%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT002-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 111.52s 14.60s
% Output : Proof 111.52s
% 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(f19,hypothesis,
( X = Z
| compose(b,Z) != Y
| compose(b,X) != Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_compose2) ).
fof(f19_nnf,plain,
! [X,Y,Z] :
( X = Z
| compose(b,Z) != Y
| compose(b,X) != Y ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X,Y,Z] :
( X = Z
| compose(b,Z) != Y
| compose(b,X) != Y ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( X0 = X2
| compose(b,X2) != X1
| compose(b,X0) != X1 ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t26,plain,
ifeq(compose(b,X1),X2,ifeq(compose(b,X3),X2,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t37,plain,
ifeq(compose(b,X1),X2,ifeq(compose(b,X3),X2,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t26]) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t30,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t10]) ).
cnf(t39,plain,
X1 = ifeq(compose(b,X2),compose(b,X1),X2,X1),
inference(cp,[status(thm)],[t37,t30]) ).
cnf(t2187,plain,
ifeq(compose(b,X1),compose(b,X2),X1,X2) = X2,
inference(orient,[status(thm)],[t39]) ).
cnf(f18,hypothesis,
( X = Z
| compose(a,Z) != Y
| compose(a,X) != Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_for_compose1) ).
fof(f18_nnf,plain,
! [X,Y,Z] :
( X = Z
| compose(a,Z) != Y
| compose(a,X) != Y ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y,Z] :
( X = Z
| compose(a,Z) != Y
| compose(a,X) != Y ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( X0 = X2
| compose(a,X2) != X1
| compose(a,X0) != X1 ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t25,plain,
ifeq(compose(a,X1),X2,ifeq(compose(a,X3),X2,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t32,plain,
ifeq(compose(a,X1),X2,ifeq(compose(a,X3),X2,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t25]) ).
cnf(t33,plain,
X1 = ifeq(compose(a,X1),compose(a,X2),X2,X1),
inference(cp,[status(thm)],[t32,t30]) ).
cnf(t242,plain,
ifeq(compose(a,X1),compose(a,X2),X2,X1) = X1,
inference(orient,[status(thm)],[t33]) ).
cnf(f21,hypothesis,
compose(compose(a,b),h) = compose(compose(a,b),g),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_h_equals_ab_g) ).
fof(f21_nnf,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(t19,plain,
compose(compose(a,b),h) = compose(compose(a,b),g),
inference(equality_encoding,[status(esa)],[c21]) ).
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(t18,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t96,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
cnf(t40746,plain,
compose(a,compose(b,h)) = compose(compose(a,b),g),
inference(step,[status(thm)],[t19,t96]) ).
cnf(t40747,plain,
compose(a,compose(b,h)) = compose(a,compose(b,g)),
inference(step,[status(thm)],[t40746,t96]) ).
cnf(t104,plain,
compose(a,compose(b,g)) = compose(a,compose(b,h)),
inference(orient,[status(thm)],[t40747]) ).
cnf(t243,plain,
compose(b,g) = ifeq(compose(a,compose(b,h)),compose(a,X1),X1,compose(b,g)),
inference(cp,[status(thm)],[t242,t104]) ).
cnf(t40542,plain,
ifeq(compose(a,compose(b,h)),compose(a,X1),X1,compose(b,g)) = compose(b,g),
inference(orient,[status(thm)],[t243]) ).
cnf(t40543,plain,
compose(b,g) = compose(b,h),
inference(cp,[status(thm)],[t40542,t30]) ).
cnf(t40597,plain,
compose(b,g) = compose(b,h),
inference(orient,[status(thm)],[t40543]) ).
cnf(t40602,plain,
X1 = ifeq(compose(b,h),compose(b,X1),g,X1),
inference(cp,[status(thm)],[t2187,t40597]) ).
cnf(t40674,plain,
ifeq(compose(b,h),compose(b,X1),g,X1) = X1,
inference(orient,[status(thm)],[t40602]) ).
cnf(t40675,plain,
h = g,
inference(cp,[status(thm)],[t40674,t30]) ).
cnf(t40683,plain,
g = h,
inference(orient,[status(thm)],[t40675]) ).
cnf(f22,negated_conjecture,
g != h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_g_equals_h) ).
fof(f22_nnf,plain,
g != h,
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
g != h,
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
g != h,
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(goal_0,negated_conjecture,
h != g,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(g0_0,plain,
h != h,
inference(rw,[status(thm)],[goal_0,t40683]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT002-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Fri Sep 25 06:55:28 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 111.52/14.60 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 111.52/14.60 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------