%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : REL003+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 08:24:43 AM UTC 2026
% Result : Theorem 0.15s 5.40s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 8 unt; 0 def)
% Number of atoms : 54 ( 53 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 44 ( 16 ~; 17 |; 7 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 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 : 12 ( 0 sgn 7 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
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(goals,conjecture,
! [X0,X1] :
( ( join(converse(X0),converse(X1)) = converse(X1)
=> join(X0,X1) = X1 )
& ( join(X0,X1) = X1
=> join(converse(X0),converse(X1)) = converse(X1) ) ),
file('theBenchmark.p',goals) ).
fof(goals_neg,negated_conjecture,
~ ! [X0,X1] :
( ( join(converse(X0),converse(X1)) = converse(X1)
=> join(X0,X1) = X1 )
& ( join(X0,X1) = X1
=> join(converse(X0),converse(X1)) = converse(X1) ) ),
inference(assume_negation,[status(cth)],[goals]) ).
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]) ).
fof(nnf_14,plain,
? [X0,X1] :
( ( join(X0,X1) != X1
& converse(X1) = join(converse(X0),converse(X1)) )
| ( converse(X1) != join(converse(X0),converse(X1))
& join(X0,X1) = X1 ) ),
inference(fof_nnf,[status(thm)],[goals_neg]) ).
fof(sk_goals_neg_sk,plain,
( ( join(sK0,sK1) != sK1
& converse(sK1) = join(converse(sK0),converse(sK1)) )
| ( converse(sK1) != join(converse(sK0),converse(sK1))
& join(sK0,sK1) = sK1 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[nnf_14]) ).
fof(sk_goals_neg,plain,
( ( join(sK0,sK1) != sK1
| converse(sK1) != join(converse(sK0),converse(sK1)) )
& ( converse(sK1) = join(converse(sK0),converse(sK1))
| join(sK0,sK1) = sK1 ) ),
inference(cnf_transformation,[status(thm)],[sk_goals_neg_sk]) ).
cnf(c_31,negated_conjecture,
( converse(sK1) = join(converse(sK0),converse(sK1))
| join(sK0,sK1) = sK1 ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_32,negated_conjecture,
( join(converse(sK0),converse(sK1)) = converse(sK1)
| join(sK0,sK1) = sK1 ),
inference(copy,[status(thm)],[c_31]) ).
cnf(c_33,negated_conjecture,
( join(sK0,sK1) != sK1
| converse(sK1) != join(converse(sK0),converse(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_goals_neg]) ).
cnf(c_34,negated_conjecture,
( join(sK0,sK1) != sK1
| join(converse(sK0),converse(sK1)) != converse(sK1) ),
inference(copy,[status(thm)],[c_33]) ).
cnf(c_65,plain,
( converse(sK1) = join(converse(sK0),converse(sK1))
| join(converse(sK0),converse(sK1)) = converse(sK1) ),
inference(paramod,[status(thm)],[c_32,c_24]) ).
cnf(c_66,plain,
( join(converse(sK0),converse(sK1)) = converse(sK1)
| join(converse(sK0),converse(sK1)) = converse(sK1) ),
inference(copy,[status(thm)],[c_65]) ).
cnf(c_62,plain,
join(converse(sK0),converse(sK1)) = converse(sK1),
inference(copy,[status(thm)],[c_66]) ).
cnf(c_67,plain,
( converse(converse(sK1)) = join(converse(converse(sK0)),converse(converse(sK1)))
| join(sK0,sK1) = sK1 ),
inference(paramod,[status(thm)],[c_32,c_24]) ).
cnf(c_68,plain,
( sK1 = join(converse(converse(sK0)),converse(converse(sK1)))
| join(sK0,sK1) = sK1 ),
inference(paramod,[status(thm)],[c_23,c_67]) ).
cnf(c_69,plain,
( sK1 = join(sK0,converse(converse(sK1)))
| join(sK0,sK1) = sK1 ),
inference(paramod,[status(thm)],[c_23,c_68]) ).
cnf(c_70,plain,
( sK1 = join(sK0,sK1)
| join(sK0,sK1) = sK1 ),
inference(paramod,[status(thm)],[c_23,c_69]) ).
cnf(c_71,plain,
( join(sK0,sK1) = sK1
| join(sK0,sK1) = sK1 ),
inference(copy,[status(thm)],[c_70]) ).
cnf(c_63,plain,
join(sK0,sK1) = sK1,
inference(copy,[status(thm)],[c_71]) ).
cnf(c_72,negated_conjecture,
( join(sK0,sK1) != sK1
| converse(sK1) != converse(sK1) ),
inference(paramod,[status(thm)],[c_62,c_34]) ).
cnf(c_73,negated_conjecture,
( sK1 != sK1
| converse(sK1) != converse(sK1) ),
inference(paramod,[status(thm)],[c_63,c_72]) ).
cnf(c_74,negated_conjecture,
sK1 != sK1,
inference(copy,[status(thm)],[c_73]) ).
cnf(c_64,negated_conjecture,
$false,
inference(copy,[status(thm)],[c_74]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : REL003+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n015.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 05:28:18 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 3222418 was started by sandbox2 on n015,
% 0.11/5.38 % Sat Sep 26 05:28:18 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.15/5.40
% 0.15/5.40 % SZS status Theorem for theBenchmark
% 0.15/5.40
% 0.15/5.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/5.40 % Length of proof is 12.
% 0.15/5.40 % Level of proof is 4.
% 0.15/5.40 % Maximum clause weight is 19.000.
% 0.15/5.40 % Given clauses 14.
% 0.15/5.40
% 0.15/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------