%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU255+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 08:45:36 AM UTC 2026
% Result : Theorem 0.77s 0.54s
% Output : CNFRefutation 0.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 11 unt; 0 def)
% Number of atoms : 156 ( 26 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 175 ( 68 ~; 82 |; 15 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 82 ( 3 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_tarski,axiom,
! [A,B] : unordered_pair(A,B) = unordered_pair(B,A),
file('theBenchmark.p',commutativity_k2_tarski) ).
fof(d5_tarski,axiom,
! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
file('theBenchmark.p',d5_tarski) ).
fof(dt_k2_wellord1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_restriction(A,B)) ),
file('theBenchmark.p',dt_k2_wellord1) ).
fof(l3_wellord1,axiom,
! [A] :
( relation(A)
=> ( antisymmetric(A)
<=> ! [B,C] :
( ( in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
=> B = C ) ) ),
file('theBenchmark.p',l3_wellord1) ).
fof(t16_wellord1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_restriction(C,B))
<=> ( in(A,cartesian_product2(B,B))
& in(A,C) ) ) ),
file('theBenchmark.p',t16_wellord1) ).
fof(t25_wellord1,conjecture,
! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
file('theBenchmark.p',t25_wellord1) ).
fof(t25_wellord1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( antisymmetric(B)
=> antisymmetric(relation_restriction(B,A)) ) ),
inference(assume_negation,[status(cth)],[t25_wellord1]) ).
fof(nnf_32,plain,
? [A,B] :
( ~ antisymmetric(relation_restriction(B,A))
& antisymmetric(B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t25_wellord1_neg]) ).
fof(sk_t25_wellord1_neg,plain,
( ~ antisymmetric(relation_restriction(sK0,sK1))
& antisymmetric(sK0)
& relation(sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(B,sK0)],[nnf_32]) ).
cnf(c_42,negated_conjecture,
~ antisymmetric(relation_restriction(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_t25_wellord1_neg]) ).
cnf(c_43,negated_conjecture,
antisymmetric(sK0),
inference(split_conjunct,[status(thm)],[sk_t25_wellord1_neg]) ).
cnf(c_44,negated_conjecture,
relation(sK0),
inference(split_conjunct,[status(thm)],[sk_t25_wellord1_neg]) ).
cnf(c_51,plain,
( in(B,A)
| ~ in(B,relation_restriction(A,C))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t16_wellord1]) ).
fof(nnf_19,plain,
! [A] :
( ( ( ? [B,C] :
( C != B
& in(ordered_pair(C,B),A)
& in(ordered_pair(B,C),A) )
| antisymmetric(A) )
& ( ! [X0,X1] :
( X1 = X0
| ~ in(ordered_pair(X1,X0),A)
| ~ in(ordered_pair(X0,X1),A) )
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[l3_wellord1]) ).
fof(sk_l3_wellord1_sk,plain,
! [A] :
( ( ( ( sK2(A) != sK3(A)
& in(ordered_pair(sK2(A),sK3(A)),A)
& in(ordered_pair(sK3(A),sK2(A)),A) )
| antisymmetric(A) )
& ( ! [X0,X1] :
( X1 = X0
| ~ in(ordered_pair(X1,X0),A)
| ~ in(ordered_pair(X0,X1),A) )
| ~ antisymmetric(A) ) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK2]),skolemize(B,sK3(A)),skolemize(C,sK2(A))],[nnf_19]) ).
fof(sk_l3_wellord1,plain,
( ! [VAR_0] :
( sK2(VAR_0) != sK3(VAR_0)
| antisymmetric(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(ordered_pair(sK2(VAR_0),sK3(VAR_0)),VAR_0)
| antisymmetric(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0] :
( in(ordered_pair(sK3(VAR_0),sK2(VAR_0)),VAR_0)
| antisymmetric(VAR_0)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2] :
( VAR_2 = VAR_1
| ~ in(ordered_pair(VAR_2,VAR_1),VAR_0)
| ~ in(ordered_pair(VAR_1,VAR_2),VAR_0)
| ~ antisymmetric(VAR_0)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_l3_wellord1_sk]) ).
