%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET787-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:36:57 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.40s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 27 ( 13 unt; 0 def)
% Number of atoms : 44 ( 9 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 33 ( 16 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 28 ( 3 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(un_eq_Union_2_c2,axiom,
~ member(sk2,un(a,b)),
file('theBenchmark.p',un_eq_Union_2_c2) ).
cnf(c_1,plain,
~ member(sk2,un(a,b)),
inference(clausify,[status(thm)],[un_eq_Union_2_c2]) ).
fof(un_eq_Union_2_c1,axiom,
member(sk2,union(cons(a,cons(b,eptset)))),
file('theBenchmark.p',un_eq_Union_2_c1) ).
cnf(c_2,plain,
member(sk2,union(cons(a,cons(b,eptset)))),
inference(clausify,[status(thm)],[un_eq_Union_2_c1]) ).
fof(clause158,axiom,
! [VAR_0] : ~ member(VAR_0,eptset),
file('theBenchmark.p',clause158) ).
cnf(c_8,plain,
~ member(A,eptset),
inference(clausify,[status(thm)],[clause158]) ).
fof(unI2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,un(VAR_2,VAR_1))
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',unI2) ).
cnf(c_9,plain,
( member(A,un(C,B))
| ~ member(A,B) ),
inference(clausify,[status(thm)],[unI2]) ).
fof(unI1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,un(VAR_1,VAR_2))
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',unI1) ).
cnf(c_10,plain,
( member(A,un(B,C))
| ~ member(A,B) ),
inference(clausify,[status(thm)],[unI1]) ).
fof(clause112,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| VAR_0 = VAR_1
| ~ member(VAR_0,cons(VAR_1,VAR_2)) ),
file('theBenchmark.p',clause112) ).
cnf(c_11,plain,
( member(A,C)
| A = B
| ~ member(A,cons(B,C)) ),
inference(clausify,[status(thm)],[clause112]) ).
fof(clause120,axiom,
! [VAR_0,VAR_1] :
( member(unionE_sk1(VAR_0,VAR_1),VAR_1)
| ~ member(VAR_0,union(VAR_1)) ),
file('theBenchmark.p',clause120) ).
cnf(c_12,plain,
( member(unionE_sk1(A,B),B)
| ~ member(A,union(B)) ),
inference(clausify,[status(thm)],[clause120]) ).
fof(clause119,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unionE_sk1(VAR_0,VAR_1))
| ~ member(VAR_0,union(VAR_1)) ),
file('theBenchmark.p',clause119) ).
cnf(c_13,plain,
( member(A,unionE_sk1(A,B))
| ~ member(A,union(B)) ),
inference(clausify,[status(thm)],[clause119]) ).
cnf(c_17,plain,
~ member(sk2,b),
inference(resolve,[status(thm)],[c_9,c_1]) ).
cnf(c_19,plain,
~ member(sk2,a),
inference(resolve,[status(thm)],[c_10,c_1]) ).
cnf(c_20,plain,
member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(a,cons(b,eptset))),
inference(resolve,[status(thm)],[c_12,c_2]) ).
cnf(c_22,plain,
member(sk2,unionE_sk1(sk2,cons(a,cons(b,eptset)))),
inference(resolve,[status(thm)],[c_13,c_2]) ).
cnf(c_31,plain,
( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),cons(b,eptset))
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(resolve,[status(thm)],[c_20,c_11]) ).
cnf(c_87,plain,
( member(unionE_sk1(sk2,cons(a,cons(b,eptset))),eptset)
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = b
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(resolve,[status(thm)],[c_31,c_11]) ).
cnf(c_82,plain,
( unionE_sk1(sk2,cons(a,cons(b,eptset))) = b
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(resolve,[status(thm)],[c_8,c_87]) ).
cnf(c_88,plain,
( member(sk2,b)
| unionE_sk1(sk2,cons(a,cons(b,eptset))) = a ),
inference(paramod,[status(thm)],[c_82,c_22]) ).
cnf(c_85,plain,
unionE_sk1(sk2,cons(a,cons(b,eptset))) = a,
inference(resolve,[status(thm)],[c_17,c_88]) ).
cnf(c_89,plain,
member(sk2,a),
inference(paramod,[status(thm)],[c_85,c_22]) ).
cnf(c_86,plain,
$false,
inference(resolve,[status(thm)],[c_19,c_89]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET787-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n026.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 26 08:18:25 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.39 % Process 525560 was started by sandbox on n026,
% 0.10/0.39 % Sat Sep 26 08:18:25 2026
% 0.10/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.39
% 0.10/0.39 % From the command line: assign(max_seconds, 300).
% 0.10/0.40
% 0.10/0.40 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.40
% 0.10/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.10/0.40 % Length of proof is 16.
% 0.10/0.40 % Level of proof is 5.
% 0.10/0.40 % Maximum clause weight is 40.000.
% 0.10/0.40 % Given clauses 39.
% 0.10/0.40
% 0.10/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------