%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET019-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 2.14s 0.68s
% Output : CNFRefutation 2.14s
% 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_120,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_195,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_196,plain,
( A = B
| member(f1(A,B),B)
| member(f1(A,B),A) ),
inference(clausify,[status(thm)],[extensionality2]) ).
cnf(c_383,plain,
( member(A,a)
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_120,c_67]) ).
cnf(c_384,plain,
( member(A,b)
| ~ member(A,a) ),
inference(resolve,[status(thm)],[c_120,c_66]) ).
cnf(c_2011,plain,
( A = b
| member(f1(A,b),A)
| member(f1(A,b),a) ),
inference(resolve,[status(thm)],[c_383,c_196]) ).
cnf(c_1146,plain,
( b = A
| member(f1(A,b),A)
| member(f1(A,b),a) ),
inference(copy,[status(thm)],[c_2011]) ).
cnf(c_2012,plain,
( b = a
| member(f1(a,b),a) ),
inference(factor,[status(thm)],[c_1146]) ).
cnf(c_1150,plain,
member(f1(a,b),a),
inference(resolve,[status(thm)],[c_65,c_2012]) ).
cnf(c_1164,plain,
( a = A
| member(f1(a,A),A)
| member(f1(a,A),b) ),
inference(resolve,[status(thm)],[c_384,c_196]) ).
cnf(c_2013,plain,
( a = b
| member(f1(a,b),b) ),
inference(factor,[status(thm)],[c_1164]) ).
cnf(c_2014,plain,
( b = a
| member(f1(a,b),b) ),
inference(copy,[status(thm)],[c_2013]) ).
cnf(c_1168,plain,
member(f1(a,b),b),
inference(resolve,[status(thm)],[c_65,c_2014]) ).
cnf(c_2015,plain,
( a = b
| ~ member(f1(a,b),b) ),
inference(resolve,[status(thm)],[c_1150,c_195]) ).
cnf(c_2016,plain,
( b = a
| ~ member(f1(a,b),b) ),
inference(copy,[status(thm)],[c_2015]) ).
cnf(c_2017,plain,
b = a,
inference(resolve,[status(thm)],[c_1168,c_2016]) ).
cnf(c_2010,plain,
$false,
inference(resolve,[status(thm)],[c_65,c_2017]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET019-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.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 06:57:14 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.35 % Process 229785 was started by sandbox on n016,
% 0.08/0.35 % Sat Sep 26 06:57:14 2026
% 0.08/0.35 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 2.14/0.68
% 2.14/0.68 % SZS status Unsatisfiable for theBenchmark
% 2.14/0.68
% 2.14/0.68 % Proof 1 at 0.26 (+ 0.04) seconds.
% 2.14/0.68 % Length of proof is 14.
% 2.14/0.68 % Level of proof is 4.
% 2.14/0.68 % Maximum clause weight is 23.000.
% 2.14/0.68 % Given clauses 294.
% 2.14/0.68
% 2.14/0.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------