%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP093-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:25:09 PM UTC 2026
% Result : Unsatisfiable 5.48s 11.37s
% Output : Proof 5.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 6
% Syntax : Number of formulae : 123 ( 119 unt; 0 def)
% Number of atoms : 135 ( 134 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 16 ( 16 usr; 12 con; 0-4 aty)
% Number of variables : 200 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,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/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,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)],[f4_sk]) ).
cnf(t5,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)],[c4]) ).
cnf(t25,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)],[t5]) ).
cnf(f1,axiom,
multiply(X,Y) = divide(X,divide(identity,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiply) ).
fof(f1_nnf,plain,
! [X,Y] : multiply(X,Y) = divide(X,divide(identity,Y)),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] : multiply(X,Y) = divide(X,divide(identity,Y)),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
multiply(X0,X1) = divide(X0,divide(identity,X1)),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t3,plain,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t10,plain,
divide(X1,divide(identity,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t3]) ).
cnf(f2,axiom,
inverse(X) = divide(identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse) ).
fof(f2_nnf,plain,
! [X] : inverse(X) = divide(identity,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : inverse(X) = divide(identity,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
inverse(X0) = divide(identity,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t1,plain,
divide(identity,X1) = inverse(X1),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t21,plain,
divide(identity,X1) = inverse(X1),
inference(orient,[status(thm)],[t1]) ).
cnf(t381,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(step,[status(thm)],[t10,t21]) ).
cnf(t23,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[t381]) ).
cnf(t27,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t23]) ).
cnf(f3,axiom,
identity = divide(X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).
fof(f3_nnf,plain,
! [X] : identity = divide(X,X),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : identity = divide(X,X),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
identity = divide(X0,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t0,plain,
divide(X1,X1) = identity,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t16,plain,
divide(X1,X1) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t28,plain,
multiply(inverse(X1),X1) = identity,
inference(cp,[status(thm)],[t27,t16]) ).
cnf(t37,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t28]) ).
cnf(t384,plain,
ifeq(identity,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)],[t25,t37]) ).
cnf(t385,plain,
ifeq(identity,identity,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)],[t384,t37]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t9,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t386,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)],[t385,t9]) ).
cnf(t387,plain,
ifeq(multiply(identity,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)],[t386,t37]) ).
cnf(t39,plain,
ifeq(multiply(identity,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(rw,[status(thm)],[t387]) ).
cnf(f0,axiom,
divide(divide(identity,divide(divide(divide(X,Y),Z),X)),Z) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f0_nnf,plain,
! [X,Y,Z] : divide(divide(identity,divide(divide(divide(X,Y),Z),X)),Z) = Y,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] : divide(divide(identity,divide(divide(divide(X,Y),Z),X)),Z) = Y,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
divide(divide(identity,divide(divide(divide(X0,X1),X2),X0)),X2) = X1,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
divide(divide(identity,divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t6,plain,
divide(divide(identity,divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t382,plain,
divide(inverse(divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
inference(step,[status(thm)],[t6,t21]) ).
cnf(t24,plain,
divide(inverse(divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
inference(rw,[status(thm)],[t382]) ).
cnf(t50,plain,
divide(inverse(divide(divide(divide(X1,X2),X3),X1)),X3) = X2,
inference(orient,[status(thm)],[t24]) ).
cnf(t57,plain,
X1 = divide(inverse(divide(identity,X2)),divide(X2,X1)),
inference(cp,[status(thm)],[t50,t16]) ).
cnf(t388,plain,
X1 = divide(inverse(inverse(X2)),divide(X2,X1)),
inference(step,[status(thm)],[t57,t21]) ).
cnf(t29,plain,
multiply(identity,X1) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t27,t21]) ).
cnf(t31,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(orient,[status(thm)],[t29]) ).
cnf(t389,plain,
X1 = divide(multiply(identity,X2),divide(X2,X1)),
inference(step,[status(thm)],[t388,t31]) ).
cnf(t67,plain,
divide(multiply(identity,X1),divide(X1,X2)) = X2,
inference(orient,[status(thm)],[t389]) ).
cnf(t22,plain,
inverse(identity) = identity,
inference(cp,[status(thm)],[t21,t16]) ).
cnf(t26,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t22]) ).
cnf(t32,plain,
multiply(identity,identity) = inverse(identity),
inference(cp,[status(thm)],[t31,t26]) ).
cnf(t383,plain,
multiply(identity,identity) = identity,
inference(step,[status(thm)],[t32,t26]) ).
cnf(t35,plain,
multiply(identity,identity) = identity,
inference(orient,[status(thm)],[t383]) ).
cnf(t68,plain,
X1 = divide(identity,divide(identity,X1)),
inference(cp,[status(thm)],[t67,t35]) ).
