%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP106-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:25:11 PM UTC 2026
% Result : Unsatisfiable 8.24s 1.58s
% Output : Proof 8.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 82
% Number of leaves : 4
% Syntax : Number of formulae : 133 ( 129 unt; 0 def)
% Number of atoms : 145 ( 144 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 42 ( 30 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 11 con; 0-4 aty)
% Number of variables : 243 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,negated_conjecture,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f2_nnf,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( multiply(a4,b4) != multiply(b4,a4)
| multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(multiply(inverse(b2),b2),a2) != a2
| multiply(inverse(a1),a1) != multiply(inverse(b1),b1) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
ifeq(multiply(inverse(a1),a1),multiply(inverse(b1),b1),ifeq(multiply(multiply(inverse(b2),b2),a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t10,plain,
ifeq(multiply(inverse(a1),a1),multiply(inverse(b1),b1),ifeq(multiply(multiply(inverse(b2),b2),a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true),true) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t512,plain,
ifeq(multiply(inverse(a1),a1),multiply(inverse(b1),b1),ifeq(multiply(multiply(inverse(b2),b2),a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true),true) = true,
inference(rw,[status(thm)],[t10]) ).
cnf(f0,axiom,
inverse(double_divide(double_divide(X,Y),inverse(double_divide(X,inverse(double_divide(Z,Y)))))) = Z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f0_nnf,plain,
! [X,Y,Z] : inverse(double_divide(double_divide(X,Y),inverse(double_divide(X,inverse(double_divide(Z,Y)))))) = Z,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] : inverse(double_divide(double_divide(X,Y),inverse(double_divide(X,inverse(double_divide(Z,Y)))))) = Z,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
inverse(double_divide(double_divide(X0,X1),inverse(double_divide(X0,inverse(double_divide(X2,X1)))))) = X2,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t2,plain,
inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(X3,X2)))))) = X3,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t4,plain,
inverse(double_divide(double_divide(X1,X2),inverse(double_divide(X1,inverse(double_divide(X3,X2)))))) = X3,
inference(orient,[status(thm)],[t2]) ).
cnf(f1,axiom,
multiply(X,Y) = inverse(double_divide(Y,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f1_nnf,plain,
! [X,Y] : multiply(X,Y) = inverse(double_divide(Y,X)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] : multiply(X,Y) = inverse(double_divide(Y,X)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
multiply(X0,X1) = inverse(double_divide(X1,X0)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t1,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t8,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t1]) ).
cnf(t4792,plain,
multiply(inverse(double_divide(X1,inverse(double_divide(X3,X2)))),double_divide(X1,X2)) = X3,
inference(step,[status(thm)],[t4,t8]) ).
cnf(t4793,plain,
multiply(multiply(inverse(double_divide(X3,X2)),X1),double_divide(X1,X2)) = X3,
inference(step,[status(thm)],[t4792,t8]) ).
cnf(t4794,plain,
multiply(multiply(multiply(X2,X3),X1),double_divide(X1,X2)) = X3,
inference(step,[status(thm)],[t4793,t8]) ).
cnf(t9,plain,
multiply(multiply(multiply(X2,X3),X1),double_divide(X1,X2)) = X3,
inference(rw,[status(thm)],[t4794]) ).
cnf(t11,plain,
multiply(multiply(multiply(X1,X2),X3),double_divide(X3,X1)) = X2,
inference(orient,[status(thm)],[t9]) ).
cnf(t13,plain,
double_divide(X1,X2) = multiply(multiply(X3,Y3),double_divide(Y3,multiply(multiply(X2,X3),X1))),
inference(cp,[status(thm)],[t11,t11]) ).
cnf(t19,plain,
multiply(multiply(X1,X2),double_divide(X2,multiply(multiply(X3,X1),Y3))) = double_divide(Y3,X3),
inference(orient,[status(thm)],[t13]) ).
cnf(t12,plain,
X1 = multiply(X2,double_divide(double_divide(X1,X3),multiply(X3,X2))),
inference(cp,[status(thm)],[t11,t11]) ).
cnf(t14,plain,
multiply(X1,double_divide(double_divide(X2,X3),multiply(X3,X1))) = X2,
inference(orient,[status(thm)],[t12]) ).
