%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP715-10 : TPTP v9.0.0. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 Jun 21 05:08:32 AM UTC 2025
% Result : Unsatisfiable 0.39s 0.61s
% Output : Proof 0.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 30
% Syntax : Number of formulae : 119 ( 96 unt; 0 typ; 0 def)
% Number of atoms : 150 ( 145 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 43 ( 16 ~; 12 |; 0 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 88 ( 81 !; 0 ?; 88 :)
% Comments :
%------------------------------------------------------------------------------
tff(x0_type,type,
x0: $i ).
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(op_b_type,type,
op_b: $i ).
tff(op_a_type,type,
op_a: $i ).
tff(unit_type,type,
unit: $i ).
tff(1,plain,
^ [A: $i] :
refl(( ( mult(A,unit) = A )
<=> ( mult(A,unit) = A ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [A: $i] : ( mult(A,unit) = A )
<=> ! [A: $i] : ( mult(A,unit) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [A: $i] : ( mult(A,unit) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f08) ).
tff(5,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [A: $i] : ( mult(A,unit) = A ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(x0,unit) = x0 ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
mult(x0,unit) = x0,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
^ [A: $i] :
refl(( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(13,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f09) ).
tff(14,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[15,11]) ).
tff(17,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,op_a) = op_a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(18,plain,
mult(unit,op_a) = op_a,
inference(unit_resolution,[status(thm)],[17,16]) ).
tff(19,plain,
( ( mult(op_b,op_a) = unit )
<=> ( mult(op_b,op_a) = unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
mult(op_b,op_a) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f11) ).
tff(21,plain,
mult(op_b,op_a) = unit,
inference(modus_ponens,[status(thm)],[20,19]) ).
tff(22,plain,
unit = mult(op_b,op_a),
inference(symmetry,[status(thm)],[21]) ).
tff(23,plain,
mult(unit,op_a) = mult(mult(op_b,op_a),op_a),
inference(monotonicity,[status(thm)],[22]) ).
tff(24,plain,
mult(mult(op_b,op_a),op_a) = mult(unit,op_a),
inference(symmetry,[status(thm)],[23]) ).
tff(25,plain,
mult(mult(op_b,op_a),op_a) = op_a,
inference(transitivity,[status(thm)],[24,18]) ).
tff(26,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,op_b) = op_b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
mult(unit,op_b) = op_b,
inference(unit_resolution,[status(thm)],[26,16]) ).
tff(28,plain,
mult(mult(op_b,op_a),op_b) = mult(unit,op_b),
inference(monotonicity,[status(thm)],[21]) ).
tff(29,plain,
( ( mult(op_a,op_b) = unit )
<=> ( mult(op_a,op_b) = unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
mult(op_a,op_b) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f10) ).
tff(31,plain,
mult(op_a,op_b) = unit,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
mult(op_a,op_b) = mult(op_b,op_a),
inference(transitivity,[status(thm)],[31,22]) ).
tff(33,plain,
mult(mult(op_a,op_b),op_b) = mult(mult(op_b,op_a),op_b),
inference(monotonicity,[status(thm)],[32]) ).
tff(34,plain,
^ [B: $i,A: $i] :
refl(( ( mult(A,mult(B,B)) = mult(mult(A,B),B) )
<=> ( mult(A,mult(B,B)) = mult(mult(A,B),B) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(B,B)) = mult(mult(A,B),B) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(B,B)) = mult(mult(A,B),B) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [B: $i,A: $i] : ( mult(A,mult(B,B)) = mult(mult(A,B),B) )
<=> ! [B: $i,A: $i] : ( mult(A,mult(B,B)) = mult(mult(A,B),B) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,axiom,
! [B: $i,A: $i] : ( mult(A,mult(B,B)) = mult(mult(A,B),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).
tff(38,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,B)) = mult(mult(A,B),B) ),
inference(modus_ponens,[status(thm)],[37,36]) ).
tff(39,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,B)) = mult(mult(A,B),B) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [B: $i,A: $i] : ( mult(A,mult(B,B)) = mult(mult(A,B),B) ),
inference(modus_ponens,[status(thm)],[39,35]) ).
