%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL009+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 : n012.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 08:24:47 AM UTC 2026
% Result : Theorem 3.47s 1.38s
% Output : CNFRefutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 5
% Syntax : Number of formulae : 36 ( 28 unt; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 26 ( 14 ~; 6 |; 4 &)
% ( 0 <=>; 2 =>; 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; 3 con; 0-2 aty)
% Number of variables : 40 ( 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] :
( join(X0,X1) = X1
=> ( join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1)
& join(composition(X0,X2),composition(X1,X2)) = composition(X1,X2) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1,X2] :
( join(X0,X1) = X1
=> ( join(composition(X2,X0),composition(X2,X1)) = composition(X2,X1)
& join(composition(X0,X2),composition(X1,X2)) = composition(X1,X2) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
cnf(c_22,plain,
composition(join(A,B),C) = join(composition(A,C),composition(B,C)),
inference(clausify,[status(thm)],[composition_distributivity]) ).
cnf(c_23,plain,
converse(converse(A)) = A,
inference(clausify,[status(thm)],[converse_idempotence]) ).
cnf(c_24,plain,
converse(join(A,B)) = join(converse(A),converse(B)),
inference(clausify,[status(thm)],[converse_additivity]) ).
cnf(c_25,plain,
converse(composition(A,B)) = composition(converse(B),converse(A)),
inference(clausify,[status(thm)],[converse_multiplicativity]) ).
fof(nnf_14,plain,
? [X0,X1,X2] :
( ( composition(X2,X1) != join(composition(X2,X0),composition(X2,X1))
| composition(X1,X2) != join(composition(X0,X2),composition(X1,X2)) )
& join(X0,X1) = X1 ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg,plain,
( ( composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1))
| composition(sK1,sK2) != join(composition(sK0,sK2),composition(sK1,sK2)) )
& join(sK0,sK1) = sK1 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[nnf_14]) ).
cnf(c_31,negated_conjecture,
join(sK0,sK1) = sK1,
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,negated_conjecture,
( composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1))
| composition(sK1,sK2) != join(composition(sK0,sK2),composition(sK1,sK2)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_2384,negated_conjecture,
( composition(sK2,sK1) != join(composition(sK2,sK0),composition(sK2,sK1))
| join(composition(sK0,sK2),composition(sK1,sK2)) != composition(sK1,sK2) ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_33,negated_conjecture,
( join(composition(sK2,sK0),composition(sK2,sK1)) != composition(sK2,sK1)
| join(composition(sK0,sK2),composition(sK1,sK2)) != composition(sK1,sK2) ),
inference(copy,[status(thm)],[c_2384]) ).
cnf(c_2385,plain,
composition(sK1,A) = join(composition(sK0,A),composition(sK1,A)),
inference(paramod,[status(thm)],[c_31,c_22]) ).
cnf(c_66,plain,
join(composition(sK0,A),composition(sK1,A)) = composition(sK1,A),
inference(copy,[status(thm)],[c_2385]) ).
cnf(c_2386,plain,
converse(sK1) = join(converse(sK0),converse(sK1)),
inference(paramod,[status(thm)],[c_31,c_24]) ).
cnf(c_67,plain,
join(converse(sK0),converse(sK1)) = converse(sK1),
inference(copy,[status(thm)],[c_2386]) ).
cnf(c_2387,negated_conjecture,
( join(composition(sK2,sK0),composition(sK2,sK1)) != composition(sK2,sK1)
| composition(sK1,sK2) != composition(sK1,sK2) ),
inference(paramod,[status(thm)],[c_66,c_33]) ).
cnf(c_68,negated_conjecture,
join(composition(sK2,sK0),composition(sK2,sK1)) != composition(sK2,sK1),
inference(copy,[status(thm)],[c_2387]) ).
cnf(c_2388,plain,
composition(converse(sK1),A) = join(composition(converse(sK0),A),composition(converse(sK1),A)),
inference(paramod,[status(thm)],[c_67,c_22]) ).
