TSTP Solution File: GRP708-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRP708-1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 : Fri Sep 16 22:29:35 EDT 2022
% Result : Unsatisfiable 0.19s 0.54s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 51
% Syntax : Number of formulae : 149 ( 105 unt; 6 typ; 0 def)
% Number of atoms : 193 ( 186 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 73 ( 29 ~; 25 |; 0 &)
% ( 19 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 6 ( 3 >; 3 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 154 ( 142 !; 0 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(op_c_type,type,
op_c: $i ).
tff(b_type,type,
b: $i ).
tff(a_type,type,
a: $i ).
tff(ld_type,type,
ld: ( $i * $i ) > $i ).
tff(rd_type,type,
rd: ( $i * $i ) > $i ).
tff(1,plain,
^ [B: $i,A: $i] :
refl(
( ( ld(A,mult(A,B)) = B )
<=> ( ld(A,mult(A,B)) = B ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
<=> ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c02) ).
tff(5,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,mult(mult(a,b),op_c))) = mult(mult(a,b),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
ld(op_c,mult(op_c,mult(mult(a,b),op_c))) = mult(mult(a,b),op_c),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(
( ( mult(op_c,A) = mult(A,op_c) )
<=> ( mult(op_c,A) = mult(A,op_c) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
<=> ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
<=> ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c08) ).
tff(14,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( mult(op_c,A) = mult(A,op_c) ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(a,b)) = mult(mult(a,b),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
mult(op_c,mult(a,b)) = mult(mult(a,b),op_c),
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
mult(mult(a,b),op_c) = mult(op_c,mult(a,b)),
inference(symmetry,[status(thm)],[18]) ).
tff(20,plain,
mult(op_c,mult(mult(a,b),op_c)) = mult(op_c,mult(op_c,mult(a,b))),
inference(monotonicity,[status(thm)],[19]) ).
tff(21,plain,
mult(op_c,mult(op_c,mult(a,b))) = mult(op_c,mult(mult(a,b),op_c)),
inference(symmetry,[status(thm)],[20]) ).
tff(22,plain,
^ [B: $i,A: $i] :
refl(
( ( mult(rd(A,B),B) = A )
<=> ( mult(rd(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
( ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(25,axiom,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c03) ).
tff(26,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [B: $i,A: $i] : ( mult(rd(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[27,23]) ).
tff(29,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(mult(a,b),op_c),op_c) = mult(a,b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
mult(rd(mult(a,b),op_c),op_c) = mult(a,b),
inference(unit_resolution,[status(thm)],[29,28]) ).
tff(31,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,rd(mult(a,b),op_c)) = mult(rd(mult(a,b),op_c),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
mult(op_c,rd(mult(a,b),op_c)) = mult(rd(mult(a,b),op_c),op_c),
inference(unit_resolution,[status(thm)],[31,16]) ).
tff(33,plain,
mult(op_c,rd(mult(a,b),op_c)) = mult(a,b),
inference(transitivity,[status(thm)],[32,30]) ).
tff(34,plain,
mult(op_c,mult(op_c,rd(mult(a,b),op_c))) = mult(op_c,mult(a,b)),
inference(monotonicity,[status(thm)],[33]) ).
tff(35,plain,
mult(op_c,mult(a,b)) = mult(op_c,mult(op_c,rd(mult(a,b),op_c))),
inference(symmetry,[status(thm)],[34]) ).
tff(36,plain,
mult(op_c,mult(op_c,mult(a,b))) = mult(op_c,mult(op_c,mult(op_c,rd(mult(a,b),op_c)))),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
mult(op_c,mult(op_c,mult(op_c,rd(mult(a,b),op_c)))) = mult(op_c,mult(op_c,mult(a,b))),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
^ [B: $i,A: $i,C: $i] :
refl(
( ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) )),
inference(bind,[status(th)],]) ).
tff(39,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) ),
inference(quant_intro,[status(thm)],[38]) ).
tff(40,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c07) ).