cnf(t20,plain,
double_divide(multiply(X1,double_divide(X2,multiply(X3,X1))),X3) = X2,
inference(cp,[status(thm)],[t19,t14]) ).
cnf(t33,plain,
double_divide(multiply(X1,double_divide(X2,multiply(X3,X1))),X3) = X2,
inference(orient,[status(thm)],[t20]) ).
cnf(t34,plain,
X1 = double_divide(double_divide(multiply(X2,X1),X3),multiply(X3,X2)),
inference(cp,[status(thm)],[t33,t19]) ).
cnf(t43,plain,
double_divide(double_divide(multiply(X1,X2),X3),multiply(X3,X1)) = X2,
inference(orient,[status(thm)],[t34]) ).
cnf(t50,plain,
multiply(multiply(X1,X2),double_divide(multiply(X2,X3),X1)) = inverse(X3),
inference(cp,[status(thm)],[t8,t43]) ).
cnf(t70,plain,
multiply(multiply(X1,X2),double_divide(multiply(X2,X3),X1)) = inverse(X3),
inference(orient,[status(thm)],[t50]) ).
cnf(t79,plain,
X1 = multiply(inverse(X2),double_divide(double_divide(multiply(X1,X2),X3),X3)),
inference(cp,[status(thm)],[t11,t70]) ).
cnf(t91,plain,
multiply(inverse(X1),double_divide(double_divide(multiply(X2,X1),X3),X3)) = X2,
inference(orient,[status(thm)],[t79]) ).
cnf(t109,plain,
double_divide(multiply(X1,X2),multiply(X3,inverse(X2))) = double_divide(X1,X3),
inference(cp,[status(thm)],[t33,t91]) ).
cnf(t132,plain,
double_divide(multiply(X1,X2),multiply(X3,inverse(X2))) = double_divide(X1,X3),
inference(orient,[status(thm)],[t109]) ).
cnf(t146,plain,
multiply(X1,X2) = double_divide(multiply(inverse(X2),double_divide(X1,X3)),X3),
inference(cp,[status(thm)],[t33,t132]) ).
cnf(t147,plain,
double_divide(multiply(inverse(X1),double_divide(X2,X3)),X3) = multiply(X2,X1),
inference(orient,[status(thm)],[t146]) ).
cnf(t38,plain,
multiply(X1,multiply(X2,double_divide(X3,multiply(X1,X2)))) = inverse(X3),
inference(cp,[status(thm)],[t8,t33]) ).
cnf(t54,plain,
multiply(X1,multiply(X2,double_divide(X3,multiply(X1,X2)))) = inverse(X3),
inference(orient,[status(thm)],[t38]) ).
cnf(t148,plain,
multiply(double_divide(multiply(X1,X2),X3),X2) = double_divide(X1,X3),
inference(cp,[status(thm)],[t147,t91]) ).
cnf(t179,plain,
multiply(double_divide(multiply(X1,X2),X3),X2) = double_divide(X1,X3),
inference(orient,[status(thm)],[t148]) ).
cnf(t180,plain,
double_divide(X1,X2) = multiply(X3,double_divide(X3,multiply(X2,X1))),
inference(cp,[status(thm)],[t179,t33]) ).
cnf(t205,plain,
multiply(X1,double_divide(X1,multiply(X2,X3))) = double_divide(X3,X2),
inference(orient,[status(thm)],[t180]) ).
cnf(t233,plain,
inverse(X1) = multiply(X2,double_divide(X1,X2)),
inference(cp,[status(thm)],[t54,t205]) ).
cnf(t268,plain,
multiply(X1,double_divide(X2,X1)) = inverse(X2),
inference(orient,[status(thm)],[t233]) ).
cnf(t276,plain,
multiply(X1,X2) = double_divide(inverse(X1),inverse(X2)),
inference(cp,[status(thm)],[t147,t268]) ).
cnf(t288,plain,
double_divide(inverse(X1),inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t276]) ).
cnf(t207,plain,
double_divide(X1,X2) = inverse(multiply(X2,X1)),
inference(cp,[status(thm)],[t205,t70]) ).
cnf(t237,plain,
inverse(multiply(X1,X2)) = double_divide(X2,X1),
inference(orient,[status(thm)],[t207]) ).
cnf(t240,plain,
double_divide(multiply(X1,double_divide(X2,multiply(X3,X1))),X3) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t237,t54]) ).
