%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU193+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 : n005.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 08:45:22 AM UTC 2026
% Result : Theorem 74.00s 10.10s
% Output : CNFRefutation 74.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 9 unt; 0 def)
% Number of atoms : 111 ( 8 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 135 ( 58 ~; 57 |; 9 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 83 ( 9 sgn 33 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(d11_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B,C] :
( relation(C)
=> ( C = relation_dom_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),A)
& in(D,B) ) ) ) ) ),
file('theBenchmark.p',d11_relat_1) ).
fof(d3_relat_1,axiom,
! [A] :
( relation(A)
=> ! [B] :
( relation(B)
=> ( subset(A,B)
<=> ! [C,D] :
( in(ordered_pair(C,D),A)
=> in(ordered_pair(C,D),B) ) ) ) ),
file('theBenchmark.p',d3_relat_1) ).
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_k7_relat_1,axiom,
! [A,B] :
( relation(A)
=> relation(relation_dom_restriction(A,B)) ),
file('theBenchmark.p',dt_k7_relat_1) ).
fof(t88_relat_1,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
file('theBenchmark.p',t88_relat_1) ).
fof(t88_relat_1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_dom_restriction(B,A),B) ),
inference(assume_negation,[status(cth)],[t88_relat_1]) ).
cnf(c_40,plain,
( in(ordered_pair(D,E),A)
| ~ in(ordered_pair(D,E),B)
| relation_dom_restriction(A,C) != B
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d11_relat_1]) ).
fof(nnf_5,plain,
! [A] :
( ! [B] :
( ( ( ? [C,D] :
( ~ in(ordered_pair(C,D),B)
& in(ordered_pair(C,D),A) )
| subset(A,B) )
& ( ! [X0,X1] :
( in(ordered_pair(X0,X1),B)
| ~ in(ordered_pair(X0,X1),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(fof_nnf,[status(thm)],[d3_relat_1]) ).
fof(sk_d3_relat_1_sk,plain,
! [A] :
( ! [B] :
( ( ( ( ~ in(ordered_pair(sK0(A,B),sK1(A,B)),B)
& in(ordered_pair(sK0(A,B),sK1(A,B)),A) )
| subset(A,B) )
& ( ! [X0,X1] :
( in(ordered_pair(X0,X1),B)
| ~ in(ordered_pair(X0,X1),A) )
| ~ subset(A,B) ) )
| ~ relation(B) )
| ~ relation(A) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(C,sK0(A,B)),skolemize(D,sK1(A,B))],[nnf_5]) ).
fof(sk_d3_relat_1,plain,
( ! [VAR_0,VAR_1] :
( ~ in(ordered_pair(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1)),VAR_1)
| subset(VAR_0,VAR_1)
| ~ relation(VAR_1)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1] :
( in(ordered_pair(sK0(VAR_0,VAR_1),sK1(VAR_0,VAR_1)),VAR_0)
| subset(VAR_0,VAR_1)
| ~ relation(VAR_1)
| ~ relation(VAR_0) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(ordered_pair(VAR_2,VAR_3),VAR_1)
| ~ in(ordered_pair(VAR_2,VAR_3),VAR_0)
| ~ subset(VAR_0,VAR_1)
| ~ relation(VAR_1)
| ~ relation(VAR_0) ) ),
inference(cnf_transformation,[status(thm)],[sk_d3_relat_1_sk]) ).
cnf(c_46,plain,
( in(ordered_pair(sK0(A,B),sK1(A,B)),A)
| subset(A,B)
| ~ relation(B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d3_relat_1]) ).
cnf(c_47,plain,
( ~ in(ordered_pair(sK0(A,B),sK1(A,B)),B)
| subset(A,B)
| ~ relation(B)
| ~ relation(A) ),
inference(split_conjunct,[status(thm)],[sk_d3_relat_1]) ).
cnf(c_48,plain,
ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)),
inference(clausify,[status(thm)],[d5_tarski]) ).
cnf(c_49,plain,
( relation(relation_dom_restriction(A,B))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k7_relat_1]) ).
fof(nnf_35,plain,
? [A,B] :
( ~ subset(relation_dom_restriction(B,A),B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t88_relat_1_neg]) ).
fof(sk_t88_relat_1_neg,plain,
( ~ subset(relation_dom_restriction(sK2,sK3),sK2)
& relation(sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(A,sK3),skolemize(B,sK2)],[nnf_35]) ).
cnf(c_78,negated_conjecture,
relation(sK2),
inference(split_conjunct,[status(thm)],[sk_t88_relat_1_neg]) ).
cnf(c_79,negated_conjecture,
~ subset(relation_dom_restriction(sK2,sK3),sK2),
inference(split_conjunct,[status(thm)],[sk_t88_relat_1_neg]) ).
cnf(c_85,plain,
( ~ in(unordered_pair(unordered_pair(sK0(A,B),sK1(A,B)),singleton(sK0(A,B))),B)
| subset(A,B)
| ~ relation(B)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_48,c_47]) ).
cnf(c_86,plain,
( in(unordered_pair(unordered_pair(sK0(A,B),sK1(A,B)),singleton(sK0(A,B))),A)
| subset(A,B)
| ~ relation(B)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_48,c_46]) ).
cnf(c_2999,plain,
( in(ordered_pair(D,E),A)
| ~ in(unordered_pair(unordered_pair(D,E),singleton(D)),B)
| relation_dom_restriction(A,C) != B
| ~ relation(B)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_48,c_40]) ).
