%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SEU126+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 : n018.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 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 5 unt; 0 def)
% Number of atoms : 91 ( 23 equ)
% Maximal formula atoms : 20 ( 4 avg)
% Number of connectives : 104 ( 35 ~; 46 |; 17 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-3 aty)
% Number of variables : 58 ( 0 sgn 40 !; 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(t12_xboole_1,conjecture,
! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
file('theBenchmark.p',t12_xboole_1) ).
fof(t12_xboole_1_neg,negated_conjecture,
~ ! [A,B] :
( subset(A,B)
=> set_union2(A,B) = B ),
inference(assume_negation,[status(cth)],[t12_xboole_1]) ).
fof(nnf_4,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ in(D,B)
& ~ in(D,A) )
| ~ in(D,C) )
& ( in(D,B)
| in(D,A)
| in(D,C) ) )
| set_union2(A,B) = C )
& ( ! [X0] :
( ( ( ~ in(X0,B)
& ~ in(X0,A) )
| in(X0,C) )
& ( in(X0,B)
| in(X0,A)
| ~ in(X0,C) ) )
| set_union2(A,B) != C ) ),
inference(fof_nnf,[status(thm)],[d2_xboole_0]) ).
fof(sk_d2_xboole_0_sk,plain,
! [A,B,C] :
( ( ( ( ( ~ in(sK0(A,B,C),B)
& ~ in(sK0(A,B,C),A) )
| ~ in(sK0(A,B,C),C) )
& ( in(sK0(A,B,C),B)
| in(sK0(A,B,C),A)
| in(sK0(A,B,C),C) ) )
| set_union2(A,B) = C )
& ( ! [X0] :
( ( ( ~ in(X0,B)
& ~ in(X0,A) )
| in(X0,C) )
& ( in(X0,B)
| in(X0,A)
| ~ in(X0,C) ) )
| set_union2(A,B) != C ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(D,sK0(A,B,C))],[nnf_4]) ).
fof(sk_d2_xboole_0,plain,
( ! [VAR_0,VAR_1,VAR_2] :
( ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_1)
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| set_union2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_0)
| ~ in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| set_union2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2] :
( in(sK0(VAR_0,VAR_1,VAR_2),VAR_1)
| in(sK0(VAR_0,VAR_1,VAR_2),VAR_0)
| in(sK0(VAR_0,VAR_1,VAR_2),VAR_2)
| set_union2(VAR_0,VAR_1) = VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_1)
| in(VAR_3,VAR_2)
| set_union2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ in(VAR_3,VAR_0)
| in(VAR_3,VAR_2)
| set_union2(VAR_0,VAR_1) != VAR_2 )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( in(VAR_3,VAR_1)
| in(VAR_3,VAR_0)
| ~ in(VAR_3,VAR_2)
| set_union2(VAR_0,VAR_1) != VAR_2 ) ),
inference(cnf_transformation,[status(thm)],[sk_d2_xboole_0_sk]) ).
cnf(c_27,plain,
( in(sK0(A,B,C),B)
| in(sK0(A,B,C),A)
| in(sK0(A,B,C),C)
| set_union2(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d2_xboole_0]) ).
cnf(c_29,plain,
( ~ in(sK0(A,B,C),B)
| ~ in(sK0(A,B,C),C)
| set_union2(A,B) = C ),
inference(split_conjunct,[status(thm)],[sk_d2_xboole_0]) ).
cnf(c_30,plain,
( in(C,B)
| ~ in(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[d3_tarski]) ).
fof(nnf_18,plain,
? [A,B] :
( set_union2(A,B) != B
& subset(A,B) ),
inference(fof_nnf,[status(thm)],[t12_xboole_1_neg]) ).
fof(sk_t12_xboole_1_neg,plain,
( set_union2(sK1,sK2) != sK2
& subset(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(A,sK1),skolemize(B,sK2)],[nnf_18]) ).
cnf(c_44,negated_conjecture,
subset(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_t12_xboole_1_neg]) ).
cnf(c_45,negated_conjecture,
set_union2(sK1,sK2) != sK2,
inference(split_conjunct,[status(thm)],[sk_t12_xboole_1_neg]) ).
cnf(c_52,plain,
( ~ in(sK0(A,B,B),B)
| set_union2(A,B) = B ),
inference(factor,[status(thm)],[c_29]) ).
cnf(c_169,plain,
( in(A,sK2)
| ~ in(A,sK1) ),
inference(resolve,[status(thm)],[c_44,c_30]) ).
cnf(c_218,negated_conjecture,
~ in(sK0(sK1,sK2,sK2),sK2),
inference(resolve,[status(thm)],[c_52,c_45]) ).
cnf(c_404,plain,
( in(sK0(sK1,A,B),A)
| in(sK0(sK1,A,B),B)
| set_union2(sK1,A) = B
| in(sK0(sK1,A,B),sK2) ),
inference(resolve,[status(thm)],[c_169,c_27]) ).
cnf(c_420,plain,
( in(sK0(sK1,A,sK2),A)
| set_union2(sK1,A) = sK2
| in(sK0(sK1,A,sK2),sK2) ),
inference(factor,[status(thm)],[c_404]) ).
cnf(c_430,plain,
( set_union2(sK1,sK2) = sK2
| in(sK0(sK1,sK2,sK2),sK2) ),
inference(factor,[status(thm)],[c_420]) ).
cnf(c_431,plain,
set_union2(sK1,sK2) = sK2,
inference(resolve,[status(thm)],[c_218,c_430]) ).
cnf(c_429,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_45,c_431]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU126+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n018.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Sat Sep 26 08:40:06 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 27267 was started by sandbox on n018,
% 0.17/0.43 % Sat Sep 26 08:40:06 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.50
% 0.17/0.50 % SZS status Theorem for theBenchmark
% 0.17/0.50
% 0.17/0.50 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.17/0.50 % Length of proof is 14.
% 0.17/0.50 % Level of proof is 5.
% 0.17/0.50 % Maximum clause weight is 33.000.
% 0.17/0.50 % Given clauses 46.
% 0.17/0.50
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------