cnf(t390,plain,
X1 = inverse(divide(identity,X1)),
inference(step,[status(thm)],[t68,t21]) ).
cnf(t391,plain,
X1 = inverse(inverse(X1)),
inference(step,[status(thm)],[t390,t21]) ).
cnf(t392,plain,
X1 = multiply(identity,X1),
inference(step,[status(thm)],[t391,t31]) ).
cnf(t77,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t392]) ).
cnf(t428,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)],[t39,t77]) ).
cnf(t429,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)],[t428,t9]) ).
cnf(t395,plain,
divide(X1,divide(X1,X2)) = X2,
inference(step,[status(thm)],[t67,t77]) ).
cnf(t80,plain,
divide(X1,divide(X1,X2)) = X2,
inference(rw,[status(thm)],[t395]) ).
cnf(t85,plain,
divide(X1,divide(X1,X2)) = X2,
inference(orient,[status(thm)],[t80]) ).
cnf(t88,plain,
inverse(X1) = divide(X2,multiply(X2,X1)),
inference(cp,[status(thm)],[t85,t27]) ).
cnf(t95,plain,
divide(X1,multiply(X1,X2)) = inverse(X2),
inference(orient,[status(thm)],[t88]) ).
cnf(t61,plain,
X1 = divide(inverse(divide(divide(identity,X2),X1)),X2),
inference(cp,[status(thm)],[t50,t16]) ).
cnf(t401,plain,
X1 = divide(inverse(divide(inverse(X2),X1)),X2),
inference(step,[status(thm)],[t61,t21]) ).
cnf(t98,plain,
divide(inverse(divide(inverse(X1),X2)),X1) = X2,
inference(orient,[status(thm)],[t401]) ).
cnf(t101,plain,
multiply(inverse(X1),X2) = divide(inverse(inverse(X2)),X1),
inference(cp,[status(thm)],[t98,t95]) ).
cnf(t393,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t31,t77]) ).
cnf(t78,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t393]) ).
cnf(t402,plain,
multiply(inverse(X1),X2) = divide(X2,X1),
inference(step,[status(thm)],[t101,t78]) ).
cnf(t108,plain,
multiply(inverse(X1),X2) = divide(X2,X1),
inference(orient,[status(thm)],[t402]) ).
cnf(t111,plain,
inverse(X1) = divide(inverse(X2),divide(X1,X2)),
inference(cp,[status(thm)],[t95,t108]) ).
cnf(t119,plain,
divide(inverse(X1),divide(X2,X1)) = inverse(X2),
inference(orient,[status(thm)],[t111]) ).
cnf(t120,plain,
inverse(X1) = divide(inverse(divide(X1,X2)),X2),
inference(cp,[status(thm)],[t119,t85]) ).
cnf(t123,plain,
divide(inverse(divide(X1,X2)),X2) = inverse(X1),
inference(orient,[status(thm)],[t120]) ).
cnf(t124,plain,
inverse(divide(divide(X1,X2),X1)) = X2,
inference(cp,[status(thm)],[t123,t50]) ).
cnf(t128,plain,
inverse(divide(divide(X1,X2),X1)) = X2,
inference(orient,[status(thm)],[t124]) ).
cnf(t132,plain,
divide(X1,X2) = inverse(divide(X2,X1)),
inference(cp,[status(thm)],[t128,t85]) ).
cnf(t144,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(orient,[status(thm)],[t132]) ).
cnf(t407,plain,
divide(divide(X1,divide(divide(X1,X2),X3)),X3) = X2,
inference(step,[status(thm)],[t50,t144]) ).
cnf(t156,plain,
divide(divide(X1,divide(divide(X1,X2),X3)),X3) = X2,
inference(rw,[status(thm)],[t407]) ).
cnf(t150,plain,
multiply(X1,divide(X2,X3)) = divide(X1,divide(X3,X2)),
inference(cp,[status(thm)],[t27,t144]) ).
cnf(t198,plain,
divide(X1,divide(X2,X3)) = multiply(X1,divide(X3,X2)),
inference(orient,[status(thm)],[t150]) ).
cnf(t416,plain,
divide(multiply(X1,divide(X3,divide(X1,X2))),X3) = X2,
inference(step,[status(thm)],[t156,t198]) ).
cnf(t417,plain,
divide(multiply(X1,multiply(X3,divide(X2,X1))),X3) = X2,
inference(step,[status(thm)],[t416,t198]) ).
cnf(t241,plain,
divide(multiply(X1,multiply(X2,divide(X3,X1))),X2) = X3,
inference(orient,[status(thm)],[t417]) ).
cnf(t147,plain,
divide(divide(X1,X2),X1) = inverse(X2),
inference(cp,[status(thm)],[t144,t85]) ).
