=> ! [A: $i] : ( multiplication(one,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(100,axiom,
! [A: $i] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
tff(101,plain,
! [A: $i] : ( multiplication(one,A) = A ),
inference(modus_ponens,[status(thm)],[100,99]) ).
tff(102,plain,
! [A: $i] : ( multiplication(one,A) = A ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [A: $i] : ( multiplication(one,A) = A ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
( ~ ! [A: $i] : ( multiplication(one,A) = A )
| ( multiplication(one,star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
multiplication(one,star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[104,103]) ).
tff(106,plain,
star(addition(one,sK1_goals_X0)) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
ifeq2(leq(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[107,70]) ).
tff(109,plain,
^ [A: $i] :
refl(
( ( leq(addition(one,multiplication(star(A),A)),star(A)) = true )
<=> ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ) )),
inference(bind,[status(th)],]) ).
tff(110,plain,
( ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true )
<=> ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ) ),
inference(quant_intro,[status(thm)],[109]) ).
tff(111,plain,
( ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true )
<=> ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(112,axiom,
! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).
tff(113,plain,
! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ),
inference(modus_ponens,[status(thm)],[112,111]) ).
tff(114,plain,
! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ),
inference(skolemize,[status(sab)],[113]) ).
tff(115,plain,
! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true ),
inference(modus_ponens,[status(thm)],[114,110]) ).
tff(116,plain,
( ~ ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true )
| ( leq(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = true ) ),
inference(quant_inst,[status(thm)],]) ).
tff(117,plain,
leq(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = true,
inference(unit_resolution,[status(thm)],[116,115]) ).
tff(118,plain,
true = leq(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[117]) ).
tff(119,plain,
ifeq2(true,true,addition(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = ifeq2(leq(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[118]) ).
tff(120,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,addition(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(121,plain,
ifeq2(true,true,addition(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[120,51]) ).
tff(122,plain,
addition(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = ifeq2(true,true,addition(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[121]) ).
tff(123,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))) = addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(124,plain,
addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))) = addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),one),
inference(unit_resolution,[status(thm)],[123,35]) ).
tff(125,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),one) = addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
addition(addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),one),star(addition(one,sK1_goals_X0))) = addition(addition(one,multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[125]) ).
tff(127,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(one,star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),one),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(128,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(one,star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),one),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[127,83]) ).
tff(129,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(one,star(addition(one,sK1_goals_X0)))) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[128,126,122,119,108,106]) ).
tff(130,plain,
addition(addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(one,star(addition(one,sK1_goals_X0)))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))) = addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))))) = addition(addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(one,star(addition(one,sK1_goals_X0)))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(132,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))))) = addition(addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(one,star(addition(one,sK1_goals_X0)))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[131,83]) ).
tff(133,plain,
addition(one,multiplication(one,star(addition(one,sK1_goals_X0)))) = addition(one,star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[105]) ).
tff(134,plain,
addition(one,star(addition(one,sK1_goals_X0))) = addition(one,multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))) = addition(addition(one,multiplication(one,star(addition(one,sK1_goals_X0)))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[134]) ).
tff(136,plain,
addition(addition(one,multiplication(one,star(addition(one,sK1_goals_X0)))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))) = addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))))) = addition(addition(one,multiplication(one,star(addition(one,sK1_goals_X0)))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(138,plain,
addition(one,addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))))) = addition(addition(one,multiplication(one,star(addition(one,sK1_goals_X0)))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[137,83]) ).
tff(139,plain,
addition(one,addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))))) = addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[96]) ).
tff(140,plain,
addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(one,addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[139]) ).
tff(141,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one) = addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[43]) ).
tff(142,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one) = addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),
inference(transitivity,[status(thm)],[141,140,138,136]) ).
tff(143,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)) = addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))))),
inference(monotonicity,[status(thm)],[142]) ).
tff(144,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)) = multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[143,132,130,96]) ).
tff(145,plain,
addition(addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[144]) ).
tff(146,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[145]) ).
tff(147,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = multiplication(star(addition(one,sK1_goals_X0)),addition(addition(sK1_goals_X0,one),one)),
inference(transitivity,[status(thm)],[146,86,76,41,19]) ).
tff(148,plain,
multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),addition(addition(sK1_goals_X0,one),one))),
inference(monotonicity,[status(thm)],[147]) ).
tff(149,plain,
multiplication(star(sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),addition(addition(sK1_goals_X0,one),one))) = multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[148]) ).
tff(150,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
<=> ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ) )),
inference(bind,[status(th)],]) ).
tff(151,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ) ),
inference(quant_intro,[status(thm)],[150]) ).
tff(152,plain,
( ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(153,axiom,
! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
tff(154,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
inference(modus_ponens,[status(thm)],[153,152]) ).
tff(155,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
inference(skolemize,[status(sab)],[154]) ).
tff(156,plain,
! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
inference(modus_ponens,[status(thm)],[155,151]) ).
tff(157,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
| ( multiplication(star(sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),addition(addition(sK1_goals_X0,one),one))) = multiplication(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(addition(sK1_goals_X0,one),one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(158,plain,
multiplication(star(sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),addition(addition(sK1_goals_X0,one),one))) = multiplication(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(addition(sK1_goals_X0,one),one)),
inference(unit_resolution,[status(thm)],[157,156]) ).
tff(159,plain,
multiplication(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(addition(sK1_goals_X0,one),one)) = multiplication(star(sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),addition(addition(sK1_goals_X0,one),one))),
inference(symmetry,[status(thm)],[158]) ).
tff(160,plain,
^ [A: $i] :
refl(
( ( addition(A,A) = A )
<=> ( addition(A,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(161,plain,
( ! [A: $i] : ( addition(A,A) = A )
<=> ! [A: $i] : ( addition(A,A) = A ) ),
inference(quant_intro,[status(thm)],[160]) ).
tff(162,plain,
( ! [A: $i] : ( addition(A,A) = A )
<=> ! [A: $i] : ( addition(A,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(163,axiom,
! [A: $i] : ( addition(A,A) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
tff(164,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(modus_ponens,[status(thm)],[163,162]) ).
tff(165,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(skolemize,[status(sab)],[164]) ).
tff(166,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(modus_ponens,[status(thm)],[165,161]) ).