cnf(c_58,plain,
( sK2(A) != sK3(A)
| antisymmetric(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_l3_wellord1]) ).
cnf(c_59,plain,
( in(ordered_pair(sK2(A),sK3(A)),A)
| antisymmetric(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_l3_wellord1]) ).
cnf(c_60,plain,
( in(ordered_pair(sK3(A),sK2(A)),A)
| antisymmetric(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_l3_wellord1]) ).
cnf(c_61,plain,
( C = B
| ~ in(ordered_pair(C,B),A)
| ~ in(ordered_pair(B,C),A)
| ~ antisymmetric(A)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_l3_wellord1]) ).
cnf(c_65,plain,
( relation(relation_restriction(A,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k2_wellord1]) ).
cnf(c_68,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_70,plain,
unordered_pair(A,B) = unordered_pair(B,A),
inference(clausify,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_516,plain,
( C = B
| ~ in(ordered_pair(C,B),A)
| ~ in(unordered_pair(unordered_pair(B,C),singleton(B)),A)
| ~ antisymmetric(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_68,c_61]) ).
cnf(c_517,plain,
( C = B
| ~ in(ordered_pair(C,B),A)
| ~ in(unordered_pair(singleton(B),unordered_pair(B,C)),A)
| ~ antisymmetric(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_70,c_516]) ).
cnf(c_518,plain,
( C = B
| ~ in(unordered_pair(unordered_pair(C,B),singleton(C)),A)
| ~ in(unordered_pair(singleton(B),unordered_pair(B,C)),A)
| ~ antisymmetric(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_68,c_517]) ).
cnf(c_74,plain,
( C = B
| ~ in(unordered_pair(singleton(C),unordered_pair(C,B)),A)
| ~ in(unordered_pair(singleton(B),unordered_pair(B,C)),A)
| ~ antisymmetric(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_70,c_518]) ).
cnf(c_519,plain,
( in(unordered_pair(unordered_pair(sK3(A),sK2(A)),singleton(sK3(A))),A)
| antisymmetric(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_68,c_60]) ).
cnf(c_75,plain,
( in(unordered_pair(singleton(sK3(A)),unordered_pair(sK3(A),sK2(A))),A)
| antisymmetric(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_70,c_519]) ).
cnf(c_520,plain,
( in(unordered_pair(unordered_pair(sK2(A),sK3(A)),singleton(sK2(A))),A)
| antisymmetric(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_68,c_59]) ).
cnf(c_521,plain,
( in(unordered_pair(unordered_pair(sK3(A),sK2(A)),singleton(sK2(A))),A)
| antisymmetric(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_70,c_520]) ).
cnf(c_76,plain,
( in(unordered_pair(singleton(sK2(A)),unordered_pair(sK3(A),sK2(A))),A)
| antisymmetric(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_70,c_521]) ).
cnf(c_97,plain,
relation(relation_restriction(sK0,A)),
inference(resolve,[status(thm)],[c_65,c_44]) ).
cnf(c_106,plain,
( C = B
| ~ in(unordered_pair(singleton(C),unordered_pair(B,C)),A)
| ~ in(unordered_pair(singleton(B),unordered_pair(B,C)),A)
| ~ antisymmetric(A)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_70,c_74]) ).
cnf(c_141,plain,
( in(unordered_pair(singleton(sK2(relation_restriction(sK0,A))),unordered_pair(sK3(relation_restriction(sK0,A)),sK2(relation_restriction(sK0,A)))),relation_restriction(sK0,A))
| antisymmetric(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_97,c_76]) ).
cnf(c_142,plain,
( in(unordered_pair(singleton(sK3(relation_restriction(sK0,A))),unordered_pair(sK3(relation_restriction(sK0,A)),sK2(relation_restriction(sK0,A)))),relation_restriction(sK0,A))
| antisymmetric(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_97,c_75]) ).
cnf(c_522,plain,
( sK2(relation_restriction(sK0,A)) != sK3(relation_restriction(sK0,A))
| antisymmetric(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_58,c_97]) ).
