%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT001-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n011.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 28.12s 24.44s
% Output : Proof 28.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 32 unt; 0 def)
% Number of atoms : 44 ( 43 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 : 60 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f18,hypothesis,
( X = Z
| compose(compose(a,b),Z) != Y
| compose(compose(a,b),X) != Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',monomorphism) ).
fof(f18_nnf,plain,
! [X,Y,Z] :
( X = Z
| compose(compose(a,b),Z) != Y
| compose(compose(a,b),X) != Y ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X,Y,Z] :
( X = Z
| compose(compose(a,b),Z) != Y
| compose(compose(a,b),X) != Y ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( X0 = X2
| compose(compose(a,b),X2) != X1
| compose(compose(a,b),X0) != X1 ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(t27,plain,
ifeq(compose(compose(a,b),X1),X2,ifeq(compose(compose(a,b),X3),X2,X1,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t31,plain,
ifeq(compose(compose(a,b),X1),X2,ifeq(compose(compose(a,b),X3),X2,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t27]) ).
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(t19,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t92,plain,
compose(compose(X1,X2),X3) = compose(X1,compose(X2,X3)),
inference(orient,[status(thm)],[t19]) ).
cnf(t48075,plain,
ifeq(compose(a,compose(b,X1)),X2,ifeq(compose(compose(a,b),X3),X2,X1,X3),X3) = X3,
inference(step,[status(thm)],[t31,t92]) ).
cnf(t48076,plain,
ifeq(compose(a,compose(b,X1)),X2,ifeq(compose(a,compose(b,X3)),X2,X1,X3),X3) = X3,
inference(step,[status(thm)],[t48075,t92]) ).
cnf(t100,plain,
ifeq(compose(a,compose(b,X1)),X2,ifeq(compose(a,compose(b,X3)),X2,X1,X3),X3) = X3,
inference(rw,[status(thm)],[t48076]) ).
cnf(t13247,plain,
ifeq(compose(a,compose(b,X1)),X2,ifeq(compose(a,compose(b,X3)),X2,X1,X3),X3) = X3,
inference(orient,[status(thm)],[t100]) ).
cnf(t11,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t29,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t11]) ).
cnf(t13248,plain,
X1 = ifeq(compose(a,compose(b,X1)),compose(a,compose(b,X2)),X2,X1),
inference(cp,[status(thm)],[t13247,t29]) ).
cnf(t41431,plain,
ifeq(compose(a,compose(b,X1)),compose(a,compose(b,X2)),X2,X1) = X1,
inference(orient,[status(thm)],[t13248]) ).
cnf(f20,hypothesis,
compose(b,h) = compose(b,g),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bh_equals_bg) ).
fof(f20_nnf,plain,
compose(b,h) = compose(b,g),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
compose(b,h) = compose(b,g),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(t10,plain,
compose(b,h) = compose(b,g),
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t101,plain,
compose(b,g) = compose(b,h),
inference(orient,[status(thm)],[t10]) ).
cnf(t41455,plain,
g = ifeq(compose(a,compose(b,h)),compose(a,compose(b,X1)),X1,g),
inference(cp,[status(thm)],[t41431,t101]) ).
cnf(t47464,plain,
ifeq(compose(a,compose(b,h)),compose(a,compose(b,X1)),X1,g) = g,
inference(orient,[status(thm)],[t41455]) ).
cnf(t47465,plain,
g = h,
inference(cp,[status(thm)],[t47464,t29]) ).
cnf(t48049,plain,
g = h,
inference(orient,[status(thm)],[t47465]) ).
cnf(f21,negated_conjecture,
h != g,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).
fof(f21_nnf,plain,
h != g,
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
h != g,
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
h != g,
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(goal_0,negated_conjecture,
h != g,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(g0_0,plain,
h != h,
inference(rw,[status(thm)],[goal_0,t48049]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : CAT001-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.34 % Computer : n011.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.02/20.86 % CPULimit : 300
% 0.02/20.86 % WCLimit : 300
% 0.02/20.86 % DateTime : Fri Sep 25 06:50:06 UTC 2026
% 0.02/20.86 % CPUTime :
% 0.02/20.86 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 28.12/24.44 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 28.12/24.44 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------