%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRP705-1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:08:31 AM UTC 2025
% Result : Unsatisfiable 7.17s 7.36s
% Output : Proof 7.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 43
% Syntax : Number of formulae : 190 ( 152 unt; 0 typ; 0 def)
% Number of atoms : 234 ( 230 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 75 ( 34 ~; 30 |; 0 &)
% ( 11 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of FOOLs : 3 ( 3 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 : 119 ( 114 !; 0 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
tff(mult_type,type,
mult: ( $i * $i ) > $i ).
tff(a_type,type,
a: $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',c05) ).
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(mult(mult(op_a,op_b),unit),unit) = mult(mult(op_a,op_b),unit) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
mult(mult(mult(op_a,op_b),unit),unit) = mult(mult(op_a,op_b),unit),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
mult(mult(op_a,op_b),unit) = mult(mult(mult(op_a,op_b),unit),unit),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
mult(mult(mult(op_a,op_b),unit),mult(mult(op_b,op_b),op_b)) = mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),
inference(monotonicity,[status(thm)],[10]) ).
tff(12,plain,
mult(mult(mult(mult(op_a,op_b),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) = mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(monotonicity,[status(thm)],[11]) ).
tff(13,plain,
mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) = mult(mult(mult(mult(op_a,op_b),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(symmetry,[status(thm)],[12]) ).
tff(14,plain,
mult(mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) = mult(mult(mult(mult(mult(op_a,op_b),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(monotonicity,[status(thm)],[13]) ).
tff(15,plain,
mult(mult(mult(mult(mult(op_a,op_b),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) = mult(mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(symmetry,[status(thm)],[14]) ).
tff(16,plain,
^ [B: $i,A: $i,C: $i] :
refl(( ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) )),
inference(bind,[status(th)],[]) ).
tff(17,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
<=> ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c07) ).
tff(20,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(op_a,op_b),unit),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)))) = mult(mult(mult(mult(mult(op_a,op_b),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(24,plain,
mult(mult(mult(op_a,op_b),unit),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)))) = mult(mult(mult(mult(mult(op_a,op_b),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(op_a,op_b),unit) = mult(op_a,op_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
mult(mult(op_a,op_b),unit) = mult(op_a,op_b),
inference(unit_resolution,[status(thm)],[25,7]) ).
tff(27,plain,
mult(mult(mult(op_a,op_b),unit),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)))) = mult(mult(op_a,op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)))),
inference(monotonicity,[status(thm)],[26]) ).
tff(28,plain,
mult(mult(op_a,op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)))) = mult(mult(mult(op_a,op_b),unit),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)))),
inference(symmetry,[status(thm)],[27]) ).
tff(29,plain,
( ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit )
<=> ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit ) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c09) ).
tff(31,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = unit,
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(33,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(unit_resolution,[status(thm)],[32,22]) ).
tff(34,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))),
inference(symmetry,[status(thm)],[33]) ).
tff(35,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(36,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))),
inference(unit_resolution,[status(thm)],[35,22]) ).
tff(37,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(symmetry,[status(thm)],[36]) ).
tff(38,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(mult(mult(op_b,op_b),op_b),unit) = mult(mult(op_b,op_b),op_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(39,plain,
mult(mult(mult(op_b,op_b),op_b),unit) = mult(mult(op_b,op_b),op_b),
inference(unit_resolution,[status(thm)],[38,7]) ).
tff(40,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,unit))) = mult(mult(mult(op_b,op_b),op_b),unit) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(41,plain,
mult(op_b,mult(op_b,mult(op_b,unit))) = mult(mult(mult(op_b,op_b),op_b),unit),
inference(unit_resolution,[status(thm)],[40,22]) ).
tff(42,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(op_b,unit) = op_b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
mult(op_b,unit) = op_b,
inference(unit_resolution,[status(thm)],[42,7]) ).
tff(44,plain,
mult(op_b,mult(op_b,unit)) = mult(op_b,op_b),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
mult(op_b,op_b) = mult(op_b,mult(op_b,unit)),
inference(symmetry,[status(thm)],[44]) ).
tff(46,plain,
mult(op_b,mult(op_b,op_b)) = mult(op_b,mult(op_b,mult(op_b,unit))),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
mult(op_b,mult(op_b,op_b)) = mult(mult(op_b,op_b),op_b),
inference(transitivity,[status(thm)],[46,41,39]) ).
tff(48,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))),
inference(symmetry,[status(thm)],[48]) ).
tff(50,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(transitivity,[status(thm)],[49,37]) ).