cnf(t186,plain,
divide(divide(X1,X2),X1) = inverse(X2),
inference(orient,[status(thm)],[t147]) ).
cnf(t254,plain,
divide(X1,X2) = divide(multiply(X1,multiply(X3,inverse(X2))),X3),
inference(cp,[status(thm)],[t241,t186]) ).
cnf(t33,plain,
multiply(X1,inverse(X2)) = divide(X1,multiply(identity,X2)),
inference(cp,[status(thm)],[t27,t31]) ).
cnf(t46,plain,
divide(X1,multiply(identity,X2)) = multiply(X1,inverse(X2)),
inference(orient,[status(thm)],[t33]) ).
cnf(t396,plain,
divide(X1,X2) = multiply(X1,inverse(X2)),
inference(step,[status(thm)],[t46,t77]) ).
cnf(t81,plain,
divide(X1,X2) = multiply(X1,inverse(X2)),
inference(rw,[status(thm)],[t396]) ).
cnf(t84,plain,
multiply(X1,inverse(X2)) = divide(X1,X2),
inference(orient,[status(thm)],[t81]) ).
cnf(t418,plain,
divide(X1,X2) = divide(multiply(X1,divide(X3,X2)),X3),
inference(step,[status(thm)],[t254,t84]) ).
cnf(t266,plain,
divide(multiply(X1,divide(X2,X3)),X2) = divide(X1,X3),
inference(orient,[status(thm)],[t418]) ).
cnf(t274,plain,
divide(X1,multiply(X2,X3)) = divide(multiply(X1,inverse(X3)),X2),
inference(cp,[status(thm)],[t266,t95]) ).
cnf(t419,plain,
divide(X1,multiply(X2,X3)) = divide(divide(X1,X3),X2),
inference(step,[status(thm)],[t274,t84]) ).
cnf(t291,plain,
divide(divide(X1,X2),X3) = divide(X1,multiply(X3,X2)),
inference(orient,[status(thm)],[t419]) ).
cnf(t296,plain,
divide(X1,multiply(inverse(X2),X3)) = multiply(divide(X1,X3),X2),
inference(cp,[status(thm)],[t291,t27]) ).
cnf(t420,plain,
divide(X1,divide(X3,X2)) = multiply(divide(X1,X3),X2),
inference(step,[status(thm)],[t296,t108]) ).
cnf(t421,plain,
multiply(X1,divide(X2,X3)) = multiply(divide(X1,X3),X2),
inference(step,[status(thm)],[t420,t198]) ).
cnf(t315,plain,
multiply(divide(X1,X2),X3) = multiply(X1,divide(X3,X2)),
inference(orient,[status(thm)],[t421]) ).
cnf(t322,plain,
multiply(X1,divide(X2,inverse(X3))) = multiply(multiply(X1,X3),X2),
inference(cp,[status(thm)],[t315,t27]) ).
cnf(t427,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X3),X2),
inference(step,[status(thm)],[t322,t27]) ).
cnf(t353,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X3,X2)),
inference(orient,[status(thm)],[t427]) ).
cnf(t430,plain,
ifeq(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(b3,c3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true) = true,
inference(step,[status(thm)],[t429,t353]) ).
cnf(t110,plain,
divide(X1,inverse(X2)) = multiply(X2,X1),
inference(cp,[status(thm)],[t108,t78]) ).
cnf(t403,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(step,[status(thm)],[t110,t27]) ).
cnf(t112,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t403]) ).
cnf(t431,plain,
ifeq(multiply(a3,multiply(c3,b3)),multiply(a3,multiply(c3,b3)),ifeq(multiply(a4,b4),multiply(b4,a4),false,true),true) = true,
inference(step,[status(thm)],[t430,t112]) ).
cnf(t432,plain,
ifeq(multiply(a4,b4),multiply(b4,a4),false,true) = true,
inference(step,[status(thm)],[t431,t9]) ).
cnf(t433,plain,
ifeq(multiply(b4,a4),multiply(b4,a4),false,true) = true,
inference(step,[status(thm)],[t432,t112]) ).
cnf(t434,plain,
false = true,
inference(step,[status(thm)],[t433,t9]) ).
cnf(t380,plain,
false = true,
inference(orient,[status(thm)],[t434]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t380]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP093-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/10.60 % Computer : n010.cluster.edu
% 0.09/10.60 % Model : x86_64 x86_64
% 0.09/10.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.60 % Memory : 8046.5625MB
% 0.09/10.60 % OS : Linux 6.8.0-71-generic
% 0.09/10.60 % CPULimit : 300
% 0.09/10.60 % WCLimit : 300
% 0.09/10.60 % DateTime : Wed Sep 23 13:30:59 UTC 2026
% 0.09/10.61 % CPUTime :
% 0.09/10.61 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.48/11.37 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.48/11.37 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------