%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT003-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 50.27s 7.82s
% Output : Proof 50.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 35 ( 31 unt; 0 def)
% Number of atoms : 43 ( 42 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 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; 0-4 aty)
% Number of variables : 51 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f12,hypothesis,
( X = Z
| compose(Z,compose(a,b)) != Y
| compose(X,compose(a,b)) != Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',epimorphism) ).
fof(f12_nnf,plain,
! [X,Y,Z] :
( X = Z
| compose(Z,compose(a,b)) != Y
| compose(X,compose(a,b)) != Y ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X,Y,Z] :
( X = Z
| compose(Z,compose(a,b)) != Y
| compose(X,compose(a,b)) != Y ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( X0 = X2
| compose(X2,compose(a,b)) != X1
| compose(X0,compose(a,b)) != X1 ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t15,plain,
ifeq(compose(X1,compose(a,b)),X2,ifeq(compose(X3,compose(a,b)),X2,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t19,plain,
ifeq(compose(X1,compose(a,b)),X2,ifeq(compose(X3,compose(a,b)),X2,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t15]) ).
cnf(t5,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t18,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t5]) ).
cnf(t20,plain,
X1 = ifeq(compose(X1,compose(a,b)),compose(X2,compose(a,b)),X2,X1),
inference(cp,[status(thm)],[t19,t18]) ).
cnf(t249,plain,
ifeq(compose(X1,compose(a,b)),compose(X2,compose(a,b)),X2,X1) = X1,
inference(orient,[status(thm)],[t20]) ).
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(t10,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t49,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(f14,hypothesis,
compose(h,a) = compose(g,a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ha_equals_ga) ).
fof(f14_nnf,plain,
compose(h,a) = compose(g,a),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
compose(h,a) = compose(g,a),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(t4,plain,
compose(h,a) = compose(g,a),
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t57,plain,
compose(g,a) = compose(h,a),
inference(orient,[status(thm)],[t4]) ).
cnf(t58,plain,
compose(g,compose(a,X1)) = compose(compose(h,a),X1),
inference(cp,[status(thm)],[t49,t57]) ).
cnf(t38625,plain,
compose(g,compose(a,X1)) = compose(h,compose(a,X1)),
inference(step,[status(thm)],[t58,t49]) ).
cnf(t89,plain,
compose(g,compose(a,X1)) = compose(h,compose(a,X1)),
inference(orient,[status(thm)],[t38625]) ).
cnf(t254,plain,
g = ifeq(compose(h,compose(a,b)),compose(X1,compose(a,b)),X1,g),
inference(cp,[status(thm)],[t249,t89]) ).
cnf(t38618,plain,
ifeq(compose(h,compose(a,b)),compose(X1,compose(a,b)),X1,g) = g,
inference(orient,[status(thm)],[t254]) ).
cnf(t38619,plain,
g = h,
inference(cp,[status(thm)],[t38618,t18]) ).
cnf(t38621,plain,
g = h,
inference(orient,[status(thm)],[t38619]) ).
cnf(f15,negated_conjecture,
g != h,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_g_equals_h) ).
fof(f15_nnf,plain,
g != h,
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
g != h,
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
g != h,
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(goal_0,negated_conjecture,
h != g,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(g0_0,plain,
h != h,
inference(rw,[status(thm)],[goal_0,t38621]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT003-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n015.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Fri Sep 25 06:54:41 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 50.27/7.82 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 50.27/7.82 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------