%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL008+3 : 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 : n017.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 08:24:46 AM UTC 2026
% Result : Theorem 13.21s 2.16s
% Output : CNFRefutation 13.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 30 unt; 0 def)
% Number of atoms : 30 ( 29 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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; 3 con; 0-2 aty)
% Number of variables : 64 ( 0 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(composition_distributivity,axiom,
! [X0,X1,X2] : composition(join(X0,X1),X2) = join(composition(X0,X2),composition(X1,X2)),
file('theBenchmark.p',composition_distributivity) ).
fof(converse_idempotence,axiom,
! [X0] : converse(converse(X0)) = X0,
file('theBenchmark.p',converse_idempotence) ).
fof(converse_additivity,axiom,
! [X0,X1] : converse(join(X0,X1)) = join(converse(X0),converse(X1)),
file('theBenchmark.p',converse_additivity) ).
fof(converse_multiplicativity,axiom,
! [X0,X1] : converse(composition(X0,X1)) = composition(converse(X1),converse(X0)),
file('theBenchmark.p',converse_multiplicativity) ).
fof(goals,conjecture,
! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] : composition(X0,join(X1,X2)) = join(composition(X0,X1),composition(X0,X2)),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_25,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_26,plain,
join(composition(A,B),composition(C,B)) = composition(join(A,C),B),
inference(copy,[status(thm)],[c_25]) ).
cnf(c_27,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_28,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_29,plain,
join(converse(A),converse(B)) = converse(join(A,B)),
inference(copy,[status(thm)],[c_28]) ).
cnf(c_30,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
cnf(c_31,plain,
composition(converse(A),converse(B)) = converse(composition(B,A)),
inference(copy,[status(thm)],[c_30]) ).
fof(nnf_17,plain,
? [X0,X1,X2] : composition(X0,join(X1,X2)) != join(composition(X0,X1),composition(X0,X2)),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
composition(sK0,join(sK1,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_17]) ).
cnf(c_43,negated_conjecture,
composition(sK0,join(sK1,sK2)) != join(composition(sK0,sK1),composition(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_44,negated_conjecture,
join(composition(sK0,sK1),composition(sK0,sK2)) != composition(sK0,join(sK1,sK2)),
inference(copy,[status(thm)],[c_43]) ).
cnf(c_4712,plain,
join(A,converse(B)) = converse(join(converse(A),B)),
inference(paramod,[status(thm)],[c_27,c_29]) ).
cnf(c_58,plain,
converse(join(converse(A),B)) = join(A,converse(B)),
inference(copy,[status(thm)],[c_4712]) ).
cnf(c_61,plain,
join(converse(composition(A,B)),composition(C,converse(A))) = composition(join(converse(B),C),converse(A)),
inference(paramod,[status(thm)],[c_31,c_26]) ).
cnf(c_4713,plain,
composition(A,converse(B)) = converse(composition(B,converse(A))),
inference(paramod,[status(thm)],[c_27,c_31]) ).
cnf(c_63,plain,
converse(composition(A,converse(B))) = composition(B,converse(A)),
inference(copy,[status(thm)],[c_4713]) ).
cnf(c_4714,plain,
join(converse(converse(composition(A,B))),converse(composition(C,converse(A)))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_61,c_29]) ).
cnf(c_4715,plain,
join(composition(A,B),converse(composition(C,converse(A)))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_27,c_4714]) ).
cnf(c_4716,plain,
join(composition(A,B),composition(A,converse(C))) = converse(composition(join(converse(B),C),converse(A))),
inference(paramod,[status(thm)],[c_63,c_4715]) ).
cnf(c_4717,plain,
join(composition(A,B),composition(A,converse(C))) = composition(A,converse(join(converse(B),C))),
inference(paramod,[status(thm)],[c_63,c_4716]) ).
cnf(c_617,plain,
join(composition(A,B),composition(A,converse(C))) = composition(A,join(B,converse(C))),
inference(paramod,[status(thm)],[c_58,c_4717]) ).
cnf(c_4718,plain,
join(composition(A,B),composition(A,C)) = composition(A,join(B,converse(converse(C)))),
inference(paramod,[status(thm)],[c_27,c_617]) ).
cnf(c_4710,plain,
join(composition(A,B),composition(A,C)) = composition(A,join(B,C)),
inference(paramod,[status(thm)],[c_27,c_4718]) ).
cnf(c_4711,plain,
$false,
inference(resolve,[status(thm)],[c_4710,c_44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : REL008+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.43 % Computer : n017.cluster.edu
% 0.17/0.43 % Model : x86_64 x86_64
% 0.17/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.43 % Memory : 8046.5625MB
% 0.17/0.43 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 05:21:03 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 4107528 was started by sandbox on n017,
% 0.17/0.44 % Sat Sep 26 05:21:03 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 13.21/2.16
% 13.21/2.16 % SZS status Theorem for theBenchmark
% 13.21/2.16
% 13.21/2.16 % Proof 1 at 1.33 (+ 0.35) seconds.
% 13.21/2.16 % Length of proof is 20.
% 13.21/2.16 % Level of proof is 6.
% 13.21/2.16 % Maximum clause weight is 37.000.
% 13.21/2.16 % Given clauses 289.
% 13.21/2.16
% 13.21/2.16 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------