TSTP Solution File: KLE169+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : KLE169+1 : TPTP v8.1.0. Released v5.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 17:24:26 EDT 2022
% Result : Theorem 4.35s 3.01s
% Output : Proof 4.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 60
% Syntax : Number of formulae : 162 ( 104 unt; 8 typ; 0 def)
% Number of atoms : 238 ( 186 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 110 ( 35 ~; 26 |; 0 &)
% ( 49 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 9 ( 9 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 221 ( 202 !; 0 ?; 221 :)
% Comments :
%------------------------------------------------------------------------------
tff(multiplication_type,type,
multiplication: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(addition_type,type,
addition: ( $i * $i ) > $i ).
tff(b_type,type,
b: $i ).
tff(star_type,type,
star: $i > $i ).
tff(one_type,type,
one: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(sigma_type,type,
sigma: $i ).
tff(1,plain,
^ [A: $i,B: $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(2,plain,
( ! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
<=> ! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
<=> ! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_associativity) ).
tff(5,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
| ( multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))) = multiplication(multiplication(star(addition(a,b)),a),multiplication(addition(a,b),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))) = multiplication(multiplication(star(addition(a,b)),a),multiplication(addition(a,b),a)),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
multiplication(multiplication(star(addition(a,b)),a),multiplication(addition(a,b),a)) = multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
^ [A: $i,B: $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(12,plain,
( ! [A: $i,B: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
<=> ! [A: $i,B: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [A: $i,B: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
<=> ! [A: $i,B: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [A: $i,B: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',left_distributivity) ).
tff(15,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
inference(skolemize,[status(sab)],[15]) ).
tff(17,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(a,b),a) = addition(multiplication(a,a),multiplication(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(19,plain,
multiplication(addition(a,b),a) = addition(multiplication(a,a),multiplication(b,a)),
inference(unit_resolution,[status(thm)],[18,17]) ).
tff(20,plain,
addition(multiplication(a,a),multiplication(b,a)) = multiplication(addition(a,b),a),
inference(symmetry,[status(thm)],[19]) ).
tff(21,plain,
multiplication(multiplication(star(addition(a,b)),a),addition(multiplication(a,a),multiplication(b,a))) = multiplication(multiplication(star(addition(a,b)),a),multiplication(addition(a,b),a)),
inference(monotonicity,[status(thm)],[20]) ).
tff(22,plain,
^ [A: $i,B: $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(23,plain,
( ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
<=> ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
<=> ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',right_distributivity) ).
tff(26,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)) )
| ( multiplication(multiplication(star(addition(a,b)),a),addition(multiplication(a,a),multiplication(b,a))) = addition(multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a)),multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
multiplication(multiplication(star(addition(a,b)),a),addition(multiplication(a,a),multiplication(b,a))) = addition(multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a)),multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a))),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
addition(multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a)),multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a))) = multiplication(multiplication(star(addition(a,b)),a),addition(multiplication(a,a),multiplication(b,a))),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
| ( multiplication(star(addition(a,b)),multiplication(a,multiplication(b,a))) = multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
multiplication(star(addition(a,b)),multiplication(a,multiplication(b,a))) = multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a)),
inference(unit_resolution,[status(thm)],[32,7]) ).
tff(34,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
| ( multiplication(a,multiplication(b,a)) = multiplication(multiplication(a,b),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
multiplication(a,multiplication(b,a)) = multiplication(multiplication(a,b),a),
inference(unit_resolution,[status(thm)],[34,7]) ).
tff(36,plain,
multiplication(multiplication(a,b),a) = multiplication(a,multiplication(b,a)),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
^ [A: $i,B: $i] :
refl(
( ( leq(A,B)
<=> ( addition(A,B) = B ) )
<=> ( leq(A,B)
<=> ( addition(A,B) = B ) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) )
<=> ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) )
<=> ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,axiom,
! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',order) ).
tff(41,plain,
! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) ),
inference(modus_ponens,[status(thm)],[42,38]) ).
