%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU125+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 08:45:05 AM UTC 2026
% Result : Theorem 2.75s 0.82s
% Output : CNFRefutation 2.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 11 unt; 0 def)
% Number of atoms : 69 ( 4 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 67 ( 26 ~; 23 |; 12 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 51 ( 0 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(commutativity_k2_xboole_0,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('theBenchmark.p',commutativity_k2_xboole_0) ).
fof(d2_xboole_0,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,B)
| in(D,A) ) ) ),
file('theBenchmark.p',d2_xboole_0) ).
fof(d3_tarski,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('theBenchmark.p',d3_tarski) ).
fof(t8_xboole_1,conjecture,
! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
file('theBenchmark.p',t8_xboole_1) ).
fof(t8_xboole_1_neg,negated_conjecture,
~ ! [A,B,C] :
( ( subset(C,B)
& subset(A,B) )
=> subset(set_union2(A,C),B) ),
inference(assume_negation,[status(cth)],[t8_xboole_1]) ).
cnf(c_19,plain,
set_union2(A,B) = set_union2(B,A),
inference(clausify,[status(thm)],[commutativity_k2_xboole_0]) ).
cnf(c_20,plain,
( in(D,B)
| in(D,A)
| ~ in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
fof(nnf_4,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_4]) ).
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_26,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_27,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_28,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
fof(nnf_17,plain,
? [A,B,C] :
( ~ subset(set_union2(A,C),B)
& subset(C,B)
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t8_xboole_1_neg]) ).
fof(sk_t8_xboole_1_neg,plain,
( ~ subset(set_union2(sK1,sK3),sK2)
& subset(sK3,sK2)
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(A,sK1),skolemize(B,sK2),skolemize(C,sK3)],[nnf_17]) ).
cnf(c_40,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t8_xboole_1_neg]) ).
cnf(c_41,negated_conjecture,
subset(sK3,sK2),
inference(split_conjunct,[status(thm)],[sk_t8_xboole_1_neg]) ).
cnf(c_42,negated_conjecture,
~ subset(set_union2(sK1,sK3),sK2),
inference(split_conjunct,[status(thm)],[sk_t8_xboole_1_neg]) ).
cnf(c_50,plain,
( in(A,B)
| in(A,C)
| ~ in(A,set_union2(B,C)) ),
inference(resolve,[status(thm)],[c_20,c_19]) ).
cnf(c_164,plain,
( in(A,sK2)
| ~ in(A,sK1) ),
inference(resolve,[status(thm)],[c_40,c_26]) ).
cnf(c_165,plain,
( in(A,sK2)
| ~ in(A,sK3) ),
inference(resolve,[status(thm)],[c_41,c_26]) ).
cnf(c_166,plain,
in(sK0(set_union2(sK1,sK3),sK2),set_union2(sK1,sK3)),
inference(resolve,[status(thm)],[c_42,c_27]) ).
cnf(c_167,negated_conjecture,
~ in(sK0(set_union2(sK1,sK3),sK2),sK2),
inference(resolve,[status(thm)],[c_28,c_42]) ).
cnf(c_663,plain,
~ in(sK0(set_union2(sK1,sK3),sK2),sK3),
inference(resolve,[status(thm)],[c_165,c_167]) ).
cnf(c_664,plain,
~ in(sK0(set_union2(sK1,sK3),sK2),sK1),
inference(resolve,[status(thm)],[c_164,c_167]) ).
cnf(c_669,plain,
( in(sK0(set_union2(sK1,sK3),sK2),A)
| ~ in(sK0(set_union2(sK1,sK3),sK2),set_union2(A,sK3)) ),
inference(resolve,[status(thm)],[c_50,c_663]) ).
cnf(c_670,plain,
~ in(sK0(set_union2(sK1,sK3),sK2),set_union2(sK1,sK3)),
inference(resolve,[status(thm)],[c_669,c_664]) ).
cnf(c_668,plain,
$false,
inference(resolve,[status(thm)],[c_166,c_670]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU125+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 08:40:40 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 576864 was started by sandbox2 on n026,
% 0.08/0.36 % Sat Sep 26 08:40:40 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 2.75/0.82
% 2.75/0.82 % SZS status Theorem for theBenchmark
% 2.75/0.82
% 2.75/0.82 % Proof 1 at 0.26 (+ 0.16) seconds.
% 2.75/0.82 % Length of proof is 20.
% 2.75/0.82 % Level of proof is 4.
% 2.75/0.82 % Maximum clause weight is 24.000.
% 2.75/0.82 % Given clauses 103.
% 2.75/0.82
% 2.75/0.82 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------