%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU199+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 : n007.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 08:45:23 AM UTC 2026
% Result : Theorem 75.10s 10.19s
% Output : CNFRefutation 75.10s
% 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(d12_relat_1,axiom,
! [A,B] :
( relation(B)
=> ! [C] :
( relation(C)
=> ( C = relation_rng_restriction(A,B)
<=> ! [D,E] :
( in(ordered_pair(D,E),C)
<=> ( in(ordered_pair(D,E),B)
& in(E,A) ) ) ) ) ),
file('theBenchmark.p',d12_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_k8_relat_1,axiom,
! [A,B] :
( relation(B)
=> relation(relation_rng_restriction(A,B)) ),
file('theBenchmark.p',dt_k8_relat_1) ).
fof(t117_relat_1,conjecture,
! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
file('theBenchmark.p',t117_relat_1) ).
fof(t117_relat_1_neg,negated_conjecture,
~ ! [A,B] :
( relation(B)
=> subset(relation_rng_restriction(A,B),B) ),
inference(assume_negation,[status(cth)],[t117_relat_1]) ).
cnf(c_40,plain,
( in(ordered_pair(D,E),A)
| ~ in(ordered_pair(D,E),B)
| relation_rng_restriction(C,A) != B
| ~ relation(B)
| ~ relation(A) ),
inference(clausify,[status(thm)],[d12_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_rng_restriction(B,A))
| ~ relation(A) ),
inference(clausify,[status(thm)],[dt_k8_relat_1]) ).
fof(nnf_35,plain,
? [A,B] :
( ~ subset(relation_rng_restriction(A,B),B)
& relation(B) ),
inference(fof_nnf,[status(thm)],[t117_relat_1_neg]) ).
fof(sk_t117_relat_1_neg,plain,
( ~ subset(relation_rng_restriction(sK3,sK2),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_t117_relat_1_neg]) ).
cnf(c_79,negated_conjecture,
~ subset(relation_rng_restriction(sK3,sK2),sK2),
inference(split_conjunct,[status(thm)],[sk_t117_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_3009,plain,
( in(ordered_pair(D,E),A)
| ~ in(unordered_pair(unordered_pair(D,E),singleton(D)),B)
| relation_rng_restriction(C,A) != 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_rng_restriction(C,A) != B
| ~ relation(B)
| ~ relation(A) ),
inference(paramod,[status(thm)],[c_48,c_3009]) ).
cnf(c_131,plain,
relation(relation_rng_restriction(A,sK2)),
inference(resolve,[status(thm)],[c_78,c_49]) ).
cnf(c_3010,plain,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(B,sK2),A),sK1(relation_rng_restriction(B,sK2),A)),singleton(sK0(relation_rng_restriction(B,sK2),A))),relation_rng_restriction(B,sK2))
| subset(relation_rng_restriction(B,sK2),A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_86,c_131]) ).
cnf(c_259,negated_conjecture,
( in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(A,sK2),sK2),sK1(relation_rng_restriction(A,sK2),sK2)),singleton(sK0(relation_rng_restriction(A,sK2),sK2))),relation_rng_restriction(A,sK2))
| subset(relation_rng_restriction(A,sK2),sK2) ),
inference(resolve,[status(thm)],[c_3010,c_78]) ).
cnf(c_3011,plain,
( ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(B,sK2),A),sK1(relation_rng_restriction(B,sK2),A)),singleton(sK0(relation_rng_restriction(B,sK2),A))),A)
| subset(relation_rng_restriction(B,sK2),A)
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_85,c_131]) ).
cnf(c_3012,negated_conjecture,
( ~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(A,sK2),sK2),sK1(relation_rng_restriction(A,sK2),sK2)),singleton(sK0(relation_rng_restriction(A,sK2),sK2))),sK2)
| subset(relation_rng_restriction(A,sK2),sK2) ),
inference(resolve,[status(thm)],[c_3011,c_78]) ).
cnf(c_264,negated_conjecture,
~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK3,sK2),sK2),sK1(relation_rng_restriction(sK3,sK2),sK2)),singleton(sK0(relation_rng_restriction(sK3,sK2),sK2))),sK2),
inference(resolve,[status(thm)],[c_3012,c_79]) ).
cnf(c_2933,plain,
in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK3,sK2),sK2),sK1(relation_rng_restriction(sK3,sK2),sK2)),singleton(sK0(relation_rng_restriction(sK3,sK2),sK2))),relation_rng_restriction(sK3,sK2)),
inference(resolve,[status(thm)],[c_259,c_79]) ).
cnf(c_3013,negated_conjecture,
( in(unordered_pair(unordered_pair(C,D),singleton(C)),sK2)
| ~ in(unordered_pair(unordered_pair(C,D),singleton(C)),A)
| relation_rng_restriction(B,sK2) != A
| ~ relation(A) ),
inference(resolve,[status(thm)],[c_92,c_78]) ).
cnf(c_3014,negated_conjecture,
( in(unordered_pair(unordered_pair(C,D),singleton(C)),sK2)
| ~ in(unordered_pair(unordered_pair(C,D),singleton(C)),relation_rng_restriction(B,sK2))
| relation_rng_restriction(A,sK2) != relation_rng_restriction(B,sK2) ),
inference(resolve,[status(thm)],[c_3013,c_131]) ).
cnf(c_3015,plain,
( in(unordered_pair(unordered_pair(A,B),singleton(A)),sK2)
| ~ in(unordered_pair(unordered_pair(A,B),singleton(A)),relation_rng_restriction(C,sK2)) ),
inference(xxres,[status(thm)],[c_3014]) ).
cnf(c_3007,plain,
~ in(unordered_pair(unordered_pair(sK0(relation_rng_restriction(sK3,sK2),sK2),sK1(relation_rng_restriction(sK3,sK2),sK2)),singleton(sK0(relation_rng_restriction(sK3,sK2),sK2))),relation_rng_restriction(A,sK2)),
inference(resolve,[status(thm)],[c_3015,c_264]) ).
cnf(c_3008,plain,
$false,
inference(resolve,[status(thm)],[c_3007,c_2933]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU199+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.45 % Computer : n007.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Sat Sep 26 08:46:08 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.46 % Process 3337577 was started by sandbox2 on n007,
% 0.19/0.46 % Sat Sep 26 08:46:08 2026
% 0.19/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.46
% 0.19/0.46 % From the command line: assign(max_seconds, 300).
% 75.10/10.19
% 75.10/10.19 % SZS status Theorem for theBenchmark
% 75.10/10.19
% 75.10/10.19 % Proof 1 at 1.50 (+ 0.19) seconds.
% 75.10/10.19 % Length of proof is 21.
% 75.10/10.19 % Level of proof is 5.
% 75.10/10.19 % Maximum clause weight is 39.000.
% 75.10/10.19 % Given clauses 479.
% 75.10/10.19
% 75.10/10.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------