%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 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 08:35:17 AM UTC 2026
% Result : Unsatisfiable 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 8
% Syntax : Number of formulae : 33 ( 14 unt; 0 def)
% Number of atoms : 66 ( 26 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 53 ( 20 ~; 33 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 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 : 32 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(complement2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,VAR_1)
| ~ little_set(VAR_0)
| member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement2) ).
cnf(c_1,plain,
( member(A,B)
| ~ little_set(A)
| member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement2]) ).
fof(extensionality1,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| little_set(f1(VAR_0,VAR_1)) ),
file('theBenchmark.p',extensionality1) ).
cnf(c_2,plain,
( A = B
| little_set(f1(A,B)) ),
inference(clausify,[status(thm)],[extensionality1]) ).
cnf(c_8,plain,
( A = B
| member(f1(A,B),C)
| member(f1(A,B),complement(C)) ),
inference(resolve,[status(thm)],[c_1,c_2]) ).
fof(prove_a_equals_c,axiom,
as != cs,
file('theBenchmark.p',prove_a_equals_c) ).
cnf(c_9,plain,
as != cs,
inference(clausify,[status(thm)],[prove_a_equals_c]) ).
cnf(c_10,plain,
cs != as,
inference(copy,[status(thm)],[c_9]) ).
fof(complement_of_b_is_c,axiom,
complement(bs) = cs,
file('theBenchmark.p',complement_of_b_is_c) ).
cnf(c_11,plain,
complement(bs) = cs,
inference(clausify,[status(thm)],[complement_of_b_is_c]) ).
cnf(c_12,plain,
cs = complement(bs),
inference(copy,[status(thm)],[c_11]) ).
fof(complement_of_a_is_b,axiom,
complement(as) = bs,
file('theBenchmark.p',complement_of_a_is_b) ).
cnf(c_13,plain,
complement(as) = bs,
inference(clausify,[status(thm)],[complement_of_a_is_b]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_15,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(extensionality3,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ member(f1(VAR_0,VAR_1),VAR_1)
| ~ member(f1(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',extensionality3) ).
cnf(c_16,plain,
( A = B
| ~ member(f1(A,B),B)
| ~ member(f1(A,B),A) ),
inference(clausify,[status(thm)],[extensionality3]) ).
fof(extensionality2,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| member(f1(VAR_0,VAR_1),VAR_1)
| member(f1(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',extensionality2) ).
cnf(c_17,plain,
( A = B
| member(f1(A,B),B)
| member(f1(A,B),A) ),
inference(clausify,[status(thm)],[extensionality2]) ).
cnf(c_18,plain,
complement(bs) != as,
inference(paramod,[status(thm)],[c_12,c_10]) ).
cnf(c_19,plain,
( A = B
| member(f1(A,B),as)
| member(f1(A,B),bs) ),
inference(paramod,[status(thm)],[c_13,c_8]) ).
cnf(c_20,plain,
( ~ member(A,as)
| ~ member(A,bs) ),
inference(paramod,[status(thm)],[c_13,c_15]) ).
cnf(c_60,plain,
( complement(A) = B
| member(f1(complement(A),B),A)
| complement(A) = B
| ~ member(f1(complement(A),B),B) ),
inference(resolve,[status(thm)],[c_16,c_8]) ).
cnf(c_21,plain,
( member(f1(complement(A),B),A)
| complement(A) = B
| ~ member(f1(complement(A),B),B) ),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_61,plain,
( complement(A) = as
| member(f1(complement(A),as),bs)
| member(f1(complement(A),as),A)
| complement(A) = as ),
inference(resolve,[status(thm)],[c_21,c_19]) ).
cnf(c_44,plain,
( member(f1(complement(A),as),bs)
| member(f1(complement(A),as),A)
| complement(A) = as ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_62,plain,
( member(f1(complement(bs),as),bs)
| complement(bs) = as ),
inference(factor,[status(thm)],[c_44]) ).
cnf(c_47,plain,
member(f1(complement(bs),as),bs),
inference(resolve,[status(thm)],[c_18,c_62]) ).
cnf(c_50,plain,
~ member(f1(complement(bs),as),as),
inference(resolve,[status(thm)],[c_20,c_47]) ).
cnf(c_51,plain,
~ member(f1(complement(bs),as),complement(bs)),
inference(resolve,[status(thm)],[c_15,c_47]) ).
cnf(c_63,plain,
( complement(bs) = as
| member(f1(complement(bs),as),complement(bs)) ),
inference(resolve,[status(thm)],[c_50,c_17]) ).
cnf(c_64,plain,
complement(bs) = as,
inference(resolve,[status(thm)],[c_51,c_63]) ).
cnf(c_59,plain,
$false,
inference(resolve,[status(thm)],[c_18,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET012-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n026.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 06:52:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.11/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.36 % Process 336025 was started by sandbox2 on n026,
% 0.11/0.36 % Sat Sep 26 06:52:10 2026
% 0.11/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.36
% 0.11/0.36 % From the command line: assign(max_seconds, 300).
% 0.11/0.38
% 0.11/0.38 % SZS status Unsatisfiable for theBenchmark
% 0.11/0.38
% 0.11/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.11/0.38 % Length of proof is 20.
% 0.11/0.38 % Level of proof is 6.
% 0.11/0.38 % Maximum clause weight is 16.000.
% 0.11/0.38 % Given clauses 24.
% 0.11/0.38
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------