cnf(c_148,negated_conjecture,
sK2(relation_restriction(sK0,sK1)) != sK3(relation_restriction(sK0,sK1)),
inference(resolve,[status(thm)],[c_522,c_42]) ).
cnf(c_523,plain,
( in(unordered_pair(singleton(sK2(relation_restriction(sK0,A))),unordered_pair(sK3(relation_restriction(sK0,A)),sK2(relation_restriction(sK0,A)))),sK0)
| ~ relation(sK0)
| antisymmetric(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_141,c_51]) ).
cnf(c_346,negated_conjecture,
( in(unordered_pair(singleton(sK2(relation_restriction(sK0,A))),unordered_pair(sK3(relation_restriction(sK0,A)),sK2(relation_restriction(sK0,A)))),sK0)
| antisymmetric(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_44,c_523]) ).
cnf(c_524,plain,
( in(unordered_pair(singleton(sK3(relation_restriction(sK0,A))),unordered_pair(sK3(relation_restriction(sK0,A)),sK2(relation_restriction(sK0,A)))),sK0)
| ~ relation(sK0)
| antisymmetric(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_142,c_51]) ).
cnf(c_371,negated_conjecture,
( in(unordered_pair(singleton(sK3(relation_restriction(sK0,A))),unordered_pair(sK3(relation_restriction(sK0,A)),sK2(relation_restriction(sK0,A)))),sK0)
| antisymmetric(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_44,c_524]) ).
cnf(c_525,negated_conjecture,
( B = A
| ~ in(unordered_pair(singleton(B),unordered_pair(A,B)),sK0)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),sK0)
| ~ antisymmetric(sK0) ),
inference(resolve,[status(thm)],[c_106,c_44]) ).
cnf(c_526,negated_conjecture,
( B = A
| ~ in(unordered_pair(singleton(B),unordered_pair(A,B)),sK0)
| ~ in(unordered_pair(singleton(A),unordered_pair(A,B)),sK0) ),
inference(resolve,[status(thm)],[c_525,c_43]) ).
cnf(c_527,negated_conjecture,
( antisymmetric(relation_restriction(sK0,A))
| sK2(relation_restriction(sK0,A)) = sK3(relation_restriction(sK0,A))
| ~ in(unordered_pair(singleton(sK2(relation_restriction(sK0,A))),unordered_pair(sK3(relation_restriction(sK0,A)),sK2(relation_restriction(sK0,A)))),sK0) ),
inference(resolve,[status(thm)],[c_526,c_371]) ).
cnf(c_528,negated_conjecture,
( antisymmetric(relation_restriction(sK0,A))
| antisymmetric(relation_restriction(sK0,A))
| sK2(relation_restriction(sK0,A)) = sK3(relation_restriction(sK0,A)) ),
inference(resolve,[status(thm)],[c_527,c_346]) ).
cnf(c_514,negated_conjecture,
( antisymmetric(relation_restriction(sK0,A))
| sK2(relation_restriction(sK0,A)) = sK3(relation_restriction(sK0,A)) ),
inference(copy,[status(thm)],[c_528]) ).
cnf(c_529,negated_conjecture,
sK2(relation_restriction(sK0,sK1)) = sK3(relation_restriction(sK0,sK1)),
inference(resolve,[status(thm)],[c_514,c_42]) ).
cnf(c_515,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_148,c_529]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU255+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 09:00:18 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 1154641 was started by sandbox2 on n020,
% 0.11/0.37 % Sat Sep 26 09:00:18 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 0.77/0.54
% 0.77/0.54 % SZS status Theorem for theBenchmark
% 0.77/0.54
% 0.77/0.54 % Proof 1 at 0.11 (+ 0.03) seconds.
% 0.77/0.54 % Length of proof is 29.
% 0.77/0.54 % Level of proof is 6.
% 0.77/0.54 % Maximum clause weight is 53.000.
% 0.77/0.54 % Given clauses 301.
% 0.77/0.54
% 0.77/0.54 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------