%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : CAT014-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 01:00:40 PM UTC 2026
% Result : Unsatisfiable 5.63s 1.29s
% Output : Proof 5.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 26 ( 22 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 1 con; 0-4 aty)
% Number of variables : 24 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( codomain(compose(X,Y)) = codomain(Y)
| codomain(X) != domain(Y) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_domain2) ).
fof(f5_nnf,plain,
! [X,Y] :
( codomain(compose(X,Y)) = codomain(Y)
| codomain(X) != domain(Y) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] :
( codomain(compose(X,Y)) = codomain(Y)
| codomain(X) != domain(Y) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( codomain(compose(X0,X1)) = codomain(X1)
| codomain(X0) != domain(X1) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(codomain(X0),domain(X1),codomain(compose(X0,X1)),codomain(X1)) = codomain(X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f1,axiom,
domain(codomain(X)) = codomain(X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_of_codomain_is_codomain) ).
fof(f1_nnf,plain,
! [X] : domain(codomain(X)) = codomain(X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : domain(codomain(X)) = codomain(X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
domain(codomain(X0)) = codomain(X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
domain(codomain(X0)) = codomain(X0),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t7,plain,
codomain(compose(X1,codomain(X1))) = codomain(codomain(X1)),
inference(hyper_resolution,[status(thm)],[hi5,hi1]) ).
cnf(f3,axiom,
compose(X,codomain(X)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain_composition) ).
fof(f3_nnf,plain,
! [X] : compose(X,codomain(X)) = X,
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : compose(X,codomain(X)) = X,
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
compose(X0,codomain(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t1,plain,
compose(X1,codomain(X1)) = X1,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t17,plain,
compose(X1,codomain(X1)) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t30,plain,
codomain(X1) = codomain(codomain(X1)),
inference(step,[status(thm)],[t7,t17]) ).
cnf(t26,plain,
codomain(codomain(X1)) = codomain(X1),
inference(orient,[status(thm)],[t30]) ).
cnf(f7,negated_conjecture,
codomain(codomain(a)) != codomain(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_is_idempotent) ).
fof(f7_nnf,plain,
codomain(codomain(a)) != codomain(a),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
codomain(codomain(a)) != codomain(a),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
codomain(codomain(a)) != codomain(a),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(goal_0,negated_conjecture,
codomain(codomain(a)) != codomain(a),
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(g0_0,plain,
codomain(a) != codomain(a),
inference(rw,[status(thm)],[goal_0,t26]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : CAT014-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n004.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Fri Sep 25 06:56:05 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.63/1.29 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.63/1.29 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------