%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP068-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:25:06 PM UTC 2026
% Result : Unsatisfiable 0.13s 1.02s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 4
% Syntax : Number of formulae : 63 ( 59 unt; 0 def)
% Number of atoms : 71 ( 70 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 28 ( 20 ~; 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 : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 110 ( 2 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
divide(X,divide(divide(divide(identity,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(identity,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(identity,Y),Z),divide(divide(divide(X,X),X),Z))) = Y,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
divide(X0,divide(divide(divide(identity,X1),X2),divide(divide(divide(X0,X0),X0),X2))) = X1,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t2,plain,
divide(X1,divide(divide(divide(identity,X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t4,plain,
divide(X1,divide(divide(divide(identity,X2),X3),divide(divide(divide(X1,X1),X1),X3))) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(f3,axiom,
identity = divide(X,X),
file('/export/starexec/sandbox/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(t9,plain,
divide(X1,X1) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t196,plain,
divide(X1,divide(divide(divide(identity,X2),X3),divide(divide(identity,X1),X3))) = X2,
inference(step,[status(thm)],[t4,t9]) ).
cnf(t10,plain,
divide(X1,divide(divide(divide(identity,X2),X3),divide(divide(identity,X1),X3))) = X2,
inference(rw,[status(thm)],[t196]) ).
cnf(t12,plain,
divide(X1,divide(divide(divide(identity,X2),X3),divide(divide(identity,X1),X3))) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t13,plain,
X1 = divide(X1,identity),
inference(cp,[status(thm)],[t12,t9]) ).
cnf(t22,plain,
divide(X1,identity) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t23,plain,
X1 = divide(X2,divide(divide(identity,X1),divide(divide(identity,X2),identity))),
inference(cp,[status(thm)],[t12,t22]) ).
cnf(t199,plain,
X1 = divide(X2,divide(divide(identity,X1),divide(identity,X2))),
inference(step,[status(thm)],[t23,t22]) ).
cnf(t27,plain,
divide(X1,divide(divide(identity,X2),divide(identity,X1))) = X2,
inference(orient,[status(thm)],[t199]) ).
cnf(t31,plain,
X1 = divide(identity,divide(divide(identity,X1),identity)),
inference(cp,[status(thm)],[t27,t9]) ).
cnf(t200,plain,
X1 = divide(identity,divide(identity,X1)),
inference(step,[status(thm)],[t31,t22]) ).
cnf(t40,plain,
divide(identity,divide(identity,X1)) = X1,
inference(orient,[status(thm)],[t200]) ).
cnf(t41,plain,
divide(divide(divide(identity,X1),X2),divide(divide(identity,identity),X2)) = divide(identity,X1),
inference(cp,[status(thm)],[t40,t12]) ).
cnf(t206,plain,
divide(divide(divide(identity,X1),X2),divide(identity,X2)) = divide(identity,X1),
inference(step,[status(thm)],[t41,t22]) ).
cnf(t71,plain,
divide(divide(divide(identity,X1),X2),divide(identity,X2)) = divide(identity,X1),
inference(orient,[status(thm)],[t206]) ).
cnf(t34,plain,
divide(divide(identity,X1),divide(identity,identity)) = divide(X2,divide(X1,divide(identity,X2))),
inference(cp,[status(thm)],[t27,t27]) ).
cnf(t203,plain,
divide(divide(identity,X1),identity) = divide(X2,divide(X1,divide(identity,X2))),
inference(step,[status(thm)],[t34,t22]) ).
cnf(t204,plain,
divide(identity,X1) = divide(X2,divide(X1,divide(identity,X2))),
inference(step,[status(thm)],[t203,t22]) ).
cnf(t47,plain,
divide(X1,divide(X2,divide(identity,X1))) = divide(identity,X2),
inference(orient,[status(thm)],[t204]) ).
cnf(t48,plain,
divide(identity,X1) = divide(divide(identity,X2),divide(X1,X2)),
inference(cp,[status(thm)],[t47,t40]) ).
cnf(t52,plain,
divide(divide(identity,X1),divide(X2,X1)) = divide(identity,X2),
inference(orient,[status(thm)],[t48]) ).
cnf(t56,plain,
divide(identity,divide(identity,X1)) = divide(divide(identity,divide(X2,X1)),divide(identity,X2)),
inference(cp,[status(thm)],[t52,t52]) ).
cnf(t205,plain,
X1 = divide(divide(identity,divide(X2,X1)),divide(identity,X2)),
inference(step,[status(thm)],[t56,t40]) ).
cnf(t59,plain,
divide(divide(identity,divide(X1,X2)),divide(identity,X1)) = X2,
inference(orient,[status(thm)],[t205]) ).
