%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP063-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n006.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 01:25:05 PM UTC 2026
% Result : Unsatisfiable 7.59s 11.86s
% Output : Proof 7.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 5
% Syntax : Number of formulae : 83 ( 79 unt; 0 def)
% Number of atoms : 91 ( 90 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 10 con; 0-4 aty)
% Number of variables : 139 ( 2 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,negated_conjecture,
( 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(f3_nnf,plain,
( 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)],[f3]) ).
fof(f3_sk,plain,
( 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)],[f3_nnf]) ).
cnf(c3,plain,
( 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)],[f3_sk]) ).
cnf(t4,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)),false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f1,axiom,
multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f1_nnf,plain,
! [X,Y,Z] : multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y,Z] : multiply(X,Y) = divide(X,divide(divide(Z,Z),Y)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
multiply(X0,X1) = divide(X0,divide(divide(X2,X2),X1)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t2,plain,
divide(X1,divide(divide(X2,X2),X3)) = multiply(X1,X3),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f2,axiom,
inverse(X) = divide(divide(Z,Z),X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f2_nnf,plain,
! [X,Z] : inverse(X) = divide(divide(Z,Z),X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Z] : inverse(X) = divide(divide(Z,Z),X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
inverse(X0) = divide(divide(X1,X1),X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t1,plain,
divide(divide(X1,X1),X2) = inverse(X2),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t6,plain,
divide(divide(X1,X1),X2) = inverse(X2),
inference(orient,[status(thm)],[t1]) ).
cnf(t889,plain,
divide(X1,inverse(X3)) = multiply(X1,X3),
inference(step,[status(thm)],[t2,t6]) ).
cnf(t11,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t889]) ).
cnf(t12,plain,
multiply(divide(X1,X1),X2) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t11,t6]) ).
cnf(t16,plain,
multiply(divide(X1,X1),X2) = inverse(inverse(X2)),
inference(orient,[status(thm)],[t12]) ).
cnf(t18,plain,
inverse(inverse(X1)) = multiply(multiply(inverse(X2),X2),X1),
inference(cp,[status(thm)],[t16,t11]) ).
cnf(t25,plain,
multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
inference(orient,[status(thm)],[t18]) ).
cnf(t896,plain,
ifeq(multiply(inverse(a1),a1),multiply(inverse(b1),b1),ifeq(inverse(inverse(a2)),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true),true) = true,
inference(step,[status(thm)],[t4,t25]) ).
cnf(t82,plain,
ifeq(multiply(inverse(a1),a1),multiply(inverse(b1),b1),ifeq(inverse(inverse(a2)),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true),true) = true,
inference(orient,[status(thm)],[t896]) ).
cnf(t159,plain,
ifeq(multiply(inverse(a1),a1),multiply(inverse(b1),b1),ifeq(a2,a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true),true) = true,
inference(rw,[status(thm)],[t82]) ).
cnf(f0,axiom,
divide(X,divide(divide(divide(divide(X,X),Y),Z),divide(divide(divide(X,X),X),Z))) = Y,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f0_nnf,plain,
! [X,Y,Z] : divide(X,divide(divide(divide(divide(X,X),Y),Z),divide(divide(divide(X,X),X),Z))) = Y,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] : divide(X,divide(divide(divide(divide(X,X),Y),Z),divide(divide(divide(X,X),X),Z))) = Y,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
divide(X0,divide(divide(divide(divide(X0,X0),X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t3,plain,
divide(X1,divide(divide(divide(divide(X1,X1),X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t890,plain,
divide(X1,divide(divide(inverse(X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
inference(step,[status(thm)],[t3,t6]) ).
cnf(t891,plain,
divide(X1,divide(divide(inverse(X2),X3),divide(inverse(X1),X3))) = X2,
inference(step,[status(thm)],[t890,t6]) ).
cnf(t34,plain,
divide(X1,divide(divide(inverse(X2),X3),divide(inverse(X1),X3))) = X2,
inference(orient,[status(thm)],[t891]) ).
cnf(t35,plain,
X1 = inverse(divide(divide(inverse(X1),X2),divide(inverse(divide(X3,X3)),X2))),
inference(cp,[status(thm)],[t34,t6]) ).
cnf(t7,plain,
inverse(X1) = divide(inverse(divide(X2,X2)),X1),
inference(cp,[status(thm)],[t6,t6]) ).
cnf(t8,plain,
divide(inverse(divide(X1,X1)),X2) = inverse(X2),
inference(orient,[status(thm)],[t7]) ).
cnf(t897,plain,
X1 = inverse(divide(divide(inverse(X1),X2),inverse(X2))),
inference(step,[status(thm)],[t35,t8]) ).
cnf(t898,plain,
X1 = inverse(multiply(divide(inverse(X1),X2),X2)),
inference(step,[status(thm)],[t897,t11]) ).
cnf(t85,plain,
inverse(multiply(divide(inverse(X1),X2),X2)) = X1,
inference(orient,[status(thm)],[t898]) ).
cnf(t36,plain,
X1 = divide(X2,inverse(divide(inverse(X2),inverse(X1)))),
inference(cp,[status(thm)],[t34,t6]) ).
cnf(t892,plain,
X1 = multiply(X2,divide(inverse(X2),inverse(X1))),
inference(step,[status(thm)],[t36,t11]) ).
cnf(t893,plain,
X1 = multiply(X2,multiply(inverse(X2),X1)),
inference(step,[status(thm)],[t892,t11]) ).
cnf(t45,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t893]) ).