tff(44,plain,
( ~ ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) )
| ( leq(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b)))
<=> ( addition(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))) = star(addition(a,b)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(45,plain,
( leq(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b)))
<=> ( addition(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))) = star(addition(a,b)) ) ),
inference(unit_resolution,[status(thm)],[44,43]) ).
tff(46,plain,
^ [A: $i] :
refl(
( leq(addition(one,multiplication(A,star(A))),star(A))
<=> leq(addition(one,multiplication(A,star(A))),star(A)) )),
inference(bind,[status(th)],]) ).
tff(47,plain,
( ! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A))
<=> ! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)) ),
inference(quant_intro,[status(thm)],[46]) ).
tff(48,plain,
( ! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A))
<=> ! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)) ),
inference(rewrite,[status(thm)],]) ).
tff(49,axiom,
! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',star_unfold_right) ).
tff(50,plain,
! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(skolemize,[status(sab)],[50]) ).
tff(52,plain,
! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A)),
inference(modus_ponens,[status(thm)],[51,47]) ).
tff(53,plain,
( ~ ! [A: $i] : leq(addition(one,multiplication(A,star(A))),star(A))
| leq(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
leq(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ ( leq(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b)))
<=> ( addition(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))) = star(addition(a,b)) ) )
| ~ leq(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b)))
| ( addition(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))) = star(addition(a,b)) ) ),
inference(tautology,[status(thm)],]) ).
tff(56,plain,
( ~ ( leq(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b)))
<=> ( addition(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))) = star(addition(a,b)) ) )
| ( addition(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))) = star(addition(a,b)) ) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
addition(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))) = star(addition(a,b)),
inference(unit_resolution,[status(thm)],[56,45]) ).
tff(58,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(a,b),star(addition(a,b))) = addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(59,plain,
multiplication(addition(a,b),star(addition(a,b))) = addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),
inference(unit_resolution,[status(thm)],[58,17]) ).
tff(60,plain,
addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))) = multiplication(addition(a,b),star(addition(a,b))),
inference(symmetry,[status(thm)],[59]) ).
tff(61,plain,
addition(one,addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b))))) = addition(one,multiplication(addition(a,b),star(addition(a,b)))),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
addition(addition(one,addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b))))),star(addition(a,b))) = addition(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))),
inference(monotonicity,[status(thm)],[61]) ).
tff(63,plain,
^ [C: $i,B: $i,A: $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(64,plain,
( ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
<=> ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
( ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
<=> ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(66,axiom,
! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_associativity) ).
tff(67,plain,
! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,plain,
! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) ),
inference(modus_ponens,[status(thm)],[68,64]) ).
tff(70,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(one,addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b)))) = addition(addition(one,addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b))))),star(addition(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(71,plain,
addition(one,addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b)))) = addition(addition(one,addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b))))),star(addition(a,b))),
inference(unit_resolution,[status(thm)],[70,69]) ).
tff(72,plain,
addition(one,addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b)))) = star(addition(a,b)),
inference(transitivity,[status(thm)],[71,62,57]) ).
tff(73,plain,
multiplication(addition(one,addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b)))),multiplication(multiplication(a,b),a)) = multiplication(star(addition(a,b)),multiplication(a,multiplication(b,a))),
inference(monotonicity,[status(thm)],[72,36]) ).
tff(74,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)) )
| ( multiplication(addition(one,addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b)))),multiplication(multiplication(a,b),a)) = addition(multiplication(one,multiplication(multiplication(a,b),a)),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
multiplication(addition(one,addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b)))),multiplication(multiplication(a,b),a)) = addition(multiplication(one,multiplication(multiplication(a,b),a)),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a))),
inference(unit_resolution,[status(thm)],[74,17]) ).
tff(76,plain,
addition(multiplication(one,multiplication(multiplication(a,b),a)),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a))) = multiplication(addition(one,addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b)))),multiplication(multiplication(a,b),a)),
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
addition(multiplication(one,multiplication(multiplication(a,b),a)),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a))) = multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a)),
inference(transitivity,[status(thm)],[76,73,33]) ).