tff(167,plain,
( ~ ! [A: $i] : ( addition(A,A) = A )
| ( addition(one,one) = one ) ),
inference(quant_inst,[status(thm)],]) ).
tff(168,plain,
addition(one,one) = one,
inference(unit_resolution,[status(thm)],[167,166]) ).
tff(169,plain,
addition(sK1_goals_X0,addition(one,one)) = addition(sK1_goals_X0,one),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(sK1_goals_X0,addition(one,one)) = addition(addition(sK1_goals_X0,one),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(171,plain,
addition(sK1_goals_X0,addition(one,one)) = addition(addition(sK1_goals_X0,one),one),
inference(unit_resolution,[status(thm)],[170,83]) ).
tff(172,plain,
addition(addition(sK1_goals_X0,one),one) = addition(sK1_goals_X0,addition(one,one)),
inference(symmetry,[status(thm)],[171]) ).
tff(173,plain,
addition(addition(sK1_goals_X0,one),one) = addition(sK1_goals_X0,one),
inference(transitivity,[status(thm)],[172,169]) ).
tff(174,plain,
multiplication(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(addition(sK1_goals_X0,one),one)) = multiplication(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(sK1_goals_X0,one)),
inference(monotonicity,[status(thm)],[173]) ).
tff(175,plain,
multiplication(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(sK1_goals_X0,one)) = multiplication(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(addition(sK1_goals_X0,one),one)),
inference(symmetry,[status(thm)],[174]) ).
tff(176,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
| ( multiplication(star(sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one))) = multiplication(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(sK1_goals_X0,one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(177,plain,
multiplication(star(sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one))) = multiplication(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(sK1_goals_X0,one)),
inference(unit_resolution,[status(thm)],[176,156]) ).
tff(178,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one)) = addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(179,plain,
multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one)) = addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),one)),
inference(unit_resolution,[status(thm)],[178,16]) ).
tff(180,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),one)) = multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one)),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
star(addition(one,sK1_goals_X0)) = multiplication(star(addition(one,sK1_goals_X0)),one),
inference(symmetry,[status(thm)],[28]) ).
tff(182,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),star(addition(one,sK1_goals_X0))) = addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),one)),
inference(monotonicity,[status(thm)],[181]) ).
tff(183,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),star(addition(one,sK1_goals_X0))) = multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),
inference(transitivity,[status(thm)],[182,180,39]) ).
tff(184,plain,
addition(addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)) = addition(multiplication(star(addition(one,sK1_goals_X0)),addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)),
inference(monotonicity,[status(thm)],[183]) ).
tff(185,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),addition(star(addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one))) = addition(addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(186,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),addition(star(addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one))) = addition(addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)),
inference(unit_resolution,[status(thm)],[185,83]) ).
tff(187,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)),
inference(unit_resolution,[status(thm)],[187,35]) ).
tff(189,plain,
multiplication(star(addition(one,sK1_goals_X0)),one) = addition(star(addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one)),
inference(transitivity,[status(thm)],[28,73,63,53,44,188]) ).
tff(190,plain,
addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),one)) = addition(multiplication(star(addition(one,sK1_goals_X0)),sK1_goals_X0),addition(star(addition(one,sK1_goals_X0)),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one))),
inference(monotonicity,[status(thm)],[189]) ).
tff(191,plain,
multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one)) = multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[179,190,186,184,143,132,130,96]) ).
tff(192,plain,
multiplication(star(sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one))) = multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[191]) ).
tff(193,plain,
multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),multiplication(star(addition(one,sK1_goals_X0)),addition(sK1_goals_X0,one))),
inference(symmetry,[status(thm)],[192]) ).
tff(194,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[106]) ).
tff(195,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[194]) ).
tff(196,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(sK1_goals_X0,one),star(addition(one,sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(197,plain,
multiplication(addition(sK1_goals_X0,one),star(addition(one,sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[196,93]) ).
tff(198,plain,
addition(sK1_goals_X0,one) = addition(one,sK1_goals_X0),
inference(symmetry,[status(thm)],[37]) ).
tff(199,plain,
multiplication(addition(sK1_goals_X0,one),star(addition(one,sK1_goals_X0))) = multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[198]) ).
tff(200,plain,
multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))) = multiplication(addition(sK1_goals_X0,one),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[199]) ).
tff(201,plain,
multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[200,197,195]) ).
tff(202,plain,
multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[201]) ).
tff(203,plain,
multiplication(star(sK1_goals_X0),addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[202]) ).
tff(204,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(star(sK1_goals_X0),addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = addition(multiplication(star(sK1_goals_X0),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(205,plain,
multiplication(star(sK1_goals_X0),addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = addition(multiplication(star(sK1_goals_X0),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[204,16]) ).
tff(206,plain,
addition(multiplication(star(sK1_goals_X0),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[205]) ).
tff(207,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
| ( multiplication(star(sK1_goals_X0),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))) = multiplication(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(208,plain,
multiplication(star(sK1_goals_X0),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))) = multiplication(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[207,156]) ).
tff(209,plain,
addition(multiplication(star(sK1_goals_X0),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(multiplication(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(addition(one,sK1_goals_X0))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[208]) ).
tff(210,plain,
addition(multiplication(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(addition(one,sK1_goals_X0))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(multiplication(star(sK1_goals_X0),multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[209]) ).
tff(211,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = addition(multiplication(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(addition(one,sK1_goals_X0))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(212,plain,
multiplication(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = addition(multiplication(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(addition(one,sK1_goals_X0))),multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[211,93]) ).
tff(213,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)) = star(sK1_goals_X0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(214,plain,
ifeq2(leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)) = star(sK1_goals_X0),
inference(unit_resolution,[status(thm)],[213,70]) ).
tff(215,plain,
( ~ ! [A: $i] : ( leq(addition(one,multiplication(star(A),A)),star(A)) = true )
| ( leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)) = true ) ),
inference(quant_inst,[status(thm)],]) ).
tff(216,plain,
leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)) = true,
inference(unit_resolution,[status(thm)],[215,115]) ).
tff(217,plain,
true = leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[216]) ).
tff(218,plain,
ifeq2(true,true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)) = ifeq2(leq(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(monotonicity,[status(thm)],[217]) ).
tff(219,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)) = addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(220,plain,
ifeq2(true,true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)) = addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[219,51]) ).
