%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU264+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:45:37 AM UTC 2026
% Result : Theorem 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% 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 : 34 ( 13 ~; 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 : 34 ( 2 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]) ).
fof(nnf_18,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,sK2)
& subset(sK3,sK2)
& relation_of2_as_subset(sK0,sK1,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK3,sK2]),skolemize(A,sK3),skolemize(B,sK2),skolemize(C,sK1),skolemize(D,sK0)],[nnf_18]) ).
cnf(c_30,negated_conjecture,
~ relation_of2_as_subset(sK0,sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t16_relset_1_neg]) ).
cnf(c_31,negated_conjecture,
subset(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_t16_relset_1_neg]) ).
cnf(c_32,negated_conjecture,
relation_of2_as_subset(sK0,sK1,sK3),
inference(split_conjunct,[status(thm)],[sk_t16_relset_1_neg]) ).
cnf(c_33,plain,
( subset(A,C)
| ~ subset(B,C)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[t1_xboole_1]) ).
cnf(c_34,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_35,plain,
( subset(relation_rng(A),C)
| ~ relation_of2_as_subset(A,B,C) ),
inference(clausify,[status(thm)],[t12_relset_1]) ).
cnf(c_60,negated_conjecture,
( relation_of2_as_subset(sK0,sK1,A)
| ~ subset(relation_rng(sK0),A) ),
inference(resolve,[status(thm)],[c_34,c_32]) ).
cnf(c_44,negated_conjecture,
~ subset(relation_rng(sK0),sK2),
inference(resolve,[status(thm)],[c_60,c_30]) ).
cnf(c_45,negated_conjecture,
subset(relation_rng(sK0),sK3),
inference(resolve,[status(thm)],[c_35,c_32]) ).
cnf(c_61,negated_conjecture,
( subset(A,sK2)
| ~ subset(A,sK3) ),
inference(resolve,[status(thm)],[c_33,c_31]) ).
cnf(c_58,negated_conjecture,
~ subset(relation_rng(sK0),sK3),
inference(resolve,[status(thm)],[c_61,c_44]) ).
cnf(c_59,plain,
$false,
inference(resolve,[status(thm)],[c_58,c_45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU264+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n020.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 09:02:20 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 1160358 was started by sandbox on n020,
% 0.09/0.37 % Sat Sep 26 09:02:20 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/0.37
% 0.15/0.37 % From the command line: assign(max_seconds, 300).
% 0.15/0.39
% 0.15/0.39 % SZS status Theorem for theBenchmark
% 0.15/0.39
% 0.15/0.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.15/0.39 % Length of proof is 14.
% 0.15/0.39 % Level of proof is 4.
% 0.15/0.39 % Maximum clause weight is 12.000.
% 0.15/0.39 % Given clauses 14.
% 0.15/0.39
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------