tff(51,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(monotonicity,[status(thm)],[50]) ).
tff(52,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b))) = unit,
inference(transitivity,[status(thm)],[51,34,31]) ).
tff(53,plain,
mult(mult(op_a,op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)))) = mult(mult(op_a,op_b),unit),
inference(monotonicity,[status(thm)],[52]) ).
tff(54,plain,
mult(mult(op_a,op_b),unit) = mult(mult(op_a,op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)))),
inference(symmetry,[status(thm)],[53]) ).
tff(55,plain,
mult(op_a,op_b) = mult(mult(op_a,op_b),unit),
inference(symmetry,[status(thm)],[26]) ).
tff(56,plain,
mult(op_a,op_b) = mult(mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(transitivity,[status(thm)],[55,54,28,24,15]) ).
tff(57,plain,
mult(mult(op_a,op_b),a) = mult(mult(mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),a),
inference(monotonicity,[status(thm)],[56]) ).
tff(58,plain,
mult(mult(mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),a) = mult(mult(op_a,op_b),a),
inference(symmetry,[status(thm)],[57]) ).
tff(59,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),a))) = mult(mult(mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(60,plain,
mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),a))) = mult(mult(mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),a),
inference(unit_resolution,[status(thm)],[59,22]) ).
tff(61,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,a)))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(62,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,a)))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)),
inference(unit_resolution,[status(thm)],[61,22]) ).
tff(63,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,a))) = mult(mult(mult(op_b,op_b),op_b),a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(64,plain,
mult(op_b,mult(op_b,mult(op_b,a))) = mult(mult(mult(op_b,op_b),op_b),a),
inference(unit_resolution,[status(thm)],[63,22]) ).
tff(65,plain,
mult(mult(mult(op_b,op_b),op_b),a) = mult(op_b,mult(op_b,mult(op_b,a))),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),a)) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,a)))),
inference(monotonicity,[status(thm)],[65]) ).
tff(67,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),a)) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)),
inference(transitivity,[status(thm)],[66,62]) ).
tff(68,plain,
mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),a))) = mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))),
inference(monotonicity,[status(thm)],[67]) ).
tff(69,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))) = mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),a))),
inference(symmetry,[status(thm)],[68]) ).
tff(70,plain,
mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))) = mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),a)))),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),a)))) = mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))),
inference(symmetry,[status(thm)],[70]) ).
tff(72,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),a)))) = mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(73,plain,
mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),a)))) = mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),a)),
inference(unit_resolution,[status(thm)],[72,22]) ).
tff(74,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),a)) = mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),a)))),
inference(symmetry,[status(thm)],[73]) ).
tff(75,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),a)) = mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))),
inference(transitivity,[status(thm)],[74,71]) ).
tff(76,plain,
( ~ ! [A: $i] : ( mult(A,unit) = A )
| ( mult(op_a,unit) = op_a ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(77,plain,
mult(op_a,unit) = op_a,
inference(unit_resolution,[status(thm)],[76,7]) ).
tff(78,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(monotonicity,[status(thm)],[37]) ).
tff(79,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b)))) = unit,
inference(transitivity,[status(thm)],[78,34,31]) ).
tff(80,plain,
mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(op_a,unit),
inference(monotonicity,[status(thm)],[79]) ).
tff(81,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(82,plain,
mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),
inference(unit_resolution,[status(thm)],[81,22]) ).
tff(83,plain,
mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) = mult(op_a,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))),
inference(symmetry,[status(thm)],[82]) ).
tff(84,plain,
mult(op_b,mult(op_b,mult(op_b,unit))) = mult(op_b,mult(op_b,op_b)),
inference(symmetry,[status(thm)],[46]) ).
tff(85,plain,
mult(mult(mult(op_b,op_b),op_b),unit) = mult(op_b,mult(op_b,mult(op_b,unit))),
inference(symmetry,[status(thm)],[41]) ).
tff(86,plain,
mult(mult(op_b,op_b),op_b) = mult(mult(mult(op_b,op_b),op_b),unit),
inference(symmetry,[status(thm)],[39]) ).
tff(87,plain,
mult(mult(op_b,op_b),op_b) = mult(op_b,mult(op_b,op_b)),
inference(transitivity,[status(thm)],[86,85,84]) ).
tff(88,plain,
mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),
inference(monotonicity,[status(thm)],[87]) ).
tff(89,plain,
mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) = op_a,
inference(transitivity,[status(thm)],[88,83,80,77]) ).