cnf(t4797,plain,
X2 = inverse(inverse(X2)),
inference(step,[status(thm)],[t240,t33]) ).
cnf(t250,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t4797]) ).
cnf(t289,plain,
multiply(inverse(X1),X2) = double_divide(X1,inverse(X2)),
inference(cp,[status(thm)],[t288,t250]) ).
cnf(t301,plain,
double_divide(X1,inverse(X2)) = multiply(inverse(X1),X2),
inference(orient,[status(thm)],[t289]) ).
cnf(t305,plain,
multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2),
inference(cp,[status(thm)],[t301,t250]) ).
cnf(t316,plain,
multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2),
inference(orient,[status(thm)],[t305]) ).
cnf(t330,plain,
inverse(X1) = double_divide(double_divide(double_divide(X2,X1),X3),multiply(X3,inverse(X2))),
inference(cp,[status(thm)],[t43,t316]) ).
cnf(t149,plain,
multiply(double_divide(X1,X2),X3) = double_divide(X1,multiply(X2,inverse(X3))),
inference(cp,[status(thm)],[t147,t14]) ).
cnf(t161,plain,
double_divide(X1,multiply(X2,inverse(X3))) = multiply(double_divide(X1,X2),X3),
inference(orient,[status(thm)],[t149]) ).
cnf(t4799,plain,
inverse(X1) = multiply(double_divide(double_divide(double_divide(X2,X1),X3),X3),X2),
inference(step,[status(thm)],[t330,t161]) ).
cnf(t206,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(cp,[status(thm)],[t205,t14]) ).
cnf(t255,plain,
double_divide(double_divide(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t206]) ).
cnf(t4800,plain,
inverse(X1) = multiply(double_divide(X2,X1),X2),
inference(step,[status(thm)],[t4799,t255]) ).
cnf(t350,plain,
multiply(double_divide(X1,X2),X1) = inverse(X2),
inference(orient,[status(thm)],[t4800]) ).
cnf(t358,plain,
double_divide(X1,double_divide(X1,X2)) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t237,t350]) ).
cnf(t4801,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(step,[status(thm)],[t358,t250]) ).
cnf(t374,plain,
double_divide(X1,double_divide(X1,X2)) = X2,
inference(orient,[status(thm)],[t4801]) ).
cnf(t384,plain,
X1 = double_divide(X2,double_divide(X1,X2)),
inference(cp,[status(thm)],[t255,t374]) ).
cnf(t413,plain,
double_divide(X1,double_divide(X2,X1)) = X2,
inference(orient,[status(thm)],[t384]) ).
cnf(t423,plain,
inverse(double_divide(X1,X2)) = multiply(X1,X2),
inference(cp,[status(thm)],[t350,t413]) ).
cnf(t4802,plain,
multiply(X2,X1) = multiply(X1,X2),
inference(step,[status(thm)],[t423,t8]) ).
cnf(t494,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t4802]) ).
cnf(t4943,plain,
ifeq(multiply(a1,inverse(a1)),multiply(inverse(b1),b1),ifeq(multiply(multiply(inverse(b2),b2),a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true),true) = true,
inference(step,[status(thm)],[t512,t494]) ).
cnf(t4798,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(step,[status(thm)],[t91,t255]) ).
cnf(t267,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(rw,[status(thm)],[t4798]) ).
cnf(t513,plain,
multiply(inverse(X1),multiply(X2,X1)) = X2,
inference(orient,[status(thm)],[t267]) ).
cnf(t377,plain,
inverse(X1) = double_divide(X2,multiply(inverse(X2),X1)),
inference(cp,[status(thm)],[t374,t301]) ).
cnf(t589,plain,
double_divide(X1,multiply(inverse(X1),X2)) = inverse(X2),
inference(orient,[status(thm)],[t377]) ).
cnf(t590,plain,
inverse(inverse(X1)) = multiply(double_divide(X2,inverse(X2)),X1),
inference(cp,[status(thm)],[t589,t161]) ).
cnf(t4805,plain,
X1 = multiply(double_divide(X2,inverse(X2)),X1),
inference(step,[status(thm)],[t590,t250]) ).
