%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU250+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 : 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 08:45:35 AM UTC 2026
% Result : Theorem 3.47s 0.92s
% Output : CNFRefutation 3.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 25 ( 5 unt; 0 def)
% Number of atoms : 69 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 68 ( 24 ~; 27 |; 11 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 50 ( 2 sgn 23 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t19_wellord1,axiom,
! [A,B,C] :
( relation(C)
=> ( in(A,relation_field(relation_restriction(C,B)))
=> ( in(A,B)
& in(A,relation_field(C)) ) ) ),
file('theBenchmark.p',t19_wellord1) ).
fof(t20_wellord1,conjecture,
! [A,B] :
( relation(B)
=> ( subset(relation_field(relation_restriction(B,A)),A)
& subset(relation_field(relation_restriction(B,A)),relation_field(B)) ) ),
file('theBenchmark.p',t20_wellord1) ).
fof(t20_wellord1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> ( subset(relation_field(relation_restriction(B,A)),A)
& subset(relation_field(relation_restriction(B,A)),relation_field(B)) ) ),
inference(assume_negation,[status(cth)],[t20_wellord1]) ).
fof(nnf_6,plain,
! [A,B] :
( ( ? [C] :
( ~ in(C,B)
& in(C,A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(fof_nnf,[status(thm)],[d3_tarski]) ).
fof(sk_d3_tarski_sk,plain,
! [A,B] :
( ( ( ~ in(sK0(A,B),B)
& in(sK0(A,B),A) )
| subset(A,B) )
& ( ! [X0] :
( in(X0,B)
| ~ in(X0,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(C,sK0(A,B))],[nnf_6]) ).
fof(sk_d3_tarski,plain,
( ! [VAR_0,VAR_1] :
( ~ in(sK0(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1] :
( in(sK0(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) )
& ! [VAR_0,VAR_1,VAR_2] :
( in(VAR_2,VAR_1)
| ~ in(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_tarski_sk]) ).
cnf(c_51,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_52,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_71,plain,
( in(B,relation_field(A))
| ~ in(B,relation_field(relation_restriction(A,C)))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t19_wellord1]) ).
cnf(c_72,plain,
( in(B,C)
| ~ in(B,relation_field(relation_restriction(A,C)))
| ~ relation(A) ),
inference(clausify,[status(thm)],[t19_wellord1]) ).
fof(nnf_41,plain,
? [A,B] :
( ( ~ subset(relation_field(relation_restriction(B,A)),A)
| ~ subset(relation_field(relation_restriction(B,A)),relation_field(B)) )
& relation(B) ),
inference(fof_nnf,[status(thm)],[t20_wellord1_neg]) ).
fof(sk_t20_wellord1_neg,plain,
( ( ~ subset(relation_field(relation_restriction(sK1,sK2)),sK2)
| ~ subset(relation_field(relation_restriction(sK1,sK2)),relation_field(sK1)) )
& relation(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK2),skolemize(B,sK1)],[nnf_41]) ).
cnf(c_84,negated_conjecture,
relation(sK1),
inference(split_conjunct,[status(thm)],[sk_t20_wellord1_neg]) ).
cnf(c_85,negated_conjecture,
( ~ subset(relation_field(relation_restriction(sK1,sK2)),sK2)
| ~ subset(relation_field(relation_restriction(sK1,sK2)),relation_field(sK1)) ),
inference(split_conjunct,[status(thm)],[sk_t20_wellord1_neg]) ).
cnf(c_100,plain,
( subset(relation_field(relation_restriction(A,B)),C)
| in(sK0(relation_field(relation_restriction(A,B)),C),relation_field(A))
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_71,c_51]) ).
cnf(c_101,plain,
( subset(relation_field(relation_restriction(A,B)),C)
| in(sK0(relation_field(relation_restriction(A,B)),C),B)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_72,c_51]) ).
cnf(c_274,plain,
( subset(relation_field(relation_restriction(sK1,A)),B)
| in(sK0(relation_field(relation_restriction(sK1,A)),B),relation_field(sK1)) ),
inference(resolve,[status(thm)],[c_100,c_84]) ).
cnf(c_284,plain,
( subset(relation_field(relation_restriction(sK1,A)),B)
| in(sK0(relation_field(relation_restriction(sK1,A)),B),A) ),
inference(resolve,[status(thm)],[c_101,c_84]) ).
cnf(c_3668,plain,
( subset(relation_field(relation_restriction(sK1,A)),relation_field(sK1))
| subset(relation_field(relation_restriction(sK1,A)),relation_field(sK1)) ),
inference(resolve,[status(thm)],[c_274,c_52]) ).
cnf(c_3272,plain,
subset(relation_field(relation_restriction(sK1,A)),relation_field(sK1)),
inference(copy,[status(thm)],[c_3668]) ).
cnf(c_3277,negated_conjecture,
~ subset(relation_field(relation_restriction(sK1,sK2)),sK2),
inference(resolve,[status(thm)],[c_3272,c_85]) ).
cnf(c_3669,plain,
( subset(relation_field(relation_restriction(sK1,A)),A)
| subset(relation_field(relation_restriction(sK1,A)),A) ),
inference(resolve,[status(thm)],[c_284,c_52]) ).
cnf(c_3666,plain,
subset(relation_field(relation_restriction(sK1,A)),A),
inference(copy,[status(thm)],[c_3669]) ).
cnf(c_3667,plain,
$false,
inference(resolve,[status(thm)],[c_3666,c_3277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU250+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.38 % Computer : n026.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 09:01:40 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 605922 was started by sandbox2 on n026,
% 0.11/0.38 % Sat Sep 26 09:01:40 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.39
% 0.11/0.39 % From the command line: assign(max_seconds, 300).
% 3.47/0.92
% 3.47/0.92 % SZS status Theorem for theBenchmark
% 3.47/0.92
% 3.47/0.92 % Proof 1 at 0.33 (+ 0.17) seconds.
% 3.47/0.92 % Length of proof is 17.
% 3.47/0.92 % Level of proof is 6.
% 3.47/0.92 % Maximum clause weight is 37.000.
% 3.47/0.92 % Given clauses 483.
% 3.47/0.92
% 3.47/0.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------