%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : 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 01:25:10 PM UTC 2026
% Result : Unsatisfiable 4.70s 11.06s
% Output : Proof 4.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 58
% Number of leaves : 6
% Syntax : Number of formulae : 119 ( 115 unt; 0 def)
% Number of atoms : 131 ( 130 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 : 176 ( 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(t26,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(t22,plain,
divide(identity,X1) = inverse(X1),
inference(orient,[status(thm)],[t1]) ).
cnf(t333,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(step,[status(thm)],[t10,t22]) ).
cnf(t24,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(rw,[status(thm)],[t333]) ).
cnf(t28,plain,
divide(X1,inverse(X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t24]) ).
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(t29,plain,
multiply(inverse(X1),X1) = identity,
inference(cp,[status(thm)],[t28,t16]) ).
cnf(t38,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t29]) ).
cnf(t336,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)],[t26,t38]) ).
cnf(t337,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)],[t336,t38]) ).
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(t338,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)],[t337,t9]) ).
cnf(t339,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)],[t338,t38]) ).
cnf(t40,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)],[t339]) ).
cnf(f0,axiom,
divide(divide(identity,X),divide(divide(divide(Y,X),Z),Y)) = Z,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f0_nnf,plain,
! [X,Y,Z] : divide(divide(identity,X),divide(divide(divide(Y,X),Z),Y)) = Z,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] : divide(divide(identity,X),divide(divide(divide(Y,X),Z),Y)) = Z,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
divide(divide(identity,X0),divide(divide(divide(X1,X0),X2),X1)) = X2,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
divide(divide(identity,X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t6,plain,
divide(divide(identity,X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
inference(orient,[status(thm)],[t4]) ).
cnf(t334,plain,
divide(inverse(X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
inference(step,[status(thm)],[t6,t22]) ).
cnf(t25,plain,
divide(inverse(X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
inference(rw,[status(thm)],[t334]) ).
cnf(t51,plain,
divide(inverse(X1),divide(divide(divide(X2,X1),X3),X2)) = X3,
inference(orient,[status(thm)],[t25]) ).
cnf(t58,plain,
divide(X1,X2) = divide(inverse(X2),divide(identity,X1)),
inference(cp,[status(thm)],[t51,t16]) ).
cnf(t340,plain,
divide(X1,X2) = divide(inverse(X2),inverse(X1)),
inference(step,[status(thm)],[t58,t22]) ).
cnf(t341,plain,
divide(X1,X2) = multiply(inverse(X2),X1),
inference(step,[status(thm)],[t340,t28]) ).
cnf(t68,plain,
multiply(inverse(X1),X2) = divide(X2,X1),
inference(orient,[status(thm)],[t341]) ).
cnf(t30,plain,
multiply(identity,X1) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t28,t22]) ).
cnf(t32,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(orient,[status(thm)],[t30]) ).
cnf(t71,plain,
divide(X1,inverse(X2)) = multiply(multiply(identity,X2),X1),
inference(cp,[status(thm)],[t68,t32]) ).
cnf(t351,plain,
multiply(X1,X2) = multiply(multiply(identity,X2),X1),
inference(step,[status(thm)],[t71,t28]) ).
cnf(t98,plain,
multiply(multiply(identity,X1),X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t351]) ).
cnf(t35,plain,
multiply(identity,inverse(X1)) = inverse(multiply(identity,X1)),
inference(cp,[status(thm)],[t32,t32]) ).
cnf(t41,plain,
inverse(multiply(identity,X1)) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t35]) ).
cnf(t23,plain,
inverse(identity) = identity,
inference(cp,[status(thm)],[t22,t16]) ).
cnf(t27,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t23]) ).
cnf(t70,plain,
divide(X1,identity) = multiply(identity,X1),
inference(cp,[status(thm)],[t68,t27]) ).
cnf(t31,plain,
multiply(X1,identity) = divide(X1,identity),
inference(cp,[status(thm)],[t28,t27]) ).
cnf(t37,plain,
divide(X1,identity) = multiply(X1,identity),
inference(orient,[status(thm)],[t31]) ).
cnf(t342,plain,
multiply(X1,identity) = multiply(identity,X1),
inference(step,[status(thm)],[t70,t37]) ).
cnf(t72,plain,
multiply(X1,identity) = multiply(identity,X1),
inference(orient,[status(thm)],[t342]) ).
cnf(t76,plain,
multiply(identity,inverse(X1)) = inverse(multiply(X1,identity)),
inference(cp,[status(thm)],[t41,t72]) ).
cnf(t73,plain,
multiply(identity,inverse(X1)) = divide(identity,X1),
inference(cp,[status(thm)],[t72,t68]) ).
cnf(t343,plain,
multiply(identity,inverse(X1)) = inverse(X1),
inference(step,[status(thm)],[t73,t22]) ).
cnf(t78,plain,
multiply(identity,inverse(X1)) = inverse(X1),
inference(orient,[status(thm)],[t343]) ).
cnf(t350,plain,
inverse(X1) = inverse(multiply(X1,identity)),
inference(step,[status(thm)],[t76,t78]) ).
cnf(t92,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(orient,[status(thm)],[t350]) ).
cnf(t94,plain,
divide(X1,multiply(X2,identity)) = multiply(inverse(X2),X1),
inference(cp,[status(thm)],[t68,t92]) ).
cnf(t356,plain,
divide(X1,multiply(X2,identity)) = divide(X1,X2),
inference(step,[status(thm)],[t94,t68]) ).
cnf(t116,plain,
divide(X1,multiply(X2,identity)) = divide(X1,X2),
inference(orient,[status(thm)],[t356]) ).