tff(42,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(modus_ponens,[status(thm)],[41,40]) ).
tff(43,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(op_c,mult(op_c,rd(mult(a,b),op_c)))) = mult(mult(op_c,mult(op_c,op_c)),rd(mult(a,b),op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
mult(op_c,mult(op_c,mult(op_c,rd(mult(a,b),op_c)))) = mult(mult(op_c,mult(op_c,op_c)),rd(mult(a,b),op_c)),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
mult(mult(op_c,mult(op_c,op_c)),rd(mult(a,b),op_c)) = mult(op_c,mult(op_c,mult(op_c,rd(mult(a,b),op_c)))),
inference(symmetry,[status(thm)],[46]) ).
tff(48,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(op_c,op_c)) = mult(mult(op_c,op_c),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
mult(op_c,mult(op_c,op_c)) = mult(mult(op_c,op_c),op_c),
inference(unit_resolution,[status(thm)],[48,16]) ).
tff(50,plain,
mult(mult(op_c,mult(op_c,op_c)),rd(mult(a,b),op_c)) = mult(mult(mult(op_c,op_c),op_c),rd(mult(a,b),op_c)),
inference(monotonicity,[status(thm)],[49]) ).
tff(51,plain,
mult(mult(mult(op_c,op_c),op_c),rd(mult(a,b),op_c)) = mult(mult(op_c,mult(op_c,op_c)),rd(mult(a,b),op_c)),
inference(symmetry,[status(thm)],[50]) ).
tff(52,plain,
^ [B: $i,A: $i] :
refl(
( ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) )
<=> ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) )
<=> ! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) )
<=> ! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c09) ).
tff(56,plain,
! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) ),
inference(skolemize,[status(sab)],[56]) ).
tff(58,plain,
! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) ),
inference(modus_ponens,[status(thm)],[57,53]) ).
tff(59,plain,
( ~ ! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) )
| ( mult(mult(op_c,op_c),mult(op_c,rd(mult(a,b),op_c))) = mult(mult(mult(op_c,op_c),op_c),rd(mult(a,b),op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(60,plain,
mult(mult(op_c,op_c),mult(op_c,rd(mult(a,b),op_c))) = mult(mult(mult(op_c,op_c),op_c),rd(mult(a,b),op_c)),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
mult(mult(op_c,op_c),mult(op_c,rd(mult(a,b),op_c))) = mult(mult(op_c,op_c),mult(a,b)),
inference(monotonicity,[status(thm)],[33]) ).
tff(62,plain,
mult(mult(op_c,op_c),mult(a,b)) = mult(mult(op_c,op_c),mult(op_c,rd(mult(a,b),op_c))),
inference(symmetry,[status(thm)],[61]) ).
tff(63,plain,
mult(mult(op_c,op_c),mult(rd(mult(a,b),op_c),op_c)) = mult(mult(op_c,op_c),mult(a,b)),
inference(monotonicity,[status(thm)],[30]) ).
tff(64,plain,
( ~ ! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) )
| ( mult(mult(op_c,op_c),mult(rd(mult(a,b),op_c),op_c)) = mult(mult(mult(op_c,op_c),rd(mult(a,b),op_c)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(65,plain,
mult(mult(op_c,op_c),mult(rd(mult(a,b),op_c),op_c)) = mult(mult(mult(op_c,op_c),rd(mult(a,b),op_c)),op_c),
inference(unit_resolution,[status(thm)],[64,58]) ).
tff(66,plain,
mult(mult(mult(op_c,op_c),rd(mult(a,b),op_c)),op_c) = mult(mult(op_c,op_c),mult(rd(mult(a,b),op_c),op_c)),
inference(symmetry,[status(thm)],[65]) ).
tff(67,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(mult(op_c,op_c),rd(mult(a,b),op_c))) = mult(mult(mult(op_c,op_c),rd(mult(a,b),op_c)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
mult(op_c,mult(mult(op_c,op_c),rd(mult(a,b),op_c))) = mult(mult(mult(op_c,op_c),rd(mult(a,b),op_c)),op_c),
inference(unit_resolution,[status(thm)],[67,16]) ).