tff(78,plain,
( ~ ! [A: $i,B: $i,C: $i] : ( multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C) )
| ( multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a)) = multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(79,plain,
multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a)) = multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),
inference(unit_resolution,[status(thm)],[78,7]) ).
tff(80,plain,
multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a) = multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a)),
inference(symmetry,[status(thm)],[79]) ).
tff(81,plain,
addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),addition(multiplication(one,multiplication(multiplication(a,b),a)),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a)))) = addition(multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a)),multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a))),
inference(monotonicity,[status(thm)],[80,77]) ).
tff(82,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),addition(multiplication(one,multiplication(multiplication(a,b),a)),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a)))) = addition(addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),multiplication(one,multiplication(multiplication(a,b),a))),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(83,plain,
addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),addition(multiplication(one,multiplication(multiplication(a,b),a)),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a)))) = addition(addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),multiplication(one,multiplication(multiplication(a,b),a))),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a))),
inference(unit_resolution,[status(thm)],[82,69]) ).
tff(84,plain,
addition(addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),multiplication(one,multiplication(multiplication(a,b),a))),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a))) = addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),addition(multiplication(one,multiplication(multiplication(a,b),a)),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a)))),
inference(symmetry,[status(thm)],[83]) ).
tff(85,plain,
^ [A: $i,B: $i] :
refl(
( ( addition(A,B) = addition(B,A) )
<=> ( addition(A,B) = addition(B,A) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
<=> ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
<=> ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,axiom,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_commutativity) ).
tff(89,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(skolemize,[status(sab)],[89]) ).
tff(91,plain,
! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
( ~ ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(one,multiplication(addition(a,b),star(addition(a,b)))) = addition(multiplication(addition(a,b),star(addition(a,b))),one) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
addition(one,multiplication(addition(a,b),star(addition(a,b)))) = addition(multiplication(addition(a,b),star(addition(a,b))),one),
inference(unit_resolution,[status(thm)],[92,91]) ).
tff(94,plain,
addition(multiplication(addition(a,b),star(addition(a,b))),one) = addition(one,multiplication(addition(a,b),star(addition(a,b)))),
inference(symmetry,[status(thm)],[93]) ).
tff(95,plain,
addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),one) = addition(multiplication(addition(a,b),star(addition(a,b))),one),
inference(monotonicity,[status(thm)],[60]) ).
tff(96,plain,
addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),one) = addition(one,multiplication(addition(a,b),star(addition(a,b)))),
inference(transitivity,[status(thm)],[95,94]) ).
tff(97,plain,
addition(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),one),star(addition(a,b))) = addition(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(one,star(addition(a,b)))) = addition(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),one),star(addition(a,b))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(one,star(addition(a,b)))) = addition(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),one),star(addition(a,b))),
inference(unit_resolution,[status(thm)],[98,69]) ).
tff(100,plain,
^ [A: $i] :
refl(
( ( addition(A,A) = A )
<=> ( addition(A,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(101,plain,
( ! [A: $i] : ( addition(A,A) = A )
<=> ! [A: $i] : ( addition(A,A) = A ) ),
inference(quant_intro,[status(thm)],[100]) ).
tff(102,plain,
( ! [A: $i] : ( addition(A,A) = A )
<=> ! [A: $i] : ( addition(A,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,axiom,
! [A: $i] : ( addition(A,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',additive_idempotence) ).
tff(104,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(modus_ponens,[status(thm)],[103,102]) ).
tff(105,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(skolemize,[status(sab)],[104]) ).
tff(106,plain,
! [A: $i] : ( addition(A,A) = A ),
inference(modus_ponens,[status(thm)],[105,101]) ).
tff(107,plain,
( ~ ! [A: $i] : ( addition(A,A) = A )
| ( addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b))))) = addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b))))) = addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),
inference(unit_resolution,[status(thm)],[107,106]) ).
tff(109,plain,
addition(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b))))),addition(one,star(addition(a,b)))) = addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(one,star(addition(a,b)))),
inference(monotonicity,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(one,star(addition(a,b))))) = addition(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b))))),addition(one,star(addition(a,b)))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(one,star(addition(a,b))))) = addition(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b))))),addition(one,star(addition(a,b)))),
inference(unit_resolution,[status(thm)],[110,69]) ).