tff(221,plain,
addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)) = ifeq2(true,true,addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[220]) ).
tff(222,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)) = addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(223,plain,
addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)) = addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one),
inference(unit_resolution,[status(thm)],[222,35]) ).
tff(224,plain,
addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one) = addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),
inference(symmetry,[status(thm)],[223]) ).
tff(225,plain,
addition(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one),star(sK1_goals_X0)) = addition(addition(one,multiplication(star(sK1_goals_X0),sK1_goals_X0)),star(sK1_goals_X0)),
inference(monotonicity,[status(thm)],[224]) ).
tff(226,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one),star(sK1_goals_X0)) = addition(star(sK1_goals_X0),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(227,plain,
addition(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one),star(sK1_goals_X0)) = addition(star(sK1_goals_X0),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one)),
inference(unit_resolution,[status(thm)],[226,35]) ).
tff(228,plain,
addition(star(sK1_goals_X0),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one)) = addition(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[227]) ).
tff(229,plain,
addition(star(sK1_goals_X0),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one)) = star(sK1_goals_X0),
inference(transitivity,[status(thm)],[228,225,221,218,214]) ).
tff(230,plain,
addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),addition(star(sK1_goals_X0),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one))) = addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(monotonicity,[status(thm)],[229]) ).
tff(231,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),addition(star(sK1_goals_X0),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one))) = addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(232,plain,
addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),addition(star(sK1_goals_X0),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one))) = addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one)),
inference(unit_resolution,[status(thm)],[231,83]) ).
tff(233,plain,
addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one)) = addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),addition(star(sK1_goals_X0),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one))),
inference(symmetry,[status(thm)],[232]) ).
tff(234,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one)) = addition(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(235,plain,
addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one)) = addition(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[234,35]) ).
tff(236,plain,
addition(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))) = addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one)),
inference(symmetry,[status(thm)],[235]) ).
tff(237,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)))) = addition(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(238,plain,
addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)))) = addition(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[237,83]) ).
tff(239,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))) = addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(240,plain,
addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))) = addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[239,83]) ).
tff(241,plain,
addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)) = addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),
inference(symmetry,[status(thm)],[240]) ).
tff(242,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),star(sK1_goals_X0)) = addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(243,plain,
ifeq2(true,true,addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),star(sK1_goals_X0)) = addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[242,51]) ).
tff(244,plain,
( ~ ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )
| ( leq(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)) = true ) ),
inference(quant_inst,[status(thm)],]) ).
tff(245,plain,
leq(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)) = true,
inference(unit_resolution,[status(thm)],[244,60]) ).
tff(246,plain,
true = leq(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[245]) ).
tff(247,plain,
ifeq2(true,true,addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),star(sK1_goals_X0)) = ifeq2(leq(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),true,addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(monotonicity,[status(thm)],[246]) ).
tff(248,plain,
ifeq2(leq(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),true,addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),star(sK1_goals_X0)) = ifeq2(true,true,addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[247]) ).
tff(249,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),true,addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),star(sK1_goals_X0)) = star(sK1_goals_X0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(250,plain,
ifeq2(leq(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),true,addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),star(sK1_goals_X0)) = star(sK1_goals_X0),
inference(unit_resolution,[status(thm)],[249,70]) ).
tff(251,plain,
star(sK1_goals_X0) = ifeq2(leq(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),true,addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[250]) ).
tff(252,plain,
star(sK1_goals_X0) = addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),
inference(transitivity,[status(thm)],[251,248,243,241]) ).
tff(253,plain,
addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0)) = addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[252]) ).
tff(254,plain,
addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0)) = addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(transitivity,[status(thm)],[253,238,236,233,230]) ).
tff(255,plain,
multiplication(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[254]) ).
tff(256,plain,
multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = multiplication(addition(multiplication(star(sK1_goals_X0),sK1_goals_X0),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[255]) ).
tff(257,plain,
addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)) = ifeq2(true,true,addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[243]) ).
tff(258,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(259,plain,
addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),
inference(unit_resolution,[status(thm)],[258,35]) ).
tff(260,plain,
addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one) = addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),
inference(symmetry,[status(thm)],[259]) ).
tff(261,plain,
addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),star(sK1_goals_X0)) = addition(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),
inference(monotonicity,[status(thm)],[260]) ).
tff(262,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),addition(one,star(sK1_goals_X0))) = addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),star(sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(263,plain,
addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),addition(one,star(sK1_goals_X0))) = addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),star(sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[262,83]) ).
tff(264,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),addition(one,star(sK1_goals_X0))) = addition(addition(one,star(sK1_goals_X0)),multiplication(sK1_goals_X0,star(sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(265,plain,
addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),addition(one,star(sK1_goals_X0))) = addition(addition(one,star(sK1_goals_X0)),multiplication(sK1_goals_X0,star(sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[264,35]) ).
tff(266,plain,
addition(addition(one,star(sK1_goals_X0)),multiplication(sK1_goals_X0,star(sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),addition(one,star(sK1_goals_X0))),
inference(symmetry,[status(thm)],[265]) ).
tff(267,plain,
addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))) = star(sK1_goals_X0),
inference(transitivity,[status(thm)],[240,257,247,250]) ).
tff(268,plain,
addition(one,addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)))) = addition(one,star(sK1_goals_X0)),
inference(monotonicity,[status(thm)],[267]) ).
tff(269,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)))) = addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(270,plain,
addition(one,addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)))) = addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[269,83]) ).
tff(271,plain,
addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))) = addition(one,addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)))),
inference(symmetry,[status(thm)],[270]) ).
tff(272,plain,
addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))) = addition(one,star(sK1_goals_X0)),
inference(transitivity,[status(thm)],[271,268]) ).
tff(273,plain,
addition(addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),multiplication(sK1_goals_X0,star(sK1_goals_X0))) = addition(addition(one,star(sK1_goals_X0)),multiplication(sK1_goals_X0,star(sK1_goals_X0))),
inference(monotonicity,[status(thm)],[272]) ).
tff(274,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(addition(one,one),addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),multiplication(sK1_goals_X0,star(sK1_goals_X0)))) = addition(addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),multiplication(sK1_goals_X0,star(sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(275,plain,
addition(addition(one,one),addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),multiplication(sK1_goals_X0,star(sK1_goals_X0)))) = addition(addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),multiplication(sK1_goals_X0,star(sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[274,83]) ).