tff(90,plain,
mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),op_b)) = mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),
inference(monotonicity,[status(thm)],[89]) ).
tff(91,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),op_b)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(92,plain,
mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),op_b)),
inference(unit_resolution,[status(thm)],[91,22]) ).
tff(93,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,op_b))) = mult(mult(mult(op_b,op_b),op_b),op_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(94,plain,
mult(op_b,mult(op_b,mult(op_b,op_b))) = mult(mult(mult(op_b,op_b),op_b),op_b),
inference(unit_resolution,[status(thm)],[93,22]) ).
tff(95,plain,
mult(mult(mult(op_b,op_b),op_b),op_b) = mult(op_b,mult(op_b,mult(op_b,op_b))),
inference(symmetry,[status(thm)],[94]) ).
tff(96,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))),
inference(monotonicity,[status(thm)],[95]) ).
tff(97,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b))) = mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(monotonicity,[status(thm)],[96]) ).
tff(98,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b))),
inference(symmetry,[status(thm)],[97]) ).
tff(99,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(100,plain,
mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))),
inference(unit_resolution,[status(thm)],[99,22]) ).
tff(101,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(102,plain,
mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))),
inference(unit_resolution,[status(thm)],[101,22]) ).
tff(103,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))),
inference(symmetry,[status(thm)],[102]) ).
tff(104,plain,
mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(monotonicity,[status(thm)],[103]) ).
tff(105,plain,
mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))))) = mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,mult(op_b,op_b)))))))),
inference(monotonicity,[status(thm)],[104]) ).
tff(106,plain,
mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b)))))) = unit,
inference(transitivity,[status(thm)],[105,31]) ).
tff(107,plain,
mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))) = mult(op_b,unit),
inference(monotonicity,[status(thm)],[106]) ).
tff(108,plain,
mult(op_b,unit) = mult(op_b,mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,mult(op_b,op_b))))))),
inference(symmetry,[status(thm)],[107]) ).
tff(109,plain,
op_b = mult(op_b,unit),
inference(symmetry,[status(thm)],[43]) ).
tff(110,plain,
op_b = mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b))),
inference(transitivity,[status(thm)],[109,108,100,98]) ).
tff(111,plain,
mult(mult(op_a,mult(mult(op_b,op_b),op_b)),op_b) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)))),
inference(monotonicity,[status(thm)],[110]) ).
tff(112,plain,
mult(op_a,mult(op_b,mult(op_b,op_b))) = mult(op_a,mult(mult(op_b,op_b),op_b)),
inference(monotonicity,[status(thm)],[47]) ).
tff(113,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(op_a,mult(op_b,mult(op_b,op_b))) = mult(mult(mult(op_a,op_b),op_b),op_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(114,plain,
mult(op_a,mult(op_b,mult(op_b,op_b))) = mult(mult(mult(op_a,op_b),op_b),op_b),
inference(unit_resolution,[status(thm)],[113,22]) ).
tff(115,plain,
mult(mult(mult(op_a,op_b),op_b),op_b) = mult(op_a,mult(op_b,mult(op_b,op_b))),
inference(symmetry,[status(thm)],[114]) ).
tff(116,plain,
mult(mult(mult(op_a,op_b),op_b),op_b) = mult(op_a,mult(mult(op_b,op_b),op_b)),
inference(transitivity,[status(thm)],[115,112]) ).
tff(117,plain,
mult(mult(mult(mult(op_a,op_b),op_b),op_b),op_b) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),op_b),
inference(monotonicity,[status(thm)],[116]) ).
tff(118,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(op_a,op_b),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(mult(op_a,op_b),op_b),op_b),op_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
mult(mult(op_a,op_b),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(mult(op_a,op_b),op_b),op_b),op_b),
inference(unit_resolution,[status(thm)],[118,22]) ).
tff(120,plain,
mult(mult(op_a,op_b),mult(mult(op_b,op_b),op_b)) = mult(mult(op_a,op_b),mult(op_b,mult(op_b,op_b))),
inference(monotonicity,[status(thm)],[87]) ).
tff(121,plain,
mult(mult(mult(op_a,op_b),unit),unit) = mult(op_a,op_b),
inference(transitivity,[status(thm)],[9,26]) ).
tff(122,plain,
mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)) = mult(mult(op_a,op_b),mult(mult(op_b,op_b),op_b)),
inference(monotonicity,[status(thm)],[121]) ).
tff(123,plain,
mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)) = mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),
inference(transitivity,[status(thm)],[122,120,119,117,111,92,90]) ).