cnf(t119,plain,
multiply(X1,identity) = divide(inverse(X2),divide(divide(divide(X3,X2),X1),X3)),
inference(cp,[status(thm)],[t51,t116]) ).
cnf(t357,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t119,t51]) ).
cnf(t120,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t357]) ).
cnf(t123,plain,
multiply(X1,identity) = multiply(identity,X1),
inference(cp,[status(thm)],[t98,t120]) ).
cnf(t361,plain,
X1 = multiply(identity,X1),
inference(step,[status(thm)],[t123,t120]) ).
cnf(t125,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t361]) ).
cnf(t390,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)],[t40,t125]) ).
cnf(t391,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)],[t390,t9]) ).
cnf(t62,plain,
X1 = divide(inverse(X2),divide(divide(identity,X1),X2)),
inference(cp,[status(thm)],[t51,t16]) ).
cnf(t365,plain,
X1 = divide(inverse(X2),divide(inverse(X1),X2)),
inference(step,[status(thm)],[t62,t22]) ).
cnf(t130,plain,
divide(inverse(X1),divide(inverse(X2),X1)) = X2,
inference(orient,[status(thm)],[t365]) ).
cnf(t362,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t32,t125]) ).
cnf(t126,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t362]) ).
cnf(t131,plain,
X1 = divide(X2,divide(inverse(X1),inverse(X2))),
inference(cp,[status(thm)],[t130,t126]) ).
cnf(t366,plain,
X1 = divide(X2,multiply(inverse(X1),X2)),
inference(step,[status(thm)],[t131,t28]) ).
cnf(t367,plain,
X1 = divide(X2,divide(X2,X1)),
inference(step,[status(thm)],[t366,t68]) ).
cnf(t137,plain,
divide(X1,divide(X1,X2)) = X2,
inference(orient,[status(thm)],[t367]) ).
cnf(t142,plain,
divide(divide(X1,X2),X3) = divide(inverse(X2),divide(X3,X1)),
inference(cp,[status(thm)],[t51,t137]) ).
cnf(t164,plain,
divide(inverse(X1),divide(X2,X3)) = divide(divide(X3,X1),X2),
inference(orient,[status(thm)],[t142]) ).
cnf(t167,plain,
divide(divide(X1,identity),X2) = divide(identity,divide(X2,X1)),
inference(cp,[status(thm)],[t164,t27]) ).
cnf(t358,plain,
divide(X1,identity) = X1,
inference(step,[status(thm)],[t37,t120]) ).
cnf(t121,plain,
divide(X1,identity) = X1,
inference(orient,[status(thm)],[t358]) ).
cnf(t368,plain,
divide(X1,X2) = divide(identity,divide(X2,X1)),
inference(step,[status(thm)],[t167,t121]) ).
cnf(t369,plain,
divide(X1,X2) = inverse(divide(X2,X1)),
inference(step,[status(thm)],[t368,t22]) ).
cnf(t177,plain,
inverse(divide(X1,X2)) = divide(X2,X1),
inference(orient,[status(thm)],[t369]) ).
cnf(t184,plain,
multiply(X1,divide(X2,X3)) = divide(X1,divide(X3,X2)),
inference(cp,[status(thm)],[t28,t177]) ).
cnf(t182,plain,
divide(divide(X1,X2),inverse(X3)) = inverse(divide(divide(X2,X3),X1)),
inference(cp,[status(thm)],[t177,t164]) ).
cnf(t376,plain,
multiply(divide(X1,X2),X3) = inverse(divide(divide(X2,X3),X1)),
inference(step,[status(thm)],[t182,t28]) ).
cnf(t377,plain,
multiply(divide(X1,X2),X3) = divide(X1,divide(X2,X3)),
inference(step,[status(thm)],[t376,t177]) ).
cnf(t247,plain,
divide(X1,divide(X2,X3)) = multiply(divide(X1,X2),X3),
inference(orient,[status(thm)],[t377]) ).
cnf(t381,plain,
multiply(X1,divide(X2,X3)) = multiply(divide(X1,X3),X2),
inference(step,[status(thm)],[t184,t247]) ).
cnf(t266,plain,
multiply(divide(X1,X2),X3) = multiply(X1,divide(X3,X2)),
inference(orient,[status(thm)],[t381]) ).
cnf(t278,plain,
multiply(X1,divide(X2,inverse(X3))) = multiply(multiply(X1,X3),X2),
inference(cp,[status(thm)],[t266,t28]) ).
cnf(t389,plain,
multiply(X1,multiply(X2,X3)) = multiply(multiply(X1,X3),X2),
inference(step,[status(thm)],[t278,t28]) ).
cnf(t317,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X3,X2)),
inference(orient,[status(thm)],[t389]) ).
cnf(t392,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)],[t391,t317]) ).
cnf(t364,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(step,[status(thm)],[t98,t125]) ).
cnf(t128,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(rw,[status(thm)],[t364]) ).
cnf(t129,plain,
multiply(X1,X2) = multiply(X2,X1),
inference(orient,[status(thm)],[t128]) ).
cnf(t393,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)],[t392,t129]) ).
cnf(t394,plain,
ifeq(multiply(a4,b4),multiply(b4,a4),false,true) = true,
inference(step,[status(thm)],[t393,t9]) ).
cnf(t395,plain,
ifeq(multiply(b4,a4),multiply(b4,a4),false,true) = true,
inference(step,[status(thm)],[t394,t129]) ).
cnf(t396,plain,
false = true,
inference(step,[status(thm)],[t395,t9]) ).
cnf(t332,plain,
false = true,
inference(orient,[status(thm)],[t396]) ).
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,t332]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP095-1 : TPTP v9.3.1. Bugfixed v2.7.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/10.37 % Computer : n006.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Wed Sep 23 13:30:54 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.70/11.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.70/11.06 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------