cnf(t73,plain,
divide(identity,divide(X1,X2)) = divide(X2,divide(identity,divide(identity,X1))),
inference(cp,[status(thm)],[t71,t59]) ).
cnf(t207,plain,
divide(identity,divide(X1,X2)) = divide(X2,X1),
inference(step,[status(thm)],[t73,t40]) ).
cnf(t84,plain,
divide(identity,divide(X1,X2)) = divide(X2,X1),
inference(orient,[status(thm)],[t207]) ).
cnf(t50,plain,
X1 = divide(X2,divide(divide(identity,X3),divide(divide(identity,X2),divide(X3,divide(identity,divide(identity,X1)))))),
inference(cp,[status(thm)],[t12,t47]) ).
cnf(t215,plain,
X1 = divide(X2,divide(divide(identity,X3),divide(divide(identity,X2),divide(X3,X1)))),
inference(step,[status(thm)],[t50,t40]) ).
cnf(t114,plain,
divide(X1,divide(divide(identity,X2),divide(divide(identity,X1),divide(X2,X3)))) = X3,
inference(orient,[status(thm)],[t215]) ).
cnf(t121,plain,
divide(X1,X2) = divide(X3,divide(divide(identity,divide(identity,X2)),divide(divide(identity,X3),divide(identity,X1)))),
inference(cp,[status(thm)],[t114,t52]) ).
cnf(t216,plain,
divide(X1,X2) = divide(X3,divide(X2,divide(divide(identity,X3),divide(identity,X1)))),
inference(step,[status(thm)],[t121,t40]) ).
cnf(t141,plain,
divide(X1,divide(X2,divide(divide(identity,X1),divide(identity,X3)))) = divide(X3,X2),
inference(orient,[status(thm)],[t216]) ).
cnf(t161,plain,
divide(divide(divide(identity,divide(identity,X1)),divide(identity,X2)),X3) = divide(X1,divide(X3,divide(X2,identity))),
inference(cp,[status(thm)],[t141,t141]) ).
cnf(t217,plain,
divide(divide(X1,divide(identity,X2)),X3) = divide(X1,divide(X3,divide(X2,identity))),
inference(step,[status(thm)],[t161,t40]) ).
cnf(t218,plain,
divide(divide(X1,divide(identity,X2)),X3) = divide(X1,divide(X3,X2)),
inference(step,[status(thm)],[t217,t22]) ).
cnf(t167,plain,
divide(divide(X1,divide(identity,X2)),X3) = divide(X1,divide(X3,X2)),
inference(orient,[status(thm)],[t218]) ).
cnf(t1,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t8,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(f4,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4_nnf,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != ifeq(divide(identity,divide(identity,a2)),a2,ifeq(divide(divide(a3,divide(identity,b3)),divide(identity,c3)),divide(a3,divide(identity,divide(b3,divide(identity,c3)))),false,true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(divide(identity,divide(identity,a2)),a2,ifeq(divide(divide(a3,divide(identity,b3)),divide(identity,c3)),divide(a3,divide(divide(identity,c3),b3)),false,true),true),
inference(rw,[status(thm)],[g0_0,t84]) ).
cnf(g0_2,plain,
true != ifeq(divide(a2,identity),a2,ifeq(divide(divide(a3,divide(identity,b3)),divide(identity,c3)),divide(a3,divide(divide(identity,c3),b3)),false,true),true),
inference(rw,[status(thm)],[g0_1,t84]) ).
cnf(g0_3,plain,
true != ifeq(divide(a2,identity),a2,ifeq(divide(a3,divide(divide(identity,c3),b3)),divide(a3,divide(divide(identity,c3),b3)),false,true),true),
inference(rw,[status(thm)],[g0_2,t167]) ).
cnf(g0_4,plain,
true != ifeq(divide(a2,identity),a2,false,true),
inference(rw,[status(thm)],[g0_3,t8]) ).
cnf(g0_5,plain,
true != ifeq(a2,a2,false,true),
inference(rw,[status(thm)],[g0_4,t22]) ).
cnf(g0_6,plain,
true != false,
inference(rw,[status(thm)],[g0_5,t8]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP068-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.53 % Computer : n010.cluster.edu
% 0.08/0.53 % Model : x86_64 x86_64
% 0.08/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.53 % Memory : 8046.5625MB
% 0.08/0.53 % OS : Linux 6.8.0-71-generic
% 0.08/0.53 % CPULimit : 300
% 0.08/0.53 % WCLimit : 300
% 0.08/0.53 % DateTime : Wed Sep 23 13:27:19 UTC 2026
% 0.08/0.53 % CPUTime :
% 0.08/0.53 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.13/1.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/1.02 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------