tff(276,plain,
one = addition(one,one),
inference(symmetry,[status(thm)],[168]) ).
tff(277,plain,
addition(one,addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),multiplication(sK1_goals_X0,star(sK1_goals_X0)))) = addition(addition(one,one),addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),multiplication(sK1_goals_X0,star(sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[276]) ).
tff(278,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),multiplication(sK1_goals_X0,star(sK1_goals_X0)))) = addition(addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),multiplication(sK1_goals_X0,star(sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(279,plain,
addition(one,addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),multiplication(sK1_goals_X0,star(sK1_goals_X0)))) = addition(addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),multiplication(sK1_goals_X0,star(sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[278,83]) ).
tff(280,plain,
addition(addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),multiplication(sK1_goals_X0,star(sK1_goals_X0))) = addition(one,addition(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),multiplication(sK1_goals_X0,star(sK1_goals_X0)))),
inference(symmetry,[status(thm)],[279]) ).
tff(281,plain,
addition(star(sK1_goals_X0),multiplication(sK1_goals_X0,star(sK1_goals_X0))) = addition(addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),multiplication(sK1_goals_X0,star(sK1_goals_X0))),
inference(monotonicity,[status(thm)],[252]) ).
tff(282,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)) = addition(star(sK1_goals_X0),multiplication(sK1_goals_X0,star(sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(283,plain,
addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)) = addition(star(sK1_goals_X0),multiplication(sK1_goals_X0,star(sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[282,35]) ).
tff(284,plain,
addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)) = star(sK1_goals_X0),
inference(transitivity,[status(thm)],[283,281,280,277,275,273,266,263,261,257,247,250]) ).
tff(285,plain,
multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[284,106]) ).
tff(286,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[285]) ).
tff(287,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
| ( multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(288,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[287,156]) ).
tff(289,plain,
multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[288]) ).
tff(290,plain,
multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(transitivity,[status(thm)],[289,286,256,212,210,206,203,193,177,175,159,149]) ).
tff(291,plain,
( ~ ! [A: $i] : ( multiplication(A,one) = A )
| ( multiplication(star(sK1_goals_X0),one) = star(sK1_goals_X0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(292,plain,
multiplication(star(sK1_goals_X0),one) = star(sK1_goals_X0),
inference(unit_resolution,[status(thm)],[291,26]) ).
tff(293,plain,
star(sK1_goals_X0) = multiplication(star(sK1_goals_X0),one),
inference(symmetry,[status(thm)],[292]) ).
tff(294,plain,
addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(monotonicity,[status(thm)],[293]) ).
tff(295,plain,
addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[294]) ).
tff(296,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(star(sK1_goals_X0),addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(297,plain,
multiplication(star(sK1_goals_X0),addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(unit_resolution,[status(thm)],[296,16]) ).
tff(298,plain,
ifeq2(true,true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = ifeq2(leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[63]) ).
tff(299,plain,
addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = ifeq2(true,true,addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[53]) ).
tff(300,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(301,plain,
addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[300,83]) ).
tff(302,plain,
addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[301,299,298,72,106]) ).
tff(303,plain,
multiplication(star(sK1_goals_X0),addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[302]) ).
tff(304,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[303]) ).
tff(305,plain,
multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(transitivity,[status(thm)],[289,304,297,295]) ).
tff(306,plain,
ifeq3(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true) = ifeq3(addition(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true),
inference(monotonicity,[status(thm)],[305,290]) ).
tff(307,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq3(A,A,B,C) = B )
<=> ( ifeq3(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(308,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[307]) ).
tff(309,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(310,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).
tff(311,plain,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[310,309]) ).
tff(312,plain,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[311]) ).
tff(313,plain,
! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[312,308]) ).
tff(314,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq3(A,A,B,C) = B )
| ( ifeq3(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true) = leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(315,plain,
ifeq3(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true) = leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(unit_resolution,[status(thm)],[314,313]) ).
tff(316,plain,
leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = ifeq3(multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),true),
inference(symmetry,[status(thm)],[315]) ).
tff(317,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(318,plain,
ifeq2(true,true,multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[317,51]) ).
tff(319,plain,
addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))) = addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[44]) ).
tff(320,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(321,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[320,83]) ).
tff(322,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))) = addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(323,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))) = addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[322,35]) ).
tff(324,plain,
addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[323]) ).
tff(325,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(326,plain,
addition(one,addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[325,83]) ).
tff(327,plain,
addition(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[301]) ).
tff(328,plain,
star(addition(one,sK1_goals_X0)) = addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(transitivity,[status(thm)],[73,63,53,327]) ).
tff(329,plain,
addition(one,star(addition(one,sK1_goals_X0))) = addition(one,addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(monotonicity,[status(thm)],[328]) ).
tff(330,plain,
addition(one,star(addition(one,sK1_goals_X0))) = addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(transitivity,[status(thm)],[329,326]) ).
tff(331,plain,
addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[330]) ).
tff(332,plain,
addition(addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(addition(one,star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[331]) ).
tff(333,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(addition(one,one),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(334,plain,
addition(addition(one,one),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[333,83]) ).
tff(335,plain,
addition(addition(one,one),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(one,addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))),
inference(monotonicity,[status(thm)],[168]) ).
tff(336,plain,
addition(one,addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(addition(one,one),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[335]) ).
tff(337,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(338,plain,
addition(one,addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))) = addition(addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[337,83]) ).
tff(339,plain,
addition(addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(one,addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[338]) ).
tff(340,plain,
addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))) = star(addition(one,sK1_goals_X0)),
inference(transitivity,[status(thm)],[301,299,298,72]) ).
tff(341,plain,
addition(addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(star(addition(one,sK1_goals_X0)),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[340]) ).
tff(342,plain,
addition(star(addition(one,sK1_goals_X0)),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(addition(one,addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[341]) ).
tff(343,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(344,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[343,35]) ).
tff(345,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[201]) ).
tff(346,plain,
addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[345]) ).
tff(347,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(348,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0)))) = addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[347,83]) ).
tff(349,plain,
( ~ ! [A: $i] : ( addition(A,A) = A )
| ( addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(350,plain,
addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[349,166]) ).
tff(351,plain,
addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[350,106]) ).
tff(352,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0)))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[351]) ).
