%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET047-5 : 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 : n014.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 08:35:29 AM UTC 2026
% Result : Unsatisfiable 0.16s 5.40s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 8 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 127 ( 32 ~; 95 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 34 ( 0 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(element_substitution1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( element(VAR_2,VAR_1)
| ~ element(VAR_2,VAR_0)
| ~ set_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',element_substitution1) ).
cnf(c_1,plain,
( element(C,B)
| ~ element(C,A)
| ~ set_equal(A,B) ),
inference(clausify,[status(thm)],[element_substitution1]) ).
fof(element_substitution2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( element(VAR_2,VAR_0)
| ~ element(VAR_2,VAR_1)
| ~ set_equal(VAR_0,VAR_1) ),
file('theBenchmark.p',element_substitution2) ).
cnf(c_2,plain,
( element(C,A)
| ~ element(C,B)
| ~ set_equal(A,B) ),
inference(clausify,[status(thm)],[element_substitution2]) ).
fof(clause_3,axiom,
! [VAR_0,VAR_1] :
( set_equal(VAR_0,VAR_1)
| element(f(VAR_0,VAR_1),VAR_1)
| element(f(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',clause_3) ).
cnf(c_3,plain,
( set_equal(A,B)
| element(f(A,B),B)
| element(f(A,B),A) ),
inference(clausify,[status(thm)],[clause_3]) ).
fof(clause_4,axiom,
! [VAR_0,VAR_1] :
( set_equal(VAR_0,VAR_1)
| ~ element(f(VAR_0,VAR_1),VAR_0)
| ~ element(f(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',clause_4) ).
cnf(c_4,plain,
( set_equal(A,B)
| ~ element(f(A,B),A)
| ~ element(f(A,B),B) ),
inference(clausify,[status(thm)],[clause_4]) ).
fof(prove_symmetry1,axiom,
( set_equal(b,a)
| set_equal(a,b) ),
file('theBenchmark.p',prove_symmetry1) ).
cnf(c_5,plain,
( set_equal(b,a)
| set_equal(a,b) ),
inference(clausify,[status(thm)],[prove_symmetry1]) ).
fof(prove_symmetry2,axiom,
( ~ set_equal(a,b)
| ~ set_equal(b,a) ),
file('theBenchmark.p',prove_symmetry2) ).
cnf(c_6,plain,
( ~ set_equal(a,b)
| ~ set_equal(b,a) ),
inference(clausify,[status(thm)],[prove_symmetry2]) ).
cnf(c_9,plain,
( element(C,A)
| ~ element(C,B)
| element(f(A,B),B)
| element(f(A,B),A) ),
inference(resolve,[status(thm)],[c_3,c_2]) ).
cnf(c_10,plain,
( element(C,B)
| ~ element(C,A)
| element(f(A,B),B)
| element(f(A,B),A) ),
inference(resolve,[status(thm)],[c_3,c_1]) ).
cnf(c_11,plain,
( element(A,b)
| ~ element(A,a)
| set_equal(a,b) ),
inference(resolve,[status(thm)],[c_5,c_2]) ).
cnf(c_12,plain,
( element(A,a)
| ~ element(A,b)
| set_equal(a,b) ),
inference(resolve,[status(thm)],[c_5,c_1]) ).
cnf(c_13,plain,
( element(f(b,a),a)
| element(f(b,a),b)
| ~ set_equal(a,b) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_14,plain,
( element(f(a,b),b)
| element(f(a,b),a)
| ~ set_equal(b,a) ),
inference(resolve,[status(thm)],[c_6,c_3]) ).
cnf(c_15,plain,
( element(f(a,b),b)
| element(f(a,b),a)
| element(f(b,a),a)
| element(f(b,a),b) ),
inference(resolve,[status(thm)],[c_13,c_3]) ).
cnf(c_17,plain,
( element(f(b,a),A)
| element(f(A,b),b)
| element(f(A,b),A)
| element(f(a,b),b)
| element(f(a,b),a)
| element(f(b,a),a) ),
inference(resolve,[status(thm)],[c_15,c_9]) ).
cnf(c_82,plain,
( element(f(a,b),b)
| element(f(a,b),a)
| element(f(a,b),b)
| element(f(a,b),a)
| element(f(b,a),a) ),
inference(factor,[status(thm)],[c_17]) ).
cnf(c_83,plain,
( element(f(a,b),b)
| element(f(a,b),b)
| element(f(a,b),a)
| element(f(b,a),a) ),
inference(copy,[status(thm)],[c_82]) ).
cnf(c_20,plain,
( element(f(a,b),b)
| element(f(a,b),a)
| element(f(b,a),a) ),
inference(copy,[status(thm)],[c_83]) ).
cnf(c_21,plain,
( element(f(b,a),A)
| element(f(a,A),A)
| element(f(a,A),a)
| element(f(a,b),b)
| element(f(a,b),a) ),
inference(resolve,[status(thm)],[c_20,c_10]) ).
cnf(c_23,plain,
( set_equal(b,a)
| ~ element(f(b,a),b)
| element(f(a,b),b)
| element(f(a,b),a) ),
inference(resolve,[status(thm)],[c_20,c_4]) ).
cnf(c_84,plain,
( element(f(b,a),b)
| element(f(a,b),b)
| element(f(a,b),b)
| element(f(a,b),a) ),
inference(factor,[status(thm)],[c_21]) ).