cnf(t4806,plain,
X1 = multiply(multiply(inverse(X2),X2),X1),
inference(step,[status(thm)],[t4805,t301]) ).
cnf(t4807,plain,
X1 = multiply(multiply(X2,inverse(X2)),X1),
inference(step,[status(thm)],[t4806,t494]) ).
cnf(t606,plain,
multiply(multiply(X1,inverse(X1)),X2) = X2,
inference(orient,[status(thm)],[t4807]) ).
cnf(t619,plain,
multiply(X1,inverse(X1)) = multiply(inverse(X2),X2),
inference(cp,[status(thm)],[t513,t606]) ).
cnf(t4810,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(step,[status(thm)],[t619,t494]) ).
cnf(t658,plain,
multiply(X1,inverse(X1)) = multiply(X2,inverse(X2)),
inference(orient,[status(thm)],[t4810]) ).
cnf(t4944,plain,
ifeq(multiply(true,inverse(true)),multiply(inverse(b1),b1),ifeq(multiply(multiply(inverse(b2),b2),a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true),true) = true,
inference(step,[status(thm)],[t4943,t658]) ).
cnf(t4945,plain,
ifeq(multiply(true,inverse(true)),multiply(b1,inverse(b1)),ifeq(multiply(multiply(inverse(b2),b2),a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true),true) = true,
inference(step,[status(thm)],[t4944,t494]) ).
cnf(t4946,plain,
ifeq(multiply(true,inverse(true)),multiply(true,inverse(true)),ifeq(multiply(multiply(inverse(b2),b2),a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true),true) = true,
inference(step,[status(thm)],[t4945,t658]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t4947,plain,
ifeq(multiply(multiply(inverse(b2),b2),a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true) = true,
inference(step,[status(thm)],[t4946,t7]) ).
cnf(t251,plain,
multiply(double_divide(X1,X2),inverse(X3)) = double_divide(X1,multiply(X2,X3)),
inference(cp,[status(thm)],[t161,t250]) ).
cnf(t676,plain,
multiply(double_divide(X1,X2),inverse(X3)) = double_divide(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t251]) ).
cnf(t691,plain,
double_divide(inverse(X1),double_divide(X2,X3)) = inverse(double_divide(X2,multiply(X3,X1))),
inference(cp,[status(thm)],[t237,t676]) ).
cnf(t317,plain,
double_divide(inverse(X1),X2) = multiply(X1,inverse(X2)),
inference(cp,[status(thm)],[t316,t250]) ).
cnf(t337,plain,
double_divide(inverse(X1),X2) = multiply(X1,inverse(X2)),
inference(orient,[status(thm)],[t317]) ).
cnf(t4811,plain,
multiply(X1,inverse(double_divide(X2,X3))) = inverse(double_divide(X2,multiply(X3,X1))),
inference(step,[status(thm)],[t691,t337]) ).
cnf(t4812,plain,
multiply(X1,multiply(X3,X2)) = inverse(double_divide(X2,multiply(X3,X1))),
inference(step,[status(thm)],[t4811,t8]) ).
cnf(t4813,plain,
multiply(X1,multiply(X3,X2)) = multiply(multiply(X3,X1),X2),
inference(step,[status(thm)],[t4812,t8]) ).
cnf(t705,plain,
multiply(multiply(X1,X2),X3) = multiply(X2,multiply(X1,X3)),
inference(orient,[status(thm)],[t4813]) ).
cnf(t4948,plain,
ifeq(multiply(b2,multiply(inverse(b2),a2)),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true) = true,
inference(step,[status(thm)],[t4947,t705]) ).
cnf(t325,plain,
multiply(double_divide(X1,inverse(X2)),X3) = double_divide(X1,double_divide(X2,X3)),
inference(cp,[status(thm)],[t161,t316]) ).
cnf(t4821,plain,
multiply(multiply(inverse(X1),X2),X3) = double_divide(X1,double_divide(X2,X3)),
inference(step,[status(thm)],[t325,t301]) ).
cnf(t4822,plain,
multiply(X2,multiply(inverse(X1),X3)) = double_divide(X1,double_divide(X2,X3)),
inference(step,[status(thm)],[t4821,t705]) ).
cnf(t817,plain,
multiply(X1,multiply(inverse(X2),X3)) = double_divide(X2,double_divide(X1,X3)),
inference(orient,[status(thm)],[t4822]) ).