tff(353,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[352]) ).
tff(354,plain,
multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)),
inference(transitivity,[status(thm)],[200,197,353,348,346,344,342,339,336,334,332,324,321,319,299,298,72]) ).
tff(355,plain,
multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[106]) ).
tff(356,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[355]) ).
tff(357,plain,
addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = addition(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[356,106]) ).
tff(358,plain,
addition(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) = addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[357]) ).
tff(359,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = addition(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(360,plain,
multiplication(addition(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = addition(multiplication(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[359,93]) ).
tff(361,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,star(sK1_goals_X0)) = addition(star(sK1_goals_X0),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(362,plain,
addition(one,star(sK1_goals_X0)) = addition(star(sK1_goals_X0),one),
inference(unit_resolution,[status(thm)],[361,35]) ).
tff(363,plain,
addition(star(sK1_goals_X0),one) = addition(one,star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[362]) ).
tff(364,plain,
multiplication(addition(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = multiplication(addition(one,star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[363]) ).
tff(365,plain,
multiplication(addition(one,star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = multiplication(addition(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[364]) ).
tff(366,plain,
addition(one,star(sK1_goals_X0)) = addition(one,addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)))),
inference(symmetry,[status(thm)],[268]) ).
tff(367,plain,
addition(one,star(sK1_goals_X0)) = addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),
inference(transitivity,[status(thm)],[366,270]) ).
tff(368,plain,
multiplication(addition(one,star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))) = multiplication(addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[367]) ).
tff(369,plain,
multiplication(addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = multiplication(addition(one,star(sK1_goals_X0)),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[368]) ).
tff(370,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(multiplication(addition(one,one),star(addition(one,sK1_goals_X0))),multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(371,plain,
multiplication(addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(multiplication(addition(one,one),star(addition(one,sK1_goals_X0))),multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[370,93]) ).
tff(372,plain,
addition(multiplication(addition(one,one),star(addition(one,sK1_goals_X0))),multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0)))) = multiplication(addition(addition(one,one),addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[371]) ).
tff(373,plain,
addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) = addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[105,105]) ).
tff(374,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(one,one),star(addition(one,sK1_goals_X0))) = addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(375,plain,
multiplication(addition(one,one),star(addition(one,sK1_goals_X0))) = addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[374,93]) ).
tff(376,plain,
multiplication(addition(one,one),star(addition(one,sK1_goals_X0))) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[375,373,350,106]) ).
tff(377,plain,
addition(multiplication(addition(one,one),star(addition(one,sK1_goals_X0))),multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0)))) = addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[376]) ).
tff(378,plain,
addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0)))) = addition(multiplication(addition(one,one),star(addition(one,sK1_goals_X0))),multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[377]) ).
tff(379,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(380,plain,
multiplication(addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(multiplication(one,star(addition(one,sK1_goals_X0))),multiplication(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0)),star(addition(one,sK1_goals_X0)))),
inference(unit_resolution,[status(thm)],[379,93]) ).
tff(381,plain,
multiplication(addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[267,106]) ).
tff(382,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(addition(one,addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),star(sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[381]) ).
tff(383,plain,
multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))) = addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[289,382,380,378,372,369,365,360,358]) ).
tff(384,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(addition(sK1_goals_X0,one),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[197]) ).
tff(385,plain,
addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(star(addition(one,sK1_goals_X0)),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[348]) ).
tff(386,plain,
addition(star(addition(one,sK1_goals_X0)),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[344]) ).
tff(387,plain,
addition(addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = addition(addition(one,one),addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[334]) ).
tff(388,plain,
addition(addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),star(addition(one,sK1_goals_X0))) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[321]) ).
tff(389,plain,
star(addition(one,sK1_goals_X0)) = multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[73,63,53,44,388,323,331,387,335,338,341,386,345,385,352,384,199]) ).
tff(390,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(391,plain,
multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),
inference(unit_resolution,[status(thm)],[390,16]) ).
tff(392,plain,
addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0)))) = multiplication(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[321,319,299,298,72,106]) ).
tff(393,plain,
multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0))))) = multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[392]) ).
tff(394,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[393]) ).
tff(395,plain,
multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))) = addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),
inference(transitivity,[status(thm)],[394,391]) ).
tff(396,plain,
leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = leq(addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[395,389]) ).
tff(397,plain,
leq(addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[396]) ).
tff(398,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(399,plain,
addition(one,star(addition(one,sK1_goals_X0))) = addition(star(addition(one,sK1_goals_X0)),one),
inference(unit_resolution,[status(thm)],[398,35]) ).
tff(400,plain,
addition(star(addition(one,sK1_goals_X0)),one) = addition(one,star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[399]) ).
tff(401,plain,
addition(multiplication(one,star(addition(one,sK1_goals_X0))),one) = addition(star(addition(one,sK1_goals_X0)),one),
inference(monotonicity,[status(thm)],[105]) ).
tff(402,plain,
addition(multiplication(one,star(addition(one,sK1_goals_X0))),one) = addition(one,star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[401,400]) ).
tff(403,plain,
multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)) = multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[402]) ).
tff(404,plain,
multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),
inference(symmetry,[status(thm)],[403]) ).
tff(405,plain,
multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0)))) = multiplication(star(sK1_goals_X0),addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(monotonicity,[status(thm)],[330]) ).
tff(406,plain,
multiplication(star(sK1_goals_X0),addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[405]) ).
tff(407,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(star(sK1_goals_X0),addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),addition(one,one)),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(408,plain,
multiplication(star(sK1_goals_X0),addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),addition(one,one)),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(unit_resolution,[status(thm)],[407,16]) ).
tff(409,plain,
addition(multiplication(star(sK1_goals_X0),addition(one,one)),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = multiplication(star(sK1_goals_X0),addition(addition(one,one),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[408]) ).
tff(410,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true,addition(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),star(sK1_goals_X0)) = star(sK1_goals_X0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(411,plain,
ifeq2(leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true,addition(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),star(sK1_goals_X0)) = star(sK1_goals_X0),
inference(unit_resolution,[status(thm)],[410,70]) ).
tff(412,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq(A,A,B,C) = B )
<=> ( ifeq(A,A,B,C) = B ) )),
inference(bind,[status(th)],]) ).
tff(413,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(quant_intro,[status(thm)],[412]) ).
