%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU264+2 : 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 : n013.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 08:45:37 AM UTC 2026
% Result : Theorem 72.78s 11.19s
% Output : CNFRefutation 72.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 19 ( 7 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 32 ( 11 ~; 7 |; 6 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 35 ( 3 sgn 18 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t12_relset_1,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
=> ( subset(relation_rng(C),B)
& subset(relation_dom(C),A) ) ),
file('theBenchmark.p',t12_relset_1) ).
fof(t14_relset_1,axiom,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(relation_rng(D),B)
=> relation_of2_as_subset(D,C,B) ) ),
file('theBenchmark.p',t14_relset_1) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( subset(B,C)
& subset(A,B) )
=> subset(A,C) ),
file('theBenchmark.p',t1_xboole_1) ).
fof(t16_relset_1,conjecture,
! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(A,B)
=> relation_of2_as_subset(D,C,B) ) ),
file('theBenchmark.p',t16_relset_1) ).
fof(t16_relset_1_neg,negated_conjecture,
~ ! [A,B,C,D] :
( relation_of2_as_subset(D,C,A)
=> ( subset(A,B)
=> relation_of2_as_subset(D,C,B) ) ),
inference(assume_negation,[status(cth)],[t16_relset_1]) ).
cnf(c_819,plain,
( subset(relation_rng(A),C)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[t12_relset_1]) ).
cnf(c_833,plain,
( relation_of2_as_subset(A,B,D)
| ~ subset(relation_rng(A),D)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[t14_relset_1]) ).
cnf(c_856,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t1_xboole_1]) ).
fof(nnf_329,plain,
? [A,B,C,D] :
( ~ relation_of2_as_subset(D,C,B)
& subset(A,B)
& relation_of2_as_subset(D,C,A) ),
inference(fof_nnf,[status(thm)],[t16_relset_1_neg]) ).
fof(sk_t16_relset_1_neg,plain,
( ~ relation_of2_as_subset(sK0,sK1,sK3)
& subset(sK2,sK3)
& relation_of2_as_subset(sK0,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(A,sK2),skolemize(B,sK3),skolemize(C,sK1),skolemize(D,sK0)],[nnf_329]) ).
cnf(c_1016,negated_conjecture,
relation_of2_as_subset(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t16_relset_1_neg]) ).
cnf(c_1017,negated_conjecture,
subset(sK2,sK3),
inference(split_conjunct,[status(thm)],[sk_t16_relset_1_neg]) ).
cnf(c_1018,negated_conjecture,
~ relation_of2_as_subset(sK0,sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_t16_relset_1_neg]) ).
cnf(c_1295,plain,
( subset(A,sK3)
| ~ subset(A,sK2) ),
inference(resolve,[status(thm)],[c_856,c_1017]) ).
cnf(c_1597,plain,
subset(relation_rng(sK0),sK2),
inference(resolve,[status(thm)],[c_819,c_1016]) ).
cnf(c_1599,plain,
subset(relation_rng(sK0),sK3),
inference(resolve,[status(thm)],[c_1597,c_1295]) ).
cnf(c_6018,plain,
( relation_of2_as_subset(sK0,A,sK3)
| ~ relation_of2_as_subset(sK0,A,B) ),
inference(resolve,[status(thm)],[c_833,c_1599]) ).
cnf(c_6025,negated_conjecture,
relation_of2_as_subset(sK0,sK1,sK3),
inference(resolve,[status(thm)],[c_6018,c_1016]) ).
cnf(c_6024,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_1018,c_6025]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU264+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.65 % Computer : n013.cluster.edu
% 0.19/0.65 % Model : x86_64 x86_64
% 0.19/0.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.65 % Memory : 8046.5625MB
% 0.19/0.65 % OS : Linux 6.8.0-71-generic
% 0.19/0.65 % CPULimit : 300
% 0.19/0.65 % WCLimit : 300
% 0.19/0.65 % DateTime : Sat Sep 26 09:01:09 UTC 2026
% 0.21/0.65 % CPUTime :
% 0.21/0.65 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.21/0.65 % Process 2397905 was started by sandbox2 on n013,
% 0.21/0.65 % Sat Sep 26 09:01:09 2026
% 0.21/0.65 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.21/0.78
% 0.21/0.78 % From the command line: assign(max_seconds, 300).
% 0.21/0.78
% 0.21/0.78 % SInE: 283 to sos, 47 to usable, of 330 axioms (tolerance 2.00, depth 0 fixpoint).
% 72.78/11.19
% 72.78/11.19 % given #500 (W,wt=15): 2789 -relation(A) | -well_ordering(c12) | -relation_isomorphism(c12,A,c12) | well_ordering(A). [resolve(1197,a,370,a),unit_del(b,372)].
% 72.78/11.19
% 72.78/11.19 % given #1000 (W,wt=20): 3621 in(A,f108(c14)) | -in(f111(A),f43(A,c13)). [resolve(1829,b,1485,b)].
% 72.78/11.19
% 72.78/11.19 % SZS status Theorem for theBenchmark
% 72.78/11.19
% 72.78/11.19 % Proof 1 at 1.61 (+ 0.33) seconds.
% 72.78/11.19 % Length of proof is 15.
% 72.78/11.19 % Level of proof is 5.
% 72.78/11.19 % Maximum clause weight is 22.000.
% 72.78/11.19 % Given clauses 1359.
% 72.78/11.19
% 72.78/11.19 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------