cnf(t4949,plain,
ifeq(double_divide(b2,double_divide(b2,a2)),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true) = true,
inference(step,[status(thm)],[t4948,t817]) ).
cnf(t4950,plain,
ifeq(a2,a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true),true) = true,
inference(step,[status(thm)],[t4949,t374]) ).
cnf(t4951,plain,
ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true) = true,
inference(step,[status(thm)],[t4950,t7]) ).
cnf(t4952,plain,
ifeq(multiply(b3,multiply(a3,c3)),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true) = true,
inference(step,[status(thm)],[t4951,t705]) ).
cnf(t4953,plain,
ifeq(multiply(b3,multiply(c3,a3)),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true) = true,
inference(step,[status(thm)],[t4952,t494]) ).
cnf(t4954,plain,
ifeq(multiply(b3,multiply(c3,a3)),multiply(a3,multiply(c3,b3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true) = true,
inference(step,[status(thm)],[t4953,t494]) ).
cnf(t4955,plain,
ifeq(multiply(b3,multiply(c3,a3)),multiply(a3,multiply(c3,b3)),ifeq(multiply(b4,a4),multiply(b4,a4),false,true),true) = true,
inference(step,[status(thm)],[t4954,t494]) ).
cnf(t4956,plain,
ifeq(multiply(b3,multiply(c3,a3)),multiply(a3,multiply(c3,b3)),false,true) = true,
inference(step,[status(thm)],[t4955,t7]) ).
cnf(t4791,plain,
ifeq(multiply(b3,multiply(c3,a3)),multiply(a3,multiply(c3,b3)),false,true) = true,
inference(orient,[status(thm)],[t4956]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(g0_0,plain,
true != ifeq(multiply(b3,multiply(c3,a3)),multiply(a3,multiply(c3,b3)),false,true),
inference(rw,[status(thm)],[goal_0,t4791]) ).
cnf(g0_1,plain,
true != ifeq(multiply(b3,multiply(c3,a3)),multiply(a3,multiply(b3,c3)),false,true),
inference(rw,[status(thm)],[g0_0,t494]) ).
cnf(g0_2,plain,
true != ifeq(multiply(b3,multiply(c3,a3)),multiply(multiply(b3,c3),a3),false,true),
inference(rw,[status(thm)],[g0_1,t494]) ).
cnf(g0_3,plain,
true != ifeq(multiply(b3,multiply(a3,c3)),multiply(multiply(b3,c3),a3),false,true),
inference(rw,[status(thm)],[g0_2,t494]) ).
cnf(g0_4,plain,
true != ifeq(multiply(b3,multiply(a3,c3)),multiply(multiply(c3,b3),a3),false,true),
inference(rw,[status(thm)],[g0_3,t494]) ).
cnf(g0_5,plain,
true != ifeq(multiply(multiply(a3,c3),b3),multiply(multiply(c3,b3),a3),false,true),
inference(rw,[status(thm)],[g0_4,t494]) ).
cnf(g0_6,plain,
true != ifeq(multiply(multiply(a3,c3),b3),multiply(a3,multiply(c3,b3)),false,true),
inference(rw,[status(thm)],[g0_5,t494]) ).
cnf(g0_7,plain,
true != ifeq(multiply(c3,multiply(a3,b3)),multiply(a3,multiply(c3,b3)),false,true),
inference(rw,[status(thm)],[g0_6,t705]) ).
cnf(g0_8,plain,
true != ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(c3,b3)),false,true),
inference(rw,[status(thm)],[g0_7,t494]) ).
cnf(g0_9,plain,
true != ifeq(multiply(multiply(b3,a3),c3),multiply(a3,multiply(c3,b3)),false,true),
inference(rw,[status(thm)],[g0_8,t494]) ).
cnf(g0_10,plain,
true != ifeq(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(c3,b3)),false,true),
inference(rw,[status(thm)],[g0_9,t705]) ).
cnf(g0_11,plain,
true != ifeq(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(c3,b3)),false,true),
inference(rw,[status(thm)],[g0_10,t494]) ).
cnf(g0_12,plain,
true != false,
inference(rw,[status(thm)],[g0_11,t7]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP106-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n010.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 13:32:28 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 8.24/1.58 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.24/1.58 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------