cnf(c_118,plain,
join(composition(converse(sK0),A),composition(converse(sK1),A)) = composition(converse(sK1),A),
inference(copy,[status(thm)],[c_2388]) ).
cnf(c_2389,plain,
converse(composition(converse(sK1),A)) = join(converse(composition(converse(sK0),A)),converse(composition(converse(sK1),A))),
inference(paramod,[status(thm)],[c_118,c_24]) ).
cnf(c_2390,plain,
composition(converse(A),converse(converse(sK1))) = join(converse(composition(converse(sK0),A)),converse(composition(converse(sK1),A))),
inference(paramod,[status(thm)],[c_25,c_2389]) ).
cnf(c_2391,plain,
composition(converse(A),sK1) = join(converse(composition(converse(sK0),A)),converse(composition(converse(sK1),A))),
inference(paramod,[status(thm)],[c_23,c_2390]) ).
cnf(c_2392,plain,
composition(converse(A),sK1) = join(composition(converse(A),converse(converse(sK0))),converse(composition(converse(sK1),A))),
inference(paramod,[status(thm)],[c_25,c_2391]) ).
cnf(c_2393,plain,
composition(converse(A),sK1) = join(composition(converse(A),sK0),converse(composition(converse(sK1),A))),
inference(paramod,[status(thm)],[c_23,c_2392]) ).
cnf(c_2394,plain,
composition(converse(A),sK1) = join(composition(converse(A),sK0),composition(converse(A),converse(converse(sK1)))),
inference(paramod,[status(thm)],[c_25,c_2393]) ).
cnf(c_2395,plain,
composition(converse(A),sK1) = join(composition(converse(A),sK0),composition(converse(A),sK1)),
inference(paramod,[status(thm)],[c_23,c_2394]) ).
cnf(c_809,plain,
join(composition(converse(A),sK0),composition(converse(A),sK1)) = composition(converse(A),sK1),
inference(copy,[status(thm)],[c_2395]) ).
cnf(c_2396,plain,
join(composition(A,sK0),composition(converse(converse(A)),sK1)) = composition(converse(converse(A)),sK1),
inference(paramod,[status(thm)],[c_23,c_809]) ).
cnf(c_2397,plain,
join(composition(A,sK0),composition(A,sK1)) = composition(converse(converse(A)),sK1),
inference(paramod,[status(thm)],[c_23,c_2396]) ).
cnf(c_2382,plain,
join(composition(A,sK0),composition(A,sK1)) = composition(A,sK1),
inference(paramod,[status(thm)],[c_23,c_2397]) ).
cnf(c_2383,plain,
$false,
inference(resolve,[status(thm)],[c_2382,c_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : REL009+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.35 % Computer : n012.cluster.edu
% 0.05/0.35 % Model : x86_64 x86_64
% 0.05/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.35 % Memory : 8046.5625MB
% 0.05/0.35 % OS : Linux 6.8.0-71-generic
% 0.05/0.35 % CPULimit : 300
% 0.05/0.35 % WCLimit : 300
% 0.05/0.35 % DateTime : Sat Sep 26 05:25:06 UTC 2026
% 0.05/0.35 % CPUTime :
% 0.05/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.05/0.35 % Process 3986000 was started by sandbox on n012,
% 0.05/0.35 % Sat Sep 26 05:25:06 2026
% 0.05/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.05/0.36
% 0.05/0.36 % From the command line: assign(max_seconds, 300).
% 3.47/1.38
% 3.47/1.38 % SZS status Theorem for theBenchmark
% 3.47/1.38
% 3.47/1.38 % Proof 1 at 0.34 (+ 0.11) seconds.
% 3.47/1.38 % Length of proof is 19.
% 3.47/1.38 % Level of proof is 6.
% 3.47/1.38 % Maximum clause weight is 37.000.
% 3.47/1.38 % Given clauses 209.
% 3.47/1.38
% 3.47/1.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------