tff(112,plain,
addition(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),one),star(addition(a,b))) = addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(one,star(addition(a,b)))),
inference(symmetry,[status(thm)],[99]) ).
tff(113,plain,
addition(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))) = addition(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),one),star(addition(a,b))),
inference(symmetry,[status(thm)],[97]) ).
tff(114,plain,
star(addition(a,b)) = addition(addition(one,multiplication(addition(a,b),star(addition(a,b)))),star(addition(a,b))),
inference(symmetry,[status(thm)],[57]) ).
tff(115,plain,
star(addition(a,b)) = addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(one,star(addition(a,b)))),
inference(transitivity,[status(thm)],[114,113,112]) ).
tff(116,plain,
addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))) = addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),addition(one,star(addition(a,b))))),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))) = star(addition(a,b)),
inference(transitivity,[status(thm)],[116,111,109,99,97,57]) ).
tff(118,plain,
multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a)) = multiplication(star(addition(a,b)),multiplication(a,multiplication(b,a))),
inference(monotonicity,[status(thm)],[117,36]) ).
tff(119,plain,
multiplication(star(addition(a,b)),multiplication(a,multiplication(b,a))) = multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a)),
inference(symmetry,[status(thm)],[118]) ).
tff(120,plain,
multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a)) = multiplication(star(addition(a,b)),multiplication(a,multiplication(b,a))),
inference(symmetry,[status(thm)],[33]) ).
tff(121,plain,
multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a)) = multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a)),
inference(transitivity,[status(thm)],[120,119]) ).
tff(122,plain,
^ [A: $i] :
refl(
( ( multiplication(one,A) = A )
<=> ( multiplication(one,A) = A ) )),
inference(bind,[status(th)],]) ).
tff(123,plain,
( ! [A: $i] : ( multiplication(one,A) = A )
<=> ! [A: $i] : ( multiplication(one,A) = A ) ),
inference(quant_intro,[status(thm)],[122]) ).
tff(124,plain,
( ! [A: $i] : ( multiplication(one,A) = A )
<=> ! [A: $i] : ( multiplication(one,A) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(125,axiom,
! [A: $i] : ( multiplication(one,A) = A ),
file('/export/starexec/sandbox/benchmark/Axioms/KLE002+0.ax',multiplicative_left_identity) ).
tff(126,plain,
! [A: $i] : ( multiplication(one,A) = A ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
! [A: $i] : ( multiplication(one,A) = A ),
inference(skolemize,[status(sab)],[126]) ).
tff(128,plain,
! [A: $i] : ( multiplication(one,A) = A ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
( ~ ! [A: $i] : ( multiplication(one,A) = A )
| ( multiplication(one,multiplication(multiplication(a,b),a)) = multiplication(multiplication(a,b),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(130,plain,
multiplication(one,multiplication(multiplication(a,b),a)) = multiplication(multiplication(a,b),a),
inference(unit_resolution,[status(thm)],[129,128]) ).
tff(131,plain,
addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),multiplication(one,multiplication(multiplication(a,b),a))) = addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),multiplication(multiplication(a,b),a)),
inference(monotonicity,[status(thm)],[130]) ).
tff(132,plain,
addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),multiplication(multiplication(a,b),a)) = addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),multiplication(one,multiplication(multiplication(a,b),a))),
inference(symmetry,[status(thm)],[131]) ).
tff(133,plain,
( ~ ! [A: $i,B: $i] : ( addition(A,B) = addition(B,A) )
| ( addition(multiplication(multiplication(a,b),a),multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a)) = addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),multiplication(multiplication(a,b),a)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(134,plain,
addition(multiplication(multiplication(a,b),a),multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a)) = addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),multiplication(multiplication(a,b),a)),
inference(unit_resolution,[status(thm)],[133,91]) ).
tff(135,plain,
addition(multiplication(multiplication(a,b),a),multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a))) = addition(multiplication(multiplication(a,b),a),multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a)),
inference(monotonicity,[status(thm)],[79]) ).
