%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU124+2 : 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 : n008.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 36.84s 6.71s
% Output : CNFRefutation 36.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 44 ( 2 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 44 ( 18 ~; 16 |; 6 &)
% ( 3 <=>; 1 =>; 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 : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 39 ( 3 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(t7_xboole_1,conjecture,
! [A,B] : subset(A,set_union2(A,B)),
file('theBenchmark.p',t7_xboole_1) ).
fof(t7_xboole_1_neg,negated_conjecture,
~ ! [A,B] : subset(A,set_union2(A,B)),
inference(assume_negation,[status(cth)],[t7_xboole_1]) ).
cnf(c_40,plain,
( ~ in(D,A)
| in(D,C)
| set_union2(A,B) != C ),
inference(clausify,[status(thm)],[d2_xboole_0]) ).
fof(nnf_7,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_7]) ).
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_46,plain,
( in(sK0(A,B),A)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
cnf(c_47,plain,
( ~ in(sK0(A,B),B)
| subset(A,B) ),
inference(split_conjunct,[status(thm)],[sk_d3_tarski]) ).
fof(nnf_30,plain,
? [A,B] : ~ subset(A,set_union2(A,B)),
inference(fof_nnf,[status(thm)],[t7_xboole_1_neg]) ).
fof(sk_t7_xboole_1_neg,plain,
~ subset(sK1,set_union2(sK1,sK2)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_30]) ).
cnf(c_77,negated_conjecture,
~ subset(sK1,set_union2(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_t7_xboole_1_neg]) ).
cnf(c_100,plain,
( ~ in(A,B)
| in(A,set_union2(B,C)) ),
inference(xxres,[status(thm)],[c_40]) ).
cnf(c_429,plain,
in(sK0(sK1,set_union2(sK1,sK2)),sK1),
inference(resolve,[status(thm)],[c_77,c_46]) ).
cnf(c_431,negated_conjecture,
~ in(sK0(sK1,set_union2(sK1,sK2)),set_union2(sK1,sK2)),
inference(resolve,[status(thm)],[c_47,c_77]) ).
cnf(c_14690,plain,
in(sK0(sK1,set_union2(sK1,sK2)),set_union2(sK1,A)),
inference(resolve,[status(thm)],[c_429,c_100]) ).
cnf(c_14691,plain,
$false,
inference(resolve,[status(thm)],[c_14690,c_431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU124+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n008.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 08:38:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 3231020 was started by sandbox on n008,
% 0.08/0.36 % Sat Sep 26 08:38:24 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.37
% 0.08/0.37 % From the command line: assign(max_seconds, 300).
% 36.84/6.71
% 36.84/6.71 % Assigning unary symbol f1 kb_weight 0 and highest precedence (18).
% 36.84/6.71
% 36.84/6.71 % given #500 (W,wt=20): 1597 -in(f3(c3,empty_set),A) | -disjoint(A,set_union2(c3,B)). [resolve(1240,a,70,b)].
% 36.84/6.71
% 36.84/6.71 % given #1000 (F,wt=23): 1116 -in(c4,set_union2(f1(c4),set_intersection2(c4,A))). [ur(96,b,433,a,c,965,a)].
% 36.84/6.71
% 36.84/6.71 % SZS status Theorem for theBenchmark
% 36.84/6.71
% 36.84/6.71 % Proof 1 at 4.12 (+ 1.81) seconds.
% 36.84/6.71 % Length of proof is 12.
% 36.84/6.71 % Level of proof is 4.
% 36.84/6.71 % Maximum clause weight is 24.000.
% 36.84/6.71 % Given clauses 1093.
% 36.84/6.71
% 36.84/6.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------