tff(41,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(B,B)) = mult(mult(A,B),B) )
| ( mult(op_a,mult(op_b,op_b)) = mult(mult(op_a,op_b),op_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(42,plain,
mult(op_a,mult(op_b,op_b)) = mult(mult(op_a,op_b),op_b),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
op_b = mult(unit,op_b),
inference(symmetry,[status(thm)],[27]) ).
tff(44,plain,
mult(op_b,op_b) = mult(mult(unit,op_b),op_b),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
mult(mult(unit,op_b),op_b) = mult(op_b,op_b),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)) = mult(op_a,mult(op_b,op_b)),
inference(monotonicity,[status(thm)],[25,45]) ).
tff(47,plain,
mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)) = op_b,
inference(transitivity,[status(thm)],[46,42,33,28,27]) ).
tff(48,plain,
mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(op_b,op_a),
inference(monotonicity,[status(thm)],[47,25]) ).
tff(49,plain,
mult(op_b,op_a) = mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
unit = mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)),
inference(transitivity,[status(thm)],[22,49]) ).
tff(51,plain,
mult(x0,unit) = mult(x0,mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
mult(x0,mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a))) = mult(x0,unit),
inference(symmetry,[status(thm)],[51]) ).
tff(53,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) )
<=> ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) ) )),
inference(bind,[status(th)],[]) ).
tff(54,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) ) ),
inference(quant_intro,[status(thm)],[53]) ).
tff(55,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,axiom,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).
tff(57,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) ),
inference(modus_ponens,[status(thm)],[56,55]) ).
tff(58,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) ),
inference(skolemize,[status(sab)],[57]) ).
tff(59,plain,
! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) )
| ( mult(mult(mult(x0,mult(mult(op_b,op_a),op_a)),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(x0,mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(61,plain,
mult(mult(mult(x0,mult(mult(op_b,op_a),op_a)),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(x0,mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a))),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
mult(x0,mult(mult(op_b,op_a),op_a)) = mult(x0,op_a),
inference(monotonicity,[status(thm)],[25]) ).
tff(63,plain,
mult(mult(x0,mult(mult(op_b,op_a),op_a)),mult(mult(unit,op_b),op_b)) = mult(mult(x0,op_a),mult(mult(unit,op_b),op_b)),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
mult(mult(mult(x0,mult(mult(op_b,op_a),op_a)),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(mult(mult(x0,op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)),
inference(monotonicity,[status(thm)],[63]) ).
tff(65,plain,
mult(mult(mult(x0,op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(mult(mult(x0,mult(mult(op_b,op_a),op_a)),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(B,B)) = mult(mult(A,B),B) )
| ( mult(mult(x0,op_a),mult(op_b,op_b)) = mult(mult(mult(x0,op_a),op_b),op_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
mult(mult(x0,op_a),mult(op_b,op_b)) = mult(mult(mult(x0,op_a),op_b),op_b),
inference(unit_resolution,[status(thm)],[66,40]) ).
tff(68,plain,
mult(mult(x0,op_a),mult(op_b,op_b)) = mult(mult(x0,op_a),mult(mult(unit,op_b),op_b)),
inference(monotonicity,[status(thm)],[44]) ).
tff(69,plain,
mult(mult(x0,op_a),mult(mult(unit,op_b),op_b)) = mult(mult(x0,op_a),mult(op_b,op_b)),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
mult(mult(x0,op_a),mult(mult(unit,op_b),op_b)) = mult(mult(mult(x0,op_a),op_b),op_b),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
mult(mult(mult(x0,op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(mult(mult(mult(x0,op_a),op_b),op_b),mult(mult(op_b,op_a),op_a)),
inference(monotonicity,[status(thm)],[70]) ).
tff(72,plain,
mult(mult(mult(mult(x0,op_a),op_b),op_b),mult(mult(op_b,op_a),op_a)) = mult(mult(mult(x0,op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(op_b,unit) = op_b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(74,plain,
mult(op_b,unit) = op_b,
inference(unit_resolution,[status(thm)],[73,7]) ).
tff(75,plain,
mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = unit,
inference(transitivity,[status(thm)],[48,21]) ).