cnf(c_26,plain,
( element(f(b,a),b)
| element(f(a,b),b)
| element(f(a,b),a) ),
inference(copy,[status(thm)],[c_84]) ).
cnf(c_85,plain,
( element(f(a,b),b)
| element(f(a,b),a)
| set_equal(b,a)
| element(f(a,b),b)
| element(f(a,b),a) ),
inference(resolve,[status(thm)],[c_23,c_26]) ).
cnf(c_86,plain,
( element(f(a,b),b)
| set_equal(b,a)
| element(f(a,b),b)
| element(f(a,b),a) ),
inference(copy,[status(thm)],[c_85]) ).
cnf(c_32,plain,
( set_equal(b,a)
| element(f(a,b),b)
| element(f(a,b),a) ),
inference(copy,[status(thm)],[c_86]) ).
cnf(c_87,plain,
( element(f(a,b),b)
| element(f(a,b),a)
| element(f(a,b),b)
| element(f(a,b),a) ),
inference(resolve,[status(thm)],[c_32,c_14]) ).
cnf(c_88,plain,
( element(f(a,b),b)
| element(f(a,b),b)
| element(f(a,b),a) ),
inference(copy,[status(thm)],[c_87]) ).
cnf(c_33,plain,
( element(f(a,b),b)
| element(f(a,b),a) ),
inference(copy,[status(thm)],[c_88]) ).
cnf(c_89,plain,
( element(f(a,b),a)
| set_equal(a,b)
| element(f(a,b),a) ),
inference(resolve,[status(thm)],[c_33,c_12]) ).
cnf(c_34,plain,
( set_equal(a,b)
| element(f(a,b),a) ),
inference(copy,[status(thm)],[c_89]) ).
cnf(c_37,plain,
( element(f(a,b),A)
| ~ set_equal(A,b)
| element(f(a,b),a) ),
inference(resolve,[status(thm)],[c_33,c_2]) ).
cnf(c_40,plain,
( ~ set_equal(a,b)
| element(f(a,b),a) ),
inference(factor,[status(thm)],[c_37]) ).
cnf(c_90,plain,
( element(f(a,b),a)
| element(f(a,b),a) ),
inference(resolve,[status(thm)],[c_40,c_34]) ).
cnf(c_45,plain,
element(f(a,b),a),
inference(copy,[status(thm)],[c_90]) ).
cnf(c_46,plain,
( element(f(a,b),b)
| set_equal(a,b) ),
inference(resolve,[status(thm)],[c_45,c_11]) ).
cnf(c_49,plain,
( set_equal(a,b)
| ~ element(f(a,b),b) ),
inference(resolve,[status(thm)],[c_45,c_4]) ).
cnf(c_53,plain,
( element(A,b)
| ~ element(A,a)
| element(f(a,b),b) ),
inference(resolve,[status(thm)],[c_46,c_1]) ).
cnf(c_91,plain,
( ~ element(f(a,b),a)
| element(f(a,b),b) ),
inference(factor,[status(thm)],[c_53]) ).
cnf(c_54,plain,
element(f(a,b),b),
inference(resolve,[status(thm)],[c_45,c_91]) ).
cnf(c_55,plain,
set_equal(a,b),
inference(resolve,[status(thm)],[c_54,c_49]) ).
cnf(c_56,plain,
( element(f(b,a),a)
| element(f(b,a),b) ),
inference(resolve,[status(thm)],[c_55,c_13]) ).
cnf(c_57,plain,
~ set_equal(b,a),
inference(resolve,[status(thm)],[c_55,c_6]) ).
cnf(c_58,plain,
( element(A,a)
| ~ element(A,b) ),
inference(resolve,[status(thm)],[c_55,c_2]) ).
cnf(c_59,plain,
( element(A,b)
| ~ element(A,a) ),
inference(resolve,[status(thm)],[c_55,c_1]) ).
cnf(c_92,plain,
( element(f(b,a),a)
| element(f(b,a),a) ),
inference(resolve,[status(thm)],[c_56,c_58]) ).
cnf(c_77,plain,
element(f(b,a),a),
inference(copy,[status(thm)],[c_92]) ).
cnf(c_78,plain,
element(f(b,a),b),
inference(resolve,[status(thm)],[c_77,c_59]) ).
cnf(c_93,plain,
( set_equal(b,a)
| ~ element(f(b,a),b) ),
inference(resolve,[status(thm)],[c_77,c_4]) ).
cnf(c_94,plain,
set_equal(b,a),
inference(resolve,[status(thm)],[c_78,c_93]) ).
cnf(c_81,plain,
$false,
inference(resolve,[status(thm)],[c_57,c_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET047-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/5.38 % Computer : n014.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Sat Sep 26 06:59:54 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/5.38 % Process 2443446 was started by sandbox2 on n014,
% 0.11/5.38 % Sat Sep 26 06:59:54 2026
% 0.11/5.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/5.39
% 0.11/5.39 % From the command line: assign(max_seconds, 300).
% 0.16/5.40
% 0.16/5.40 % SZS status Unsatisfiable for theBenchmark
% 0.16/5.40
% 0.16/5.40 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.16/5.40 % Length of proof is 36.
% 0.16/5.40 % Level of proof is 19.
% 0.16/5.40 % Maximum clause weight is 40.000.
% 0.16/5.40 % Given clauses 36.
% 0.16/5.40
% 0.16/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------