cnf(c_92,plain,
( in(unordered_pair(unordered_pair(D,E),singleton(D)),A)
| ~ in(unordered_pair(unordered_pair(D,E),singleton(D)),B)
| relation_dom_restriction(A,C) != B
| ~ relation(B)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_48,c_2999]) ).
cnf(c_131,plain,
relation(relation_dom_restriction(sK2,A)),
inference(resolve,[status(thm)],[c_78,c_49]) ).
cnf(c_3000,plain,
( in(unordered_pair(unordered_pair(sK0(relation_dom_restriction(sK2,B),A),sK1(relation_dom_restriction(sK2,B),A)),singleton(sK0(relation_dom_restriction(sK2,B),A))),relation_dom_restriction(sK2,B))
| subset(relation_dom_restriction(sK2,B),A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_86,c_131]) ).
cnf(c_259,negated_conjecture,
( in(unordered_pair(unordered_pair(sK0(relation_dom_restriction(sK2,A),sK2),sK1(relation_dom_restriction(sK2,A),sK2)),singleton(sK0(relation_dom_restriction(sK2,A),sK2))),relation_dom_restriction(sK2,A))
| subset(relation_dom_restriction(sK2,A),sK2) ),
inference(resolve,[status(thm)],[c_3000,c_78]) ).
cnf(c_3001,plain,
( ~ in(unordered_pair(unordered_pair(sK0(relation_dom_restriction(sK2,B),A),sK1(relation_dom_restriction(sK2,B),A)),singleton(sK0(relation_dom_restriction(sK2,B),A))),A)
| subset(relation_dom_restriction(sK2,B),A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_85,c_131]) ).
cnf(c_3002,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(sK0(relation_dom_restriction(sK2,A),sK2),sK1(relation_dom_restriction(sK2,A),sK2)),singleton(sK0(relation_dom_restriction(sK2,A),sK2))),sK2)
| subset(relation_dom_restriction(sK2,A),sK2) ),
inference(resolve,[status(thm)],[c_3001,c_78]) ).
cnf(c_264,negated_conjecture,
~ in(unordered_pair(unordered_pair(sK0(relation_dom_restriction(sK2,sK3),sK2),sK1(relation_dom_restriction(sK2,sK3),sK2)),singleton(sK0(relation_dom_restriction(sK2,sK3),sK2))),sK2),
inference(resolve,[status(thm)],[c_3002,c_79]) ).
cnf(c_2923,plain,
in(unordered_pair(unordered_pair(sK0(relation_dom_restriction(sK2,sK3),sK2),sK1(relation_dom_restriction(sK2,sK3),sK2)),singleton(sK0(relation_dom_restriction(sK2,sK3),sK2))),relation_dom_restriction(sK2,sK3)),
inference(resolve,[status(thm)],[c_259,c_79]) ).
cnf(c_3003,negated_conjecture,
( in(unordered_pair(unordered_pair(C,D),singleton(C)),sK2)
| ~ in(unordered_pair(unordered_pair(C,D),singleton(C)),A)
| relation_dom_restriction(sK2,B) != A
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_92,c_78]) ).
cnf(c_3004,negated_conjecture,
( in(unordered_pair(unordered_pair(C,D),singleton(C)),sK2)
| ~ in(unordered_pair(unordered_pair(C,D),singleton(C)),relation_dom_restriction(sK2,B))
| relation_dom_restriction(sK2,A) != relation_dom_restriction(sK2,B) ),
inference(resolve,[status(thm)],[c_3003,c_131]) ).
cnf(c_3005,plain,
( in(unordered_pair(unordered_pair(A,B),singleton(A)),sK2)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),relation_dom_restriction(sK2,C)) ),
inference(xxres,[status(thm)],[c_3004]) ).
cnf(c_2997,plain,
~ in(unordered_pair(unordered_pair(sK0(relation_dom_restriction(sK2,sK3),sK2),sK1(relation_dom_restriction(sK2,sK3),sK2)),singleton(sK0(relation_dom_restriction(sK2,sK3),sK2))),relation_dom_restriction(sK2,A)),
inference(resolve,[status(thm)],[c_3005,c_264]) ).
cnf(c_2998,plain,
$false,
inference(resolve,[status(thm)],[c_2997,c_2923]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEU193+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.62 % Computer : n005.cluster.edu
% 0.15/0.62 % Model : x86_64 x86_64
% 0.15/0.62 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.62 % Memory : 8046.5625MB
% 0.15/0.62 % OS : Linux 6.8.0-71-generic
% 0.15/0.62 % CPULimit : 300
% 0.15/0.62 % WCLimit : 300
% 0.15/0.62 % DateTime : Sat Sep 26 08:47:32 UTC 2026
% 0.15/0.62 % CPUTime :
% 0.15/0.62 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.62 % Process 1740862 was started by sandbox2 on n005,
% 0.15/0.62 % Sat Sep 26 08:47:32 2026
% 0.15/0.62 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.64
% 0.15/0.64 % From the command line: assign(max_seconds, 300).
% 74.00/10.10
% 74.00/10.10 % SZS status Theorem for theBenchmark
% 74.00/10.10
% 74.00/10.10 % Proof 1 at 1.27 (+ 0.13) seconds.
% 74.00/10.10 % Length of proof is 21.
% 74.00/10.10 % Level of proof is 5.
% 74.00/10.10 % Maximum clause weight is 39.000.
% 74.00/10.10 % Given clauses 479.
% 74.00/10.10
% 74.00/10.10 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------