tff(76,plain,
mult(op_b,mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a))) = mult(op_b,unit),
inference(monotonicity,[status(thm)],[75]) ).
tff(77,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) )
| ( mult(mult(mult(op_b,mult(mult(op_b,op_a),op_a)),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(op_b,mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(78,plain,
mult(mult(mult(op_b,mult(mult(op_b,op_a),op_a)),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(op_b,mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a))),
inference(unit_resolution,[status(thm)],[77,59]) ).
tff(79,plain,
mult(op_b,mult(mult(op_b,op_a),op_a)) = mult(op_b,op_a),
inference(monotonicity,[status(thm)],[25]) ).
tff(80,plain,
mult(op_b,mult(mult(op_b,op_a),op_a)) = unit,
inference(transitivity,[status(thm)],[79,21]) ).
tff(81,plain,
mult(mult(op_b,mult(mult(op_b,op_a),op_a)),mult(mult(unit,op_b),op_b)) = mult(unit,mult(op_b,op_b)),
inference(monotonicity,[status(thm)],[80,45]) ).
tff(82,plain,
mult(unit,mult(op_b,op_b)) = mult(mult(op_b,mult(mult(op_b,op_a),op_a)),mult(mult(unit,op_b),op_b)),
inference(symmetry,[status(thm)],[81]) ).
tff(83,plain,
( ~ ! [B: $i,A: $i] : ( mult(A,mult(B,B)) = mult(mult(A,B),B) )
| ( mult(unit,mult(op_b,op_b)) = mult(mult(unit,op_b),op_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(84,plain,
mult(unit,mult(op_b,op_b)) = mult(mult(unit,op_b),op_b),
inference(unit_resolution,[status(thm)],[83,40]) ).
tff(85,plain,
mult(mult(unit,op_b),op_b) = mult(unit,mult(op_b,op_b)),
inference(symmetry,[status(thm)],[84]) ).
tff(86,plain,
mult(op_b,op_b) = mult(mult(op_b,mult(mult(op_b,op_a),op_a)),mult(mult(unit,op_b),op_b)),
inference(transitivity,[status(thm)],[44,85,82]) ).
tff(87,plain,
mult(mult(op_b,op_b),mult(mult(op_b,op_a),op_a)) = mult(mult(mult(op_b,mult(mult(op_b,op_a),op_a)),mult(mult(unit,op_b),op_b)),mult(mult(op_b,op_a),op_a)),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
mult(mult(mult(op_b,op_a),op_a),op_b) = mult(op_a,op_b),
inference(monotonicity,[status(thm)],[25]) ).
tff(89,plain,
mult(mult(mult(op_b,op_a),op_a),op_b) = mult(op_b,op_a),
inference(transitivity,[status(thm)],[88,31,22]) ).
tff(90,plain,
mult(mult(mult(mult(op_b,op_a),op_a),op_b),op_b) = mult(mult(op_b,op_a),op_b),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
mult(mult(mult(mult(op_b,op_a),op_a),op_b),op_b) = op_b,
inference(transitivity,[status(thm)],[90,28,27]) ).
tff(92,plain,
mult(mult(mult(mult(mult(op_b,op_a),op_a),op_b),op_b),op_b) = mult(op_b,op_b),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) )
| ( mult(mult(mult(mult(mult(op_b,op_a),op_a),op_b),op_b),op_b) = mult(mult(mult(op_b,op_a),op_a),mult(mult(op_b,op_b),op_b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
mult(mult(mult(mult(mult(op_b,op_a),op_a),op_b),op_b),op_b) = mult(mult(mult(op_b,op_a),op_a),mult(mult(op_b,op_b),op_b)),
inference(unit_resolution,[status(thm)],[93,59]) ).
tff(95,plain,
mult(mult(mult(op_b,op_a),op_a),mult(mult(op_b,op_b),op_b)) = mult(mult(mult(mult(mult(op_b,op_a),op_a),op_b),op_b),op_b),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
mult(mult(mult(op_b,op_a),op_a),mult(mult(op_b,op_b),op_b)) = mult(op_b,op_b),
inference(transitivity,[status(thm)],[95,92]) ).