tff(69,plain,
mult(op_c,mult(mult(op_c,op_c),rd(mult(a,b),op_c))) = mult(op_c,mult(mult(a,b),op_c)),
inference(transitivity,[status(thm)],[68,66,63,62,60,51,47,37,21]) ).
tff(70,plain,
ld(op_c,mult(op_c,mult(mult(op_c,op_c),rd(mult(a,b),op_c)))) = ld(op_c,mult(op_c,mult(mult(a,b),op_c))),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
mult(mult(mult(op_c,op_c),rd(mult(a,b),op_c)),op_c) = mult(op_c,mult(mult(op_c,op_c),rd(mult(a,b),op_c))),
inference(symmetry,[status(thm)],[68]) ).
tff(72,plain,
mult(mult(op_c,op_c),mult(a,b)) = mult(mult(op_c,op_c),mult(rd(mult(a,b),op_c),op_c)),
inference(symmetry,[status(thm)],[63]) ).
tff(73,plain,
( ~ ! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) )
| ( mult(mult(op_c,op_c),mult(a,b)) = mult(mult(mult(op_c,op_c),a),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(74,plain,
mult(mult(op_c,op_c),mult(a,b)) = mult(mult(mult(op_c,op_c),a),b),
inference(unit_resolution,[status(thm)],[73,58]) ).
tff(75,plain,
mult(mult(mult(op_c,op_c),a),b) = mult(mult(op_c,op_c),mult(a,b)),
inference(symmetry,[status(thm)],[74]) ).
tff(76,plain,
^ [B: $i,A: $i] :
refl(
( ( rd(mult(A,B),B) = A )
<=> ( rd(mult(A,B),B) = A ) )),
inference(bind,[status(th)],]) ).
tff(77,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
<=> ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ) ),
inference(rewrite,[status(thm)],]) ).
tff(79,axiom,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c04) ).
tff(80,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(skolemize,[status(sab)],[80]) ).
tff(82,plain,
! [B: $i,A: $i] : ( rd(mult(A,B),B) = A ),
inference(modus_ponens,[status(thm)],[81,77]) ).
tff(83,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(mult(op_c,op_c),a),op_c),op_c) = mult(mult(op_c,op_c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(84,plain,
rd(mult(mult(mult(op_c,op_c),a),op_c),op_c) = mult(mult(op_c,op_c),a),
inference(unit_resolution,[status(thm)],[83,82]) ).
tff(85,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,mult(mult(op_c,op_c),a)) = mult(mult(mult(op_c,op_c),a),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
mult(op_c,mult(mult(op_c,op_c),a)) = mult(mult(mult(op_c,op_c),a),op_c),
inference(unit_resolution,[status(thm)],[85,16]) ).
tff(87,plain,
( ~ ! [B: $i,A: $i] : ( mult(rd(A,B),B) = A )
| ( mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,op_c)) = mult(mult(op_c,op_c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(88,plain,
mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,op_c)) = mult(mult(op_c,op_c),a),
inference(unit_resolution,[status(thm)],[87,28]) ).
tff(89,plain,
mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,op_c))) = mult(op_c,mult(mult(op_c,op_c),a)),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,op_c))) = mult(mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(91,plain,
mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,op_c))) = mult(mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),op_c),
inference(unit_resolution,[status(thm)],[90,44]) ).
tff(92,plain,
mult(mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),op_c) = mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,op_c))),
inference(symmetry,[status(thm)],[91]) ).
tff(93,plain,
mult(mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),op_c) = mult(mult(mult(op_c,op_c),a),op_c),
inference(transitivity,[status(thm)],[92,89,86]) ).
tff(94,plain,
rd(mult(mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),op_c),op_c) = rd(mult(mult(mult(op_c,op_c),a),op_c),op_c),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ~ ! [B: $i,A: $i] : ( rd(mult(A,B),B) = A )
| ( rd(mult(mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),op_c),op_c) = mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(96,plain,
rd(mult(mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),op_c),op_c) = mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),
inference(unit_resolution,[status(thm)],[95,82]) ).