tff(124,plain,
mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),a))) = mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))))),
inference(monotonicity,[status(thm)],[123,75]) ).
tff(125,plain,
mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))))) = mult(mult(mult(mult(mult(op_a,op_b),unit),unit),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),a))),
inference(symmetry,[status(thm)],[124]) ).
tff(126,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))))) = mult(mult(mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(127,plain,
mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))))) = mult(mult(mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))),
inference(unit_resolution,[status(thm)],[126,22]) ).
tff(128,plain,
mult(mult(mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))) = mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),mult(op_b,mult(op_b,mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))))),
inference(symmetry,[status(thm)],[127]) ).
tff(129,plain,
^ [A: $i] :
refl(( ( mult(unit,A) = A )
<=> ( mult(unit,A) = A ) )),
inference(bind,[status(th)],[]) ).
tff(130,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(quant_intro,[status(thm)],[129]) ).
tff(131,plain,
( ! [A: $i] : ( mult(unit,A) = A )
<=> ! [A: $i] : ( mult(unit,A) = A ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,axiom,
! [A: $i] : ( mult(unit,A) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c06) ).
tff(133,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(skolemize,[status(sab)],[133]) ).
tff(135,plain,
! [A: $i] : ( mult(unit,A) = A ),
inference(modus_ponens,[status(thm)],[134,130]) ).
tff(136,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,mult(op_b,a)) = mult(op_b,a) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(137,plain,
mult(unit,mult(op_b,a)) = mult(op_b,a),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,unit) = unit ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(139,plain,
mult(unit,unit) = unit,
inference(unit_resolution,[status(thm)],[138,135]) ).
tff(140,plain,
mult(unit,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(unit,unit),
inference(monotonicity,[status(thm)],[79]) ).
tff(141,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(unit,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(unit,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(142,plain,
mult(unit,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))) = mult(mult(mult(unit,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),
inference(unit_resolution,[status(thm)],[141,22]) ).
tff(143,plain,
mult(mult(mult(unit,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) = mult(unit,mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,mult(op_b,op_b))))),
inference(symmetry,[status(thm)],[142]) ).
tff(144,plain,
( ~ ! [A: $i] : ( mult(unit,A) = A )
| ( mult(unit,op_b) = op_b ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
mult(unit,op_b) = op_b,
inference(unit_resolution,[status(thm)],[144,135]) ).
tff(146,plain,
mult(mult(unit,op_b),op_b) = mult(op_b,op_b),
inference(monotonicity,[status(thm)],[145]) ).
tff(147,plain,
mult(mult(mult(unit,op_b),op_b),op_b) = mult(mult(op_b,op_b),op_b),
inference(monotonicity,[status(thm)],[146]) ).
tff(148,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(unit,mult(op_b,mult(op_b,op_b))) = mult(mult(mult(unit,op_b),op_b),op_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(149,plain,
mult(unit,mult(op_b,mult(op_b,op_b))) = mult(mult(mult(unit,op_b),op_b),op_b),
inference(unit_resolution,[status(thm)],[148,22]) ).
tff(150,plain,
mult(unit,mult(mult(op_b,op_b),op_b)) = mult(unit,mult(op_b,mult(op_b,op_b))),
inference(monotonicity,[status(thm)],[87]) ).
tff(151,plain,
mult(unit,mult(mult(op_b,op_b),op_b)) = mult(mult(op_b,op_b),op_b),
inference(transitivity,[status(thm)],[150,149,147]) ).
tff(152,plain,
mult(mult(unit,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) = mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)),
inference(monotonicity,[status(thm)],[151]) ).
tff(153,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)) = mult(mult(unit,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(symmetry,[status(thm)],[152]) ).
tff(154,plain,
mult(mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) = mult(mult(mult(unit,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),
inference(monotonicity,[status(thm)],[153,87]) ).
tff(155,plain,
mult(mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) = unit,
inference(transitivity,[status(thm)],[154,143,140,139]) ).
tff(156,plain,
mult(mult(mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,a)) = mult(unit,mult(op_b,a)),
inference(monotonicity,[status(thm)],[155]) ).
tff(157,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))) = mult(mult(mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(158,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))) = mult(mult(mult(mult(mult(op_b,op_b),op_b),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,a)),
inference(unit_resolution,[status(thm)],[157,22]) ).
tff(159,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))) = mult(op_b,a),
inference(transitivity,[status(thm)],[158,156,137]) ).