tff(414,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(415,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom_002) ).
tff(416,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[415,414]) ).
tff(417,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(skolemize,[status(sab)],[416]) ).
tff(418,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B ),
inference(modus_ponens,[status(thm)],[417,413]) ).
tff(419,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true) = leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(420,plain,
ifeq(true,true,leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true) = leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[419,418]) ).
tff(421,plain,
leq(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),star(sK1_goals_X0)) = leq(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)),
inference(monotonicity,[status(thm)],[260]) ).
tff(422,plain,
leq(addition(one,multiplication(sK1_goals_X0,star(sK1_goals_X0))),star(sK1_goals_X0)) = leq(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[421]) ).
tff(423,plain,
true = leq(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),star(sK1_goals_X0)),
inference(transitivity,[status(thm)],[246,422]) ).
tff(424,plain,
ifeq(true,true,leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true) = ifeq(leq(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),star(sK1_goals_X0)),true,leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true),
inference(monotonicity,[status(thm)],[423]) ).
tff(425,plain,
ifeq(leq(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),star(sK1_goals_X0)),true,leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true) = ifeq(true,true,leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true),
inference(symmetry,[status(thm)],[424]) ).
tff(426,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
<=> ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ) )),
inference(bind,[status(th)],]) ).
tff(427,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ) ),
inference(quant_intro,[status(thm)],[426]) ).
tff(428,plain,
( ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
<=> ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ) ),
inference(rewrite,[status(thm)],]) ).
tff(429,axiom,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_left) ).
tff(430,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ),
inference(modus_ponens,[status(thm)],[429,428]) ).
tff(431,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ),
inference(skolemize,[status(sab)],[430]) ).
tff(432,plain,
! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true ),
inference(modus_ponens,[status(thm)],[431,427]) ).
tff(433,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
| ( ifeq(leq(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),star(sK1_goals_X0)),true,leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true) = true ) ),
inference(quant_inst,[status(thm)],]) ).
tff(434,plain,
ifeq(leq(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),star(sK1_goals_X0)),true,leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true) = true,
inference(unit_resolution,[status(thm)],[433,432]) ).
tff(435,plain,
true = ifeq(leq(addition(multiplication(sK1_goals_X0,star(sK1_goals_X0)),one),star(sK1_goals_X0)),true,leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true),
inference(symmetry,[status(thm)],[434]) ).
tff(436,plain,
true = leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),
inference(transitivity,[status(thm)],[435,425,420]) ).
tff(437,plain,
ifeq2(true,true,addition(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),star(sK1_goals_X0)) = ifeq2(leq(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),true,addition(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(monotonicity,[status(thm)],[436]) ).
tff(438,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,addition(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),star(sK1_goals_X0)) = addition(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(439,plain,
ifeq2(true,true,addition(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),star(sK1_goals_X0)) = addition(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[438,51]) ).
tff(440,plain,
addition(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)) = ifeq2(true,true,addition(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),star(sK1_goals_X0)),
inference(symmetry,[status(thm)],[439]) ).
tff(441,plain,
addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),one)) = addition(multiplication(star(sK1_goals_X0),one),star(sK1_goals_X0)),
inference(monotonicity,[status(thm)],[292]) ).
tff(442,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(star(sK1_goals_X0),addition(one,one)) = addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),one)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(443,plain,
multiplication(star(sK1_goals_X0),addition(one,one)) = addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),one)),
inference(unit_resolution,[status(thm)],[442,16]) ).
tff(444,plain,
multiplication(star(sK1_goals_X0),addition(one,one)) = multiplication(star(sK1_goals_X0),one),
inference(transitivity,[status(thm)],[443,441,440,437,411,293]) ).
tff(445,plain,
addition(multiplication(star(sK1_goals_X0),addition(one,one)),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(monotonicity,[status(thm)],[444]) ).
tff(446,plain,
addition(multiplication(star(sK1_goals_X0),one),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))) = addition(multiplication(star(sK1_goals_X0),addition(one,one)),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[445]) ).
tff(447,plain,
addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))) = multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),addition(one,star(addition(one,sK1_goals_X0))))),
inference(symmetry,[status(thm)],[391]) ).
tff(448,plain,
addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))) = multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),
inference(transitivity,[status(thm)],[447,393,304,297,446,409,406,404]) ).
tff(449,plain,
leq(addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[448,354]) ).
tff(450,plain,
leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))) = leq(addition(multiplication(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),multiplication(star(sK1_goals_X0),addition(one,star(addition(one,sK1_goals_X0))))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[449]) ).
tff(451,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(452,plain,
ifeq(true,true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),
inference(unit_resolution,[status(thm)],[451,418]) ).
tff(453,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))) = multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[384,199]) ).
tff(454,plain,
addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),one) = addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),one),
inference(monotonicity,[status(thm)],[453]) ).
tff(455,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)) = addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(456,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)) = addition(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),multiplication(one,star(addition(one,sK1_goals_X0)))),one),
inference(unit_resolution,[status(thm)],[455,83]) ).
tff(457,plain,
addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)) = addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(transitivity,[status(thm)],[456,454,141]) ).
tff(458,plain,
leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))) = leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[457]) ).
tff(459,plain,
leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))) = leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[458]) ).
tff(460,plain,
true = leq(addition(one,multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[62]) ).
tff(461,plain,
true = leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[460,459]) ).
tff(462,plain,
ifeq(true,true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = ifeq(leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true),
inference(monotonicity,[status(thm)],[461]) ).
tff(463,plain,
ifeq(leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = ifeq(true,true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true),
inference(symmetry,[status(thm)],[462]) ).
tff(464,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
| ( ifeq(leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = true ) ),
inference(quant_inst,[status(thm)],]) ).
tff(465,plain,
ifeq(leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true) = true,
inference(unit_resolution,[status(thm)],[464,432]) ).
tff(466,plain,
true = ifeq(leq(addition(multiplication(sK1_goals_X0,star(addition(one,sK1_goals_X0))),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true,leq(multiplication(star(sK1_goals_X0),addition(multiplication(one,star(addition(one,sK1_goals_X0))),one)),star(addition(one,sK1_goals_X0))),true),
inference(symmetry,[status(thm)],[465]) ).
tff(467,plain,
true = leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),
inference(transitivity,[status(thm)],[466,463,452,450,397]) ).