tff(97,plain,
mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)) = rd(mult(mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),op_c),op_c),
inference(symmetry,[status(thm)],[96]) ).
tff(98,plain,
mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)) = mult(mult(op_c,op_c),a),
inference(transitivity,[status(thm)],[97,94,84]) ).
tff(99,plain,
mult(mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),b) = mult(mult(mult(op_c,op_c),a),b),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,b))) = mult(mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),b) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(101,plain,
mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,b))) = mult(mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),b),
inference(unit_resolution,[status(thm)],[100,44]) ).
tff(102,plain,
mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,b))) = mult(op_c,mult(mult(op_c,op_c),rd(mult(a,b),op_c))),
inference(transitivity,[status(thm)],[101,99,75,72,65,71]) ).
tff(103,plain,
ld(op_c,mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,b)))) = ld(op_c,mult(op_c,mult(mult(op_c,op_c),rd(mult(a,b),op_c)))),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(op_c,mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,b)))) = mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,b)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(105,plain,
ld(op_c,mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,b)))) = mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,b)),
inference(unit_resolution,[status(thm)],[104,7]) ).
tff(106,plain,
mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,b)) = ld(op_c,mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,b)))),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,b) = mult(b,op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(108,plain,
mult(op_c,b) = mult(b,op_c),
inference(unit_resolution,[status(thm)],[107,16]) ).
tff(109,plain,
mult(b,op_c) = mult(op_c,b),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(mult(op_c,op_c),op_c),mult(mult(mult(op_c,op_c),op_c),rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)))) = rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
ld(mult(mult(op_c,op_c),op_c),mult(mult(mult(op_c,op_c),op_c),rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)))) = rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),
inference(unit_resolution,[status(thm)],[110,7]) ).
tff(112,plain,
( ~ ! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) )
| ( mult(mult(op_c,op_c),mult(op_c,a)) = mult(mult(mult(op_c,op_c),op_c),a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(113,plain,
mult(mult(op_c,op_c),mult(op_c,a)) = mult(mult(mult(op_c,op_c),op_c),a),
inference(unit_resolution,[status(thm)],[112,58]) ).
tff(114,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,a) = mult(a,op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(115,plain,
mult(op_c,a) = mult(a,op_c),
inference(unit_resolution,[status(thm)],[114,16]) ).
tff(116,plain,
mult(mult(op_c,op_c),mult(op_c,a)) = mult(mult(op_c,op_c),mult(a,op_c)),
inference(monotonicity,[status(thm)],[115]) ).
tff(117,plain,
mult(mult(op_c,op_c),mult(a,op_c)) = mult(mult(op_c,op_c),mult(op_c,a)),
inference(symmetry,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [B: $i,A: $i] : ( mult(mult(op_c,op_c),mult(A,B)) = mult(mult(mult(op_c,op_c),A),B) )
| ( mult(mult(op_c,op_c),mult(a,op_c)) = mult(mult(mult(op_c,op_c),a),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(119,plain,
mult(mult(op_c,op_c),mult(a,op_c)) = mult(mult(mult(op_c,op_c),a),op_c),
inference(unit_resolution,[status(thm)],[118,58]) ).
tff(120,plain,
mult(mult(mult(op_c,op_c),a),op_c) = mult(mult(op_c,op_c),mult(a,op_c)),
inference(symmetry,[status(thm)],[119]) ).
tff(121,plain,
( ~ ! [A: $i] : ( mult(op_c,A) = mult(A,op_c) )
| ( mult(op_c,rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))) = mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(122,plain,
mult(op_c,rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))) = mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c),
inference(unit_resolution,[status(thm)],[121,16]) ).
tff(123,plain,
mult(op_c,mult(op_c,rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)))) = mult(op_c,mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),op_c)),
inference(monotonicity,[status(thm)],[122]) ).