tff(136,plain,
addition(multiplication(multiplication(a,b),a),multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a))) = addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),multiplication(one,multiplication(multiplication(a,b),a))),
inference(transitivity,[status(thm)],[135,134,132]) ).
tff(137,plain,
addition(addition(multiplication(multiplication(a,b),a),multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a))),multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a))) = addition(addition(multiplication(multiplication(multiplication(star(addition(a,b)),a),a),a),multiplication(one,multiplication(multiplication(a,b),a))),multiplication(addition(addition(multiplication(a,star(addition(a,b))),multiplication(b,star(addition(a,b)))),star(addition(a,b))),multiplication(multiplication(a,b),a))),
inference(monotonicity,[status(thm)],[136,121]) ).
tff(138,plain,
( ~ ! [C: $i,B: $i,A: $i] : ( addition(A,addition(B,C)) = addition(addition(A,B),C) )
| ( addition(multiplication(multiplication(a,b),a),addition(multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a)),multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a)))) = addition(addition(multiplication(multiplication(a,b),a),multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a))),multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(139,plain,
addition(multiplication(multiplication(a,b),a),addition(multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a)),multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a)))) = addition(addition(multiplication(multiplication(a,b),a),multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a))),multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a))),
inference(unit_resolution,[status(thm)],[138,69]) ).
tff(140,plain,
multiplication(multiplication(star(addition(a,b)),a),multiplication(addition(a,b),a)) = multiplication(multiplication(star(addition(a,b)),a),addition(multiplication(a,a),multiplication(b,a))),
inference(symmetry,[status(thm)],[21]) ).
tff(141,plain,
multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))) = addition(multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a)),multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a))),
inference(transitivity,[status(thm)],[9,140,30]) ).
tff(142,plain,
addition(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))) = addition(multiplication(multiplication(a,b),a),addition(multiplication(multiplication(star(addition(a,b)),a),multiplication(a,a)),multiplication(multiplication(star(addition(a,b)),a),multiplication(b,a)))),
inference(monotonicity,[status(thm)],[35,141]) ).
tff(143,plain,
addition(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))) = multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))),
inference(transitivity,[status(thm)],[142,139,137,84,81,31,21,10]) ).
tff(144,plain,
( ~ ! [A: $i,B: $i] :
( leq(A,B)
<=> ( addition(A,B) = B ) )
| ( leq(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))))
<=> ( addition(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))) = multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(145,plain,
( leq(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))))
<=> ( addition(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))) = multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))) ) ),
inference(unit_resolution,[status(thm)],[144,43]) ).
tff(146,plain,
( ~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a))))
<=> ~ leq(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))) ),
inference(rewrite,[status(thm)],]) ).
tff(147,plain,
( ~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a))))
<=> ~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))) ),
inference(rewrite,[status(thm)],]) ).
tff(148,axiom,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a) ).
tff(149,plain,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(sigma),multiplication(a,multiplication(sigma,a)))),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
~ leq(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))),
inference(modus_ponens,[status(thm)],[149,146]) ).
tff(151,plain,
( ~ ( leq(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))))
<=> ( addition(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))) = multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))) ) )
| leq(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))))
| ( addition(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))) != multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))) ) ),
inference(tautology,[status(thm)],]) ).
tff(152,plain,
( ~ ( leq(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))))
<=> ( addition(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))) = multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))) ) )
| ( addition(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))) != multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))) ) ),
inference(unit_resolution,[status(thm)],[151,150]) ).
tff(153,plain,
addition(multiplication(a,multiplication(b,a)),multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a)))) != multiplication(star(addition(a,b)),multiplication(a,multiplication(addition(a,b),a))),
inference(unit_resolution,[status(thm)],[152,145]) ).
tff(154,plain,
$false,
inference(unit_resolution,[status(thm)],[153,143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE169+1 : TPTP v8.1.0. Released v5.2.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.34 % Computer : n013.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Thu Sep 1 09:02:47 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 4.35/3.01 % SZS status Theorem
% 4.35/3.01 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------