%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT002-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 01:00:34 PM UTC 2026
% Result : Unsatisfiable 160.41s 21.06s
% Output : Proof 160.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 46 ( 38 unt; 0 def)
% Number of atoms : 62 ( 61 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 38 ( 22 ~; 16 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 72 ( 2 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f13,hypothesis,
( X = Z
| compose(b,Z) != Y
| compose(b,X) != Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_compose2) ).
fof(f13_nnf,plain,
! [X,Y,Z] :
( X = Z
| compose(b,Z) != Y
| compose(b,X) != Y ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X,Y,Z] :
( X = Z
| compose(b,Z) != Y
| compose(b,X) != Y ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( X0 = X2
| compose(b,X2) != X1
| compose(b,X0) != X1 ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(t15,plain,
ifeq(compose(b,X1),X2,ifeq(compose(b,X3),X2,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(t26,plain,
ifeq(compose(b,X1),X2,ifeq(compose(b,X3),X2,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t15]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t19,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t29,plain,
X1 = ifeq(compose(b,X2),compose(b,X1),X2,X1),
inference(cp,[status(thm)],[t26,t19]) ).
cnf(t691,plain,
ifeq(compose(b,X1),compose(b,X2),X1,X2) = X2,
inference(orient,[status(thm)],[t29]) ).
cnf(f12,hypothesis,
( X = Z
| compose(a,Z) != Y
| compose(a,X) != Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_compose1) ).
fof(f12_nnf,plain,
! [X,Y,Z] :
( X = Z
| compose(a,Z) != Y
| compose(a,X) != Y ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,Z] :
( X = Z
| compose(a,Z) != Y
| compose(a,X) != Y ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( X0 = X2
| compose(a,X2) != X1
| compose(a,X0) != X1 ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t14,plain,
ifeq(compose(a,X1),X2,ifeq(compose(a,X3),X2,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t20,plain,
ifeq(compose(a,X1),X2,ifeq(compose(a,X3),X2,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t14]) ).
cnf(t21,plain,
X1 = ifeq(compose(a,X1),compose(a,X2),X2,X1),
inference(cp,[status(thm)],[t20,t19]) ).
cnf(t259,plain,
ifeq(compose(a,X1),compose(a,X2),X2,X1) = X1,
inference(orient,[status(thm)],[t21]) ).
cnf(f15,hypothesis,
compose(compose(a,b),h) = compose(compose(a,b),g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_h_equals_ab_g) ).
fof(f15_nnf,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(t10,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(f8,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity_of_compose) ).
fof(f8_nnf,plain,
! [X,Y,Z] : compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z] : compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
compose(X0,compose(X1,X2)) = compose(compose(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t9,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t56,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t55310,plain,
compose(a,compose(b,h)) = compose(compose(a,b),g),
inference(step,[status(thm)],[t10,t56]) ).
cnf(t55311,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(step,[status(thm)],[t55310,t56]) ).
cnf(t62,plain,
compose(a,compose(b,g)) = compose(a,compose(b,h)),
inference(orient,[status(thm)],[t55311]) ).
cnf(t260,plain,
compose(b,g) = ifeq(compose(a,compose(b,h)),compose(a,X1),X1,compose(b,g)),
inference(cp,[status(thm)],[t259,t62]) ).
cnf(t50519,plain,
ifeq(compose(a,compose(b,h)),compose(a,X1),X1,compose(b,g)) = compose(b,g),
inference(orient,[status(thm)],[t260]) ).
cnf(t50520,plain,
compose(b,g) = compose(b,h),
inference(cp,[status(thm)],[t50519,t19]) ).
cnf(t50575,plain,
compose(b,g) = compose(b,h),
inference(orient,[status(thm)],[t50520]) ).
cnf(t50580,plain,
X1 = ifeq(compose(b,h),compose(b,X1),g,X1),
inference(cp,[status(thm)],[t691,t50575]) ).
cnf(t55298,plain,
ifeq(compose(b,h),compose(b,X1),g,X1) = X1,
inference(orient,[status(thm)],[t50580]) ).
cnf(t55299,plain,
h = g,
inference(cp,[status(thm)],[t55298,t19]) ).
cnf(t55309,plain,
g = h,
inference(orient,[status(thm)],[t55299]) ).
cnf(f16,negated_conjecture,
g != h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_g_equals_h) ).
fof(f16_nnf,plain,
g != h,
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
g != h,
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
g != h,
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(goal_0,negated_conjecture,
h != g,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(g0_0,plain,
h != h,
inference(rw,[status(thm)],[goal_0,t55309]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT002-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n026.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 : Fri Sep 25 06:53:41 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 160.41/21.06 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 160.41/21.06 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------