tff(124,plain,
mult(op_c,mult(op_c,rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)))) = mult(mult(op_c,op_c),a),
inference(transitivity,[status(thm)],[123,97,94,84]) ).
tff(125,plain,
mult(op_c,mult(op_c,mult(op_c,rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))))) = mult(op_c,mult(mult(op_c,op_c),a)),
inference(monotonicity,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(A,C))) = mult(mult(A,mult(B,A)),C) )
| ( mult(op_c,mult(op_c,mult(op_c,rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))))) = mult(mult(op_c,mult(op_c,op_c)),rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
mult(op_c,mult(op_c,mult(op_c,rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))))) = mult(mult(op_c,mult(op_c,op_c)),rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))),
inference(unit_resolution,[status(thm)],[126,44]) ).
tff(128,plain,
mult(mult(op_c,mult(op_c,op_c)),rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))) = mult(op_c,mult(op_c,mult(op_c,rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))))),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
mult(mult(op_c,op_c),op_c) = mult(op_c,mult(op_c,op_c)),
inference(symmetry,[status(thm)],[49]) ).
tff(130,plain,
mult(mult(mult(op_c,op_c),op_c),rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))) = mult(mult(op_c,mult(op_c,op_c)),rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
mult(mult(mult(op_c,op_c),op_c),rd(mult(mult(op_c,op_c),a),mult(op_c,op_c))) = mult(mult(mult(op_c,op_c),op_c),a),
inference(transitivity,[status(thm)],[130,128,125,86,120,117,113]) ).
tff(132,plain,
ld(mult(mult(op_c,op_c),op_c),mult(mult(mult(op_c,op_c),op_c),rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)))) = ld(mult(mult(op_c,op_c),op_c),mult(mult(mult(op_c,op_c),op_c),a)),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
ld(mult(mult(op_c,op_c),op_c),mult(mult(mult(op_c,op_c),op_c),a)) = ld(mult(mult(op_c,op_c),op_c),mult(mult(mult(op_c,op_c),op_c),rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)))),
inference(symmetry,[status(thm)],[132]) ).
tff(134,plain,
( ~ ! [B: $i,A: $i] : ( ld(A,mult(A,B)) = B )
| ( ld(mult(mult(op_c,op_c),op_c),mult(mult(mult(op_c,op_c),op_c),a)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(135,plain,
ld(mult(mult(op_c,op_c),op_c),mult(mult(mult(op_c,op_c),op_c),a)) = a,
inference(unit_resolution,[status(thm)],[134,7]) ).
tff(136,plain,
a = ld(mult(mult(op_c,op_c),op_c),mult(mult(mult(op_c,op_c),op_c),a)),
inference(symmetry,[status(thm)],[135]) ).
tff(137,plain,
a = rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),
inference(transitivity,[status(thm)],[136,133,111]) ).
tff(138,plain,
mult(a,mult(b,op_c)) = mult(rd(mult(mult(op_c,op_c),a),mult(op_c,op_c)),mult(op_c,b)),
inference(monotonicity,[status(thm)],[137,109]) ).
tff(139,plain,
mult(a,mult(b,op_c)) = mult(mult(a,b),op_c),
inference(transitivity,[status(thm)],[138,106,103,70,9]) ).
tff(140,plain,
( ( mult(a,mult(b,op_c)) != mult(mult(a,b),op_c) )
<=> ( mult(a,mult(b,op_c)) != mult(mult(a,b),op_c) ) ),
inference(rewrite,[status(thm)],]) ).
tff(141,axiom,
mult(a,mult(b,op_c)) != mult(mult(a,b),op_c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
tff(142,plain,
mult(a,mult(b,op_c)) != mult(mult(a,b),op_c),
inference(modus_ponens,[status(thm)],[141,140]) ).
tff(143,plain,
$false,
inference(unit_resolution,[status(thm)],[142,139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : GRP708-1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n029.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 : Wed Aug 31 20:28:43 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.
% 0.19/0.54 % SZS status Unsatisfiable
% 0.19/0.54 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------