%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL014+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Sun Sep 27 08:24:49 AM UTC 2026
% Result : Theorem 0.14s 0.38s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 15 unt; 0 def)
% Number of atoms : 27 ( 26 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 16 ( 10 ~; 4 |; 2 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 6 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(composition_identity,axiom,
! [X0] : composition(X0,one) = X0,
file('theBenchmark.p',composition_identity) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(goals,conjecture,
! [X0] :
( composition(one,X0) = X0
& composition(X0,one) = X0 ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0] :
( composition(one,X0) = X0
& composition(X0,one) = X0 ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_21,plain,
composition(A,one) = A,
inference(clausify,[status(thm)],[composition_identity]) ).
cnf(c_23,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_25,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
fof(nnf_14,plain,
? [X0] :
( composition(one,X0) != X0
| composition(X0,one) != X0 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( composition(one,sK0) != sK0
| composition(sK0,one) != sK0 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
( composition(one,sK0) != sK0
| composition(sK0,one) != sK0 ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_110,negated_conjecture,
( composition(one,sK0) != sK0
| sK0 != sK0 ),
inference(paramod,[status(thm)],[c_21,c_31]) ).
cnf(c_32,negated_conjecture,
composition(one,sK0) != sK0,
inference(copy,[status(thm)],[c_110]) ).
cnf(c_111,plain,
converse(A) = composition(converse(one),converse(A)),
inference(paramod,[status(thm)],[c_21,c_25]) ).
cnf(c_43,plain,
composition(converse(one),converse(A)) = converse(A),
inference(copy,[status(thm)],[c_111]) ).
cnf(c_112,plain,
composition(converse(one),A) = converse(converse(A)),
inference(paramod,[status(thm)],[c_23,c_43]) ).
cnf(c_101,plain,
composition(converse(one),A) = A,
inference(paramod,[status(thm)],[c_23,c_112]) ).
cnf(c_113,plain,
one = converse(one),
inference(paramod,[status(thm)],[c_101,c_21]) ).
cnf(c_103,plain,
converse(one) = one,
inference(copy,[status(thm)],[c_113]) ).
cnf(c_108,plain,
composition(one,A) = A,
inference(paramod,[status(thm)],[c_103,c_101]) ).
cnf(c_109,plain,
$false,
inference(resolve,[status(thm)],[c_108,c_32]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL014+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n026.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 : Sat Sep 26 05:30:25 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 181568 was started by sandbox on n026,
% 0.08/0.36 % Sat Sep 26 05:30:25 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 0.14/0.38
% 0.14/0.38 % SZS status Theorem for theBenchmark
% 0.14/0.38
% 0.14/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/0.38 % Length of proof is 14.
% 0.14/0.38 % Level of proof is 6.
% 0.14/0.38 % Maximum clause weight is 25.000.
% 0.14/0.38 % Given clauses 20.
% 0.14/0.38
% 0.14/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------