tff(468,plain,
ifeq2(true,true,multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = ifeq2(leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(monotonicity,[status(thm)],[467,383,354]) ).
tff(469,plain,
ifeq2(leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = ifeq2(true,true,multiplication(multiplication(star(sK1_goals_X0),one),star(addition(one,sK1_goals_X0))),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(symmetry,[status(thm)],[468]) ).
tff(470,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(471,plain,
ifeq2(leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))) = star(addition(one,sK1_goals_X0)),
inference(unit_resolution,[status(thm)],[470,70]) ).
tff(472,plain,
star(addition(one,sK1_goals_X0)) = ifeq2(leq(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),true,addition(multiplication(star(sK1_goals_X0),multiplication(one,star(addition(one,sK1_goals_X0)))),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))),
inference(symmetry,[status(thm)],[471]) ).
tff(473,plain,
multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))) = multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0)))),
inference(transitivity,[status(thm)],[200,197,353,348,346,344,342,339,336,334,332,324,321,319,299,298,72,472,469,318,289,286,256,212,210,206,203,193,177,175,159,149]) ).
tff(474,plain,
leq(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = leq(star(sK1_goals_X0),multiplication(star(sK1_goals_X0),addition(multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0))),star(addition(one,sK1_goals_X0))))),
inference(monotonicity,[status(thm)],[473]) ).
tff(475,plain,
leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))) = leq(star(sK1_goals_X0),multiplication(addition(one,sK1_goals_X0),star(addition(one,sK1_goals_X0)))),
inference(monotonicity,[status(thm)],[389]) ).
tff(476,plain,
leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0))) = true,
inference(transitivity,[status(thm)],[475,474,316,306,9]) ).
tff(477,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
| ( ifeq(leq(addition(multiplication(addition(sK2_goals_X0,one),star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(addition(sK2_goals_X0,one)),one),star(sK2_goals_X0)),true) = true ) ),
inference(quant_inst,[status(thm)],]) ).
tff(478,plain,
ifeq(leq(addition(multiplication(addition(sK2_goals_X0,one),star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(addition(sK2_goals_X0,one)),one),star(sK2_goals_X0)),true) = true,
inference(unit_resolution,[status(thm)],[477,432]) ).
tff(479,plain,
( ~ ! [A: $i] : ( multiplication(A,one) = A )
| ( multiplication(star(addition(one,sK2_goals_X0)),one) = star(addition(one,sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(480,plain,
multiplication(star(addition(one,sK2_goals_X0)),one) = star(addition(one,sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[479,26]) ).
tff(481,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,sK2_goals_X0) = addition(sK2_goals_X0,one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(482,plain,
addition(one,sK2_goals_X0) = addition(sK2_goals_X0,one),
inference(unit_resolution,[status(thm)],[481,35]) ).
tff(483,plain,
addition(sK2_goals_X0,one) = addition(one,sK2_goals_X0),
inference(symmetry,[status(thm)],[482]) ).
tff(484,plain,
star(addition(sK2_goals_X0,one)) = star(addition(one,sK2_goals_X0)),
inference(monotonicity,[status(thm)],[483]) ).
tff(485,plain,
multiplication(star(addition(sK2_goals_X0,one)),one) = multiplication(star(addition(one,sK2_goals_X0)),one),
inference(monotonicity,[status(thm)],[484]) ).
tff(486,plain,
multiplication(star(addition(sK2_goals_X0,one)),one) = star(addition(one,sK2_goals_X0)),
inference(transitivity,[status(thm)],[485,480]) ).
tff(487,plain,
leq(multiplication(star(addition(sK2_goals_X0,one)),one),star(sK2_goals_X0)) = leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[486]) ).
tff(488,plain,
leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)) = leq(multiplication(star(addition(sK2_goals_X0,one)),one),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[487]) ).
tff(489,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(490,plain,
addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[489,83]) ).
tff(491,plain,
addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),
inference(symmetry,[status(thm)],[490]) ).
tff(492,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(493,plain,
addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),
inference(unit_resolution,[status(thm)],[492,35]) ).
tff(494,plain,
addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one) = addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),
inference(symmetry,[status(thm)],[493]) ).
tff(495,plain,
addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)) = addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[494]) ).
tff(496,plain,
addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[495]) ).
tff(497,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))) = addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(498,plain,
addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))) = addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[497,83]) ).
tff(499,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(500,plain,
addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),one),
inference(unit_resolution,[status(thm)],[499,35]) ).
tff(501,plain,
addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),one) = addition(one,addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0))),
inference(symmetry,[status(thm)],[500]) ).
tff(502,plain,
( ~ ! [B: $i,A: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)) = addition(star(sK2_goals_X0),multiplication(sK2_goals_X0,star(sK2_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(503,plain,
addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)) = addition(star(sK2_goals_X0),multiplication(sK2_goals_X0,star(sK2_goals_X0))),
inference(unit_resolution,[status(thm)],[502,35]) ).
tff(504,plain,
addition(star(sK2_goals_X0),multiplication(sK2_goals_X0,star(sK2_goals_X0))) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[503]) ).
tff(505,plain,
( ~ ! [A: $i] : ( multiplication(one,A) = A )
| ( multiplication(one,star(sK2_goals_X0)) = star(sK2_goals_X0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(506,plain,
multiplication(one,star(sK2_goals_X0)) = star(sK2_goals_X0),
inference(unit_resolution,[status(thm)],[505,103]) ).
tff(507,plain,
addition(multiplication(one,star(sK2_goals_X0)),multiplication(sK2_goals_X0,star(sK2_goals_X0))) = addition(star(sK2_goals_X0),multiplication(sK2_goals_X0,star(sK2_goals_X0))),
inference(monotonicity,[status(thm)],[506]) ).
tff(508,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(one,sK2_goals_X0),star(sK2_goals_X0)) = addition(multiplication(one,star(sK2_goals_X0)),multiplication(sK2_goals_X0,star(sK2_goals_X0))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(509,plain,
multiplication(addition(one,sK2_goals_X0),star(sK2_goals_X0)) = addition(multiplication(one,star(sK2_goals_X0)),multiplication(sK2_goals_X0,star(sK2_goals_X0))),
inference(unit_resolution,[status(thm)],[508,93]) ).
