%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET019-4 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/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 08:35:21 AM UTC 2026
% Result : Unsatisfiable 1.31s 0.66s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 52 ( 16 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 15 ~; 25 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove__a_equals_b,axiom,
a != b,
file('theBenchmark.p',prove__a_equals_b) ).
cnf(c_64,plain,
a != b,
inference(clausify,[status(thm)],[prove__a_equals_b]) ).
cnf(c_65,plain,
b != a,
inference(copy,[status(thm)],[c_64]) ).
fof(b_contains_a,axiom,
subset(a,b),
file('theBenchmark.p',b_contains_a) ).
cnf(c_66,plain,
subset(a,b),
inference(clausify,[status(thm)],[b_contains_a]) ).
fof(a_contains_b,axiom,
subset(b,a),
file('theBenchmark.p',a_contains_b) ).
cnf(c_67,plain,
subset(b,a),
inference(clausify,[status(thm)],[a_contains_b]) ).
fof(subset1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subset(VAR_0,VAR_1) ),
file('theBenchmark.p',subset1) ).
cnf(c_117,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset1]) ).
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_192,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_193,plain,
( A = B
| member(f1(A,B),B)
| member(f1(A,B),A) ),
inference(clausify,[status(thm)],[extensionality2]) ).
cnf(c_371,plain,
( member(A,a)
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_117,c_67]) ).
cnf(c_372,plain,
( member(A,b)
| ~ member(A,a) ),
inference(resolve,[status(thm)],[c_117,c_66]) ).
cnf(c_1816,plain,
( A = b
| member(f1(A,b),A)
| member(f1(A,b),a) ),
inference(resolve,[status(thm)],[c_371,c_193]) ).
cnf(c_922,plain,
( b = A
| member(f1(A,b),A)
| member(f1(A,b),a) ),
inference(copy,[status(thm)],[c_1816]) ).
cnf(c_1817,plain,
( b = a
| member(f1(a,b),a) ),
inference(factor,[status(thm)],[c_922]) ).
cnf(c_926,plain,
member(f1(a,b),a),
inference(resolve,[status(thm)],[c_65,c_1817]) ).
cnf(c_935,plain,
( a = A
| member(f1(a,A),A)
| member(f1(a,A),b) ),
inference(resolve,[status(thm)],[c_372,c_193]) ).
cnf(c_1818,plain,
( a = b
| member(f1(a,b),b) ),
inference(factor,[status(thm)],[c_935]) ).
cnf(c_1819,plain,
( b = a
| member(f1(a,b),b) ),
inference(copy,[status(thm)],[c_1818]) ).
cnf(c_939,plain,
member(f1(a,b),b),
inference(resolve,[status(thm)],[c_65,c_1819]) ).
cnf(c_1820,plain,
( a = b
| ~ member(f1(a,b),b) ),
inference(resolve,[status(thm)],[c_926,c_192]) ).
cnf(c_1821,plain,
( b = a
| ~ member(f1(a,b),b) ),
inference(copy,[status(thm)],[c_1820]) ).
cnf(c_1822,plain,
b = a,
inference(resolve,[status(thm)],[c_939,c_1821]) ).
cnf(c_1815,plain,
$false,
inference(resolve,[status(thm)],[c_65,c_1822]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET019-4 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.44 % Computer : n008.cluster.edu
% 0.18/0.44 % Model : x86_64 x86_64
% 0.18/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.44 % Memory : 8046.5625MB
% 0.18/0.44 % OS : Linux 6.8.0-71-generic
% 0.18/0.44 % CPULimit : 300
% 0.18/0.44 % WCLimit : 300
% 0.18/0.44 % DateTime : Sat Sep 26 06:53:09 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.45 % Process 3008834 was started by sandbox2 on n008,
% 0.18/0.45 % Sat Sep 26 06:53:09 2026
% 0.18/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.46
% 0.18/0.46 % From the command line: assign(max_seconds, 300).
% 1.31/0.66
% 1.31/0.66 % SZS status Unsatisfiable for theBenchmark
% 1.31/0.66
% 1.31/0.66 % Proof 1 at 0.16 (+ 0.03) seconds.
% 1.31/0.66 % Length of proof is 14.
% 1.31/0.66 % Level of proof is 4.
% 1.31/0.66 % Maximum clause weight is 23.000.
% 1.31/0.66 % Given clauses 288.
% 1.31/0.66
% 1.31/0.66 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------