cnf(t46,plain,
X1 = inverse(inverse(multiply(inverse(divide(X2,X2)),X1))),
inference(cp,[status(thm)],[t45,t16]) ).
cnf(t13,plain,
multiply(inverse(divide(X1,X1)),X2) = inverse(inverse(X2)),
inference(cp,[status(thm)],[t11,t8]) ).
cnf(t19,plain,
multiply(inverse(divide(X1,X1)),X2) = inverse(inverse(X2)),
inference(orient,[status(thm)],[t13]) ).
cnf(t894,plain,
X1 = inverse(inverse(inverse(inverse(X1)))),
inference(step,[status(thm)],[t46,t19]) ).
cnf(t50,plain,
inverse(inverse(inverse(inverse(X1)))) = X1,
inference(orient,[status(thm)],[t894]) ).
cnf(t90,plain,
inverse(inverse(inverse(X1))) = inverse(multiply(divide(X1,X2),X2)),
inference(cp,[status(thm)],[t85,t50]) ).
cnf(t111,plain,
inverse(multiply(divide(X1,X2),X2)) = inverse(inverse(inverse(X1))),
inference(orient,[status(thm)],[t90]) ).
cnf(t126,plain,
multiply(divide(X1,X2),X2) = divide(X3,divide(divide(inverse(inverse(inverse(X1))),Y3),divide(inverse(X3),Y3))),
inference(cp,[status(thm)],[t34,t111]) ).
cnf(t922,plain,
multiply(divide(X1,X2),X2) = inverse(inverse(X1)),
inference(step,[status(thm)],[t126,t34]) ).
cnf(t51,plain,
multiply(X1,inverse(inverse(inverse(X2)))) = divide(X1,X2),
inference(cp,[status(thm)],[t11,t50]) ).
cnf(t63,plain,
multiply(X1,inverse(inverse(inverse(X2)))) = divide(X1,X2),
inference(orient,[status(thm)],[t51]) ).
cnf(t49,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(cp,[status(thm)],[t45,t45]) ).
cnf(t58,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t49]) ).
cnf(t64,plain,
divide(inverse(inverse(X1)),X2) = multiply(X1,inverse(inverse(inverse(X2)))),
inference(cp,[status(thm)],[t63,t58]) ).
cnf(t895,plain,
divide(inverse(inverse(X1)),X2) = divide(X1,X2),
inference(step,[status(thm)],[t64,t63]) ).
cnf(t66,plain,
divide(inverse(inverse(X1)),X2) = divide(X1,X2),
inference(orient,[status(thm)],[t895]) ).
cnf(t120,plain,
inverse(inverse(inverse(inverse(inverse(X1))))) = inverse(multiply(divide(X1,X2),X2)),
inference(cp,[status(thm)],[t111,t66]) ).
cnf(t899,plain,
inverse(X1) = inverse(multiply(divide(X1,X2),X2)),
inference(step,[status(thm)],[t120,t50]) ).
cnf(t900,plain,
inverse(X1) = inverse(inverse(inverse(X1))),
inference(step,[status(thm)],[t899,t111]) ).
cnf(t138,plain,
inverse(inverse(inverse(X1))) = inverse(X1),
inference(orient,[status(thm)],[t900]) ).
cnf(t901,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t50,t138]) ).
cnf(t139,plain,
inverse(inverse(X1)) = X1,
inference(rw,[status(thm)],[t901]) ).
cnf(t148,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t139]) ).
cnf(t923,plain,
multiply(divide(X1,X2),X2) = X1,
inference(step,[status(thm)],[t922,t148]) ).
cnf(t173,plain,
multiply(divide(X1,X2),X2) = X1,
inference(orient,[status(thm)],[t923]) ).
cnf(t175,plain,
divide(X1,X1) = multiply(inverse(X2),X2),
inference(cp,[status(thm)],[t173,t6]) ).
cnf(t263,plain,
divide(X1,X1) = multiply(inverse(X2),X2),
inference(orient,[status(thm)],[t175]) ).
cnf(t934,plain,
ifeq(divide(f1,f1),multiply(inverse(b1),b1),ifeq(a2,a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true),true) = true,
inference(step,[status(thm)],[t159,t263]) ).
cnf(t935,plain,
ifeq(divide(f1,f1),divide(f1,f1),ifeq(a2,a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true),true) = true,
inference(step,[status(thm)],[t934,t263]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t936,plain,
ifeq(a2,a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true) = true,
inference(step,[status(thm)],[t935,t5]) ).
cnf(t937,plain,
ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true) = true,
inference(step,[status(thm)],[t936,t5]) ).
cnf(t522,plain,
ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true) = true,
inference(orient,[status(thm)],[t937]) ).
cnf(t731,plain,
ifeq(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3)),false,true) = true,
inference(rw,[status(thm)],[t522]) ).
cnf(t976,plain,
false = true,
inference(step,[status(thm)],[t731,t5]) ).
cnf(t888,plain,
false = true,
inference(orient,[status(thm)],[t976]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t888]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP063-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/10.38 % Computer : n006.cluster.edu
% 0.11/10.38 % Model : x86_64 x86_64
% 0.11/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.38 % Memory : 8046.5625MB
% 0.11/10.38 % OS : Linux 6.8.0-71-generic
% 0.11/10.38 % CPULimit : 300
% 0.11/10.38 % WCLimit : 300
% 0.11/10.38 % DateTime : Wed Sep 23 13:26:14 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.59/11.86 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.59/11.86 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------