tff(97,plain,
mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(mult(op_b,op_b),mult(mult(op_b,op_a),op_a)),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = op_b,
inference(transitivity,[status(thm)],[97,87,78,76,74]) ).
tff(99,plain,
mult(mult(x0,op_a),mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a))) = mult(mult(x0,op_a),op_b),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) )
| ( mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(mult(x0,op_a),mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(101,plain,
mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(mult(x0,op_a),mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a))),
inference(unit_resolution,[status(thm)],[100,59]) ).
tff(102,plain,
mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(mult(x0,op_a),op_b),
inference(transitivity,[status(thm)],[101,99]) ).
tff(103,plain,
mult(mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)),op_b) = mult(mult(mult(x0,op_a),op_b),op_b),
inference(monotonicity,[status(thm)],[102]) ).
tff(104,plain,
mult(mult(mult(x0,op_a),op_b),op_b) = mult(mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)),op_b),
inference(symmetry,[status(thm)],[103]) ).
tff(105,plain,
mult(mult(mult(mult(x0,op_a),op_b),op_b),mult(mult(op_b,op_a),op_a)) = mult(mult(mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)),op_b),mult(mult(op_b,op_a),op_a)),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
mult(mult(mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)),op_b),mult(mult(op_b,op_a),op_a)) = mult(mult(mult(mult(x0,op_a),op_b),op_b),mult(mult(op_b,op_a),op_a)),
inference(symmetry,[status(thm)],[105]) ).
tff(107,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(mult(mult(A,B),C),B) = mult(A,mult(mult(B,C),B)) )
| ( mult(mult(mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)),op_b),mult(mult(op_b,op_a),op_a)) = mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(mult(op_b,op_a),op_a),op_b),mult(mult(op_b,op_a),op_a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
mult(mult(mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)),op_b),mult(mult(op_b,op_a),op_a)) = mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(mult(op_b,op_a),op_a),op_b),mult(mult(op_b,op_a),op_a))),
inference(unit_resolution,[status(thm)],[107,59]) ).
tff(109,plain,
mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(mult(op_b,op_a),op_a),op_b),mult(mult(op_b,op_a),op_a))) = mult(mult(mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)),op_b),mult(mult(op_b,op_a),op_a)),
inference(symmetry,[status(thm)],[108]) ).
tff(110,plain,
mult(mult(mult(mult(op_b,op_a),op_a),op_b),mult(mult(op_b,op_a),op_a)) = mult(mult(op_b,op_a),op_a),
inference(monotonicity,[status(thm)],[89,25]) ).
tff(111,plain,
mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(mult(op_b,op_a),op_a),op_b),mult(mult(op_b,op_a),op_a))) = mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)) = mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(mult(op_b,op_a),op_a),op_b),mult(mult(op_b,op_a),op_a))),
inference(symmetry,[status(thm)],[111]) ).
tff(113,plain,
mult(mult(x0,op_a),mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a))) = mult(mult(mult(mult(x0,op_a),mult(mult(op_b,op_a),op_a)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a)),
inference(symmetry,[status(thm)],[101]) ).
tff(114,plain,
mult(mult(x0,op_a),op_b) = mult(mult(x0,op_a),mult(mult(mult(mult(op_b,op_a),op_a),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_a),op_a))),
inference(symmetry,[status(thm)],[99]) ).
tff(115,plain,
mult(mult(x0,op_a),op_b) = x0,
inference(transitivity,[status(thm)],[114,113,112,109,106,72,65,61,52,9]) ).
tff(116,plain,
( ( mult(mult(x0,op_a),op_b) != x0 )
<=> ( mult(mult(x0,op_a),op_b) != x0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(117,axiom,
mult(mult(x0,op_a),op_b) != x0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal) ).
tff(118,plain,
mult(mult(x0,op_a),op_b) != x0,
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
$false,
inference(unit_resolution,[status(thm)],[118,115]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GRP715-10 : TPTP v9.0.0. Released v8.1.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n007.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 Jun 19 16:58:49 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.39/0.61 % SZS status Unsatisfiable
% 0.39/0.61 % SZS output start Proof
% See solution above
% 0.39/0.63 % E exiting
%------------------------------------------------------------------------------