%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT003-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 01:00:35 PM UTC 2026
% Result : Unsatisfiable 43.70s 6.71s
% Output : Proof 43.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 22 unt; 0 def)
% Number of atoms : 36 ( 35 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 23 ( 14 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 37 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,axiom,
compose(X,compose(Y,Z)) = compose(compose(X,Y),Z),
file('/export/starexec/sandbox/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(f9,axiom,
compose(X,domain(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_domain) ).
fof(f9_nnf,plain,
! [X] : compose(X,domain(X)) = X,
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X] : compose(X,domain(X)) = X,
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
compose(X0,domain(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(p66,plain,
compose(X0,compose(X1,domain(compose(X0,X1)))) = compose(X0,X1),
inference(superposition,[status(thm)],[c8,c9]) ).
cnf(p736,plain,
compose(compose(X0,X1),X2) = compose(X0,compose(X1,X2)),
inference(superposition,[status(thm)],[c8,p66]) ).
cnf(f20,hypothesis,
compose(h,a) = compose(g,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ha_equals_ga) ).
fof(f20_nnf,plain,
compose(h,a) = compose(g,a),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
compose(h,a) = compose(g,a),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(p73,plain,
compose(g,compose(a,X0)) = compose(compose(h,a),X0),
inference(superposition,[status(thm)],[c20,c8]) ).
cnf(p742,plain,
compose(g,compose(a,X0)) = compose(h,compose(a,X0)),
inference(demodulation,[status(thm)],[p736,p73]) ).
cnf(f18,hypothesis,
( X = Z
| compose(Z,compose(a,b)) != Y
| compose(X,compose(a,b)) != Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',epimorphism) ).
fof(f18_nnf,plain,
! [X,Y,Z] :
( X = Z
| compose(Z,compose(a,b)) != Y
| compose(X,compose(a,b)) != Y ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y,Z] :
( X = Z
| compose(Z,compose(a,b)) != Y
| compose(X,compose(a,b)) != Y ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( X0 = X2
| compose(X2,compose(a,b)) != X1
| compose(X0,compose(a,b)) != X1 ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p184,plain,
( X0 = X1
| compose(X0,compose(a,b)) != compose(X1,compose(a,b)) ),
inference(equality_resolution,[status(thm)],[c18]) ).
cnf(p2637,plain,
g = h,
inference(resolution,[status(thm)],[p742,p184]) ).
cnf(f21,negated_conjecture,
g != h,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_g_equals_h) ).
fof(f21_nnf,plain,
g != h,
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
g != h,
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
g != h,
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p2638,plain,
h != h,
inference(demodulation,[status(thm)],[p2637,c21]) ).
cnf(p2643,plain,
$false,
inference(equality_resolution,[status(thm)],[p2638]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.38 % Computer : n009.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Fri Sep 25 06:51:14 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 43.70/6.71 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 43.70/6.71 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------