tff(160,plain,
mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))))) = mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)) = mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))))),
inference(symmetry,[status(thm)],[160]) ).
tff(162,plain,
mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(monotonicity,[status(thm)],[47]) ).
tff(163,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),op_b),op_b),op_b) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(164,plain,
mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),op_b),op_b),op_b),
inference(unit_resolution,[status(thm)],[163,22]) ).
tff(165,plain,
mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),op_b),op_b),op_b) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(op_b,mult(op_b,op_b))),
inference(symmetry,[status(thm)],[164]) ).
tff(166,plain,
mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)))) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),op_b),
inference(symmetry,[status(thm)],[111]) ).
tff(167,plain,
mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),op_b)) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),op_b)))),
inference(symmetry,[status(thm)],[92]) ).
tff(168,plain,
mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),op_b)),
inference(symmetry,[status(thm)],[90]) ).
tff(169,plain,
mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),op_b),
inference(transitivity,[status(thm)],[168,167,166]) ).
tff(170,plain,
mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),op_b) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),op_b),op_b),
inference(monotonicity,[status(thm)],[169]) ).
tff(171,plain,
mult(mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),op_b),op_b) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),op_b),op_b),op_b),
inference(monotonicity,[status(thm)],[170]) ).
tff(172,plain,
mult(mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),op_b),op_b) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),
inference(transitivity,[status(thm)],[171,165,162]) ).
tff(173,plain,
mult(mult(mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))))),
inference(monotonicity,[status(thm)],[172,161]) ).
tff(174,plain,
mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))))) = mult(mult(mult(mult(op_a,mult(mult(mult(op_b,op_b),op_b),op_b)),op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a))),
inference(symmetry,[status(thm)],[173]) ).
tff(175,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))))) = mult(mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(176,plain,
mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))))) = mult(mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))),
inference(unit_resolution,[status(thm)],[175,22]) ).
tff(177,plain,
mult(mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))) = mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))))),
inference(symmetry,[status(thm)],[176]) ).
tff(178,plain,
mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)) = mult(op_a,mult(mult(op_b,op_b),op_b)),
inference(monotonicity,[status(thm)],[89]) ).
tff(179,plain,
mult(mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))),
inference(monotonicity,[status(thm)],[178]) ).
tff(180,plain,
mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))) = mult(mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))),
inference(symmetry,[status(thm)],[179]) ).
tff(181,plain,
( ~ ! [B: $i,A: $i,C: $i] : ( mult(A,mult(B,mult(B,C))) = mult(mult(mult(A,B),B),C) )
| ( mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,a)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(182,plain,
mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,a)),
inference(unit_resolution,[status(thm)],[181,22]) ).
tff(183,plain,
mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,a)) = mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(mult(op_b,op_b),op_b),mult(mult(mult(op_b,op_b),op_b),mult(op_b,a)))),
inference(symmetry,[status(thm)],[182]) ).
tff(184,plain,
mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,a)) = mult(op_a,mult(op_b,a)),
inference(monotonicity,[status(thm)],[89]) ).
tff(185,plain,
mult(op_a,mult(op_b,a)) = mult(mult(mult(mult(op_a,mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(mult(op_b,op_b),op_b)),mult(op_b,a)),
inference(symmetry,[status(thm)],[184]) ).
tff(186,plain,
mult(op_a,mult(op_b,a)) = mult(mult(op_a,op_b),a),
inference(transitivity,[status(thm)],[185,183,180,177,174,128,125,60,58]) ).
tff(187,plain,
( ( mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a) )
<=> ( mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(188,axiom,
mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
tff(189,plain,
mult(op_a,mult(op_b,a)) != mult(mult(op_a,op_b),a),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
$false,
inference(unit_resolution,[status(thm)],[189,186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.14 % Problem : GRP705-1 : TPTP v9.0.0. Released v4.0.0.
% 0.13/0.14 % Command : run_E %s %d THM
% 0.13/0.36 % Computer : n003.cluster.edu
% 0.13/0.36 % Model : x86_64 x86_64
% 0.13/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.36 % Memory : 8042.1875MB
% 0.13/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.36 % CPULimit : 300
% 0.13/0.36 % WCLimit : 300
% 0.13/0.36 % DateTime : Thu Jun 19 16:57:09 EDT 2025
% 0.13/0.36 % CPUTime :
% 7.17/7.36 % SZS status Unsatisfiable
% 7.17/7.36 % SZS output start Proof
% See solution above
% 7.21/7.38 % E exiting
%------------------------------------------------------------------------------