tff(510,plain,
multiplication(addition(sK2_goals_X0,one),star(sK2_goals_X0)) = multiplication(addition(one,sK2_goals_X0),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[483]) ).
tff(511,plain,
multiplication(addition(sK2_goals_X0,one),star(sK2_goals_X0)) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(transitivity,[status(thm)],[510,509,507,504]) ).
tff(512,plain,
addition(multiplication(addition(sK2_goals_X0,one),star(sK2_goals_X0)),one) = addition(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),star(sK2_goals_X0)),one),
inference(monotonicity,[status(thm)],[511]) ).
tff(513,plain,
addition(multiplication(addition(sK2_goals_X0,one),star(sK2_goals_X0)),one) = addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),
inference(transitivity,[status(thm)],[512,501,498,496,491]) ).
tff(514,plain,
leq(addition(multiplication(addition(sK2_goals_X0,one),star(sK2_goals_X0)),one),star(sK2_goals_X0)) = leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[513]) ).
tff(515,plain,
leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),star(sK2_goals_X0)) = leq(addition(multiplication(addition(sK2_goals_X0,one),star(sK2_goals_X0)),one),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[514]) ).
tff(516,plain,
( ~ ! [A: $i] : ( multiplication(A,one) = A )
| ( multiplication(star(sK2_goals_X0),one) = star(sK2_goals_X0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(517,plain,
multiplication(star(sK2_goals_X0),one) = star(sK2_goals_X0),
inference(unit_resolution,[status(thm)],[516,26]) ).
tff(518,plain,
star(sK2_goals_X0) = multiplication(star(sK2_goals_X0),one),
inference(symmetry,[status(thm)],[517]) ).
tff(519,plain,
( ~ ! [B: $i,A: $i] : ( ifeq2(leq(A,B),true,addition(A,B),B) = B )
| ( ifeq2(leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)) = star(sK2_goals_X0) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(520,plain,
ifeq2(leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)) = star(sK2_goals_X0),
inference(unit_resolution,[status(thm)],[519,70]) ).
tff(521,plain,
( ~ ! [A: $i] : ( leq(addition(one,multiplication(A,star(A))),star(A)) = true )
| ( leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) = true ) ),
inference(quant_inst,[status(thm)],]) ).
tff(522,plain,
leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) = true,
inference(unit_resolution,[status(thm)],[521,60]) ).
tff(523,plain,
true = leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[522]) ).
tff(524,plain,
ifeq2(true,true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)) = ifeq2(leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[523]) ).
tff(525,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq2(A,A,B,C) = B )
| ( ifeq2(true,true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)) = addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(526,plain,
ifeq2(true,true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)) = addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[525,51]) ).
tff(527,plain,
addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) = ifeq2(true,true,addition(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[526]) ).
tff(528,plain,
addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))) = multiplication(star(sK2_goals_X0),one),
inference(transitivity,[status(thm)],[490,495,527,524,520,518]) ).
tff(529,plain,
leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),star(sK2_goals_X0)) = leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[528]) ).
tff(530,plain,
leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)) = leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),addition(one,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[529]) ).
tff(531,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(532,plain,
ifeq(true,true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[531,418]) ).
tff(533,plain,
leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)) = leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)),
inference(monotonicity,[status(thm)],[494]) ).
tff(534,plain,
leq(addition(one,multiplication(sK2_goals_X0,star(sK2_goals_X0))),star(sK2_goals_X0)) = leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),
inference(symmetry,[status(thm)],[533]) ).
tff(535,plain,
true = leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),
inference(transitivity,[status(thm)],[523,534]) ).
tff(536,plain,
ifeq(true,true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = ifeq(leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true),
inference(monotonicity,[status(thm)],[535]) ).
tff(537,plain,
ifeq(leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = ifeq(true,true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true),
inference(symmetry,[status(thm)],[536]) ).
tff(538,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(leq(addition(multiplication(A,B),C),B),true,leq(multiplication(star(A),C),B),true) = true )
| ( ifeq(leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = true ) ),
inference(quant_inst,[status(thm)],]) ).
tff(539,plain,
ifeq(leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true) = true,
inference(unit_resolution,[status(thm)],[538,432]) ).
tff(540,plain,
true = ifeq(leq(addition(multiplication(sK2_goals_X0,star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(sK2_goals_X0),one),star(sK2_goals_X0)),true),
inference(symmetry,[status(thm)],[539]) ).
tff(541,plain,
true = leq(addition(multiplication(addition(sK2_goals_X0,one),star(sK2_goals_X0)),one),star(sK2_goals_X0)),
inference(transitivity,[status(thm)],[540,537,532,530,515]) ).
tff(542,plain,
ifeq(true,true,leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),true) = ifeq(leq(addition(multiplication(addition(sK2_goals_X0,one),star(sK2_goals_X0)),one),star(sK2_goals_X0)),true,leq(multiplication(star(addition(sK2_goals_X0,one)),one),star(sK2_goals_X0)),true),
inference(monotonicity,[status(thm)],[541,488]) ).
tff(543,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( ifeq(A,A,B,C) = B )
| ( ifeq(true,true,leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),true) = leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(544,plain,
ifeq(true,true,leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),true) = leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),
inference(unit_resolution,[status(thm)],[543,418]) ).
tff(545,plain,
leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)) = ifeq(true,true,leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),true),
inference(symmetry,[status(thm)],[544]) ).
tff(546,plain,
leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)) = true,
inference(transitivity,[status(thm)],[545,542,478]) ).
tff(547,plain,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) = tuple(true,true),
inference(monotonicity,[status(thm)],[546,476]) ).
tff(548,plain,
( ( tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true) )
<=> ( tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true) ) ),
inference(rewrite,[status(thm)],]) ).
tff(549,axiom,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(550,plain,
tuple(leq(star(addition(one,sK2_goals_X0)),star(sK2_goals_X0)),leq(star(sK1_goals_X0),star(addition(one,sK1_goals_X0)))) != tuple(true,true),
inference(modus_ponens,[status(thm)],[549,548]) ).
tff(551,plain,
$false,
inference(unit_resolution,[status(thm)],[550,547]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE044-10 : TPTP v8.1.0. Released v7.3.0.
% 0.06/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n019.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Thu Sep 1 08:05:05 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 69.06/44.69 % SZS status Unsatisfiable
% 69.06/44.69 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------