%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET027-3 : 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 : 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 08:35:24 AM UTC 2026
% Result : Unsatisfiable 3.29s 0.83s
% Output : CNFRefutation 3.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 11 unt; 0 def)
% Number of atoms : 29 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 10 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 16 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_a_subset_c,axiom,
~ subset(a,c),
file('theBenchmark.p',prove_a_subset_c) ).
cnf(c_64,plain,
~ subset(a,c),
inference(clausify,[status(thm)],[prove_a_subset_c]) ).
fof(b_subset_c,axiom,
subset(b,c),
file('theBenchmark.p',b_subset_c) ).
cnf(c_65,plain,
subset(b,c),
inference(clausify,[status(thm)],[b_subset_c]) ).
fof(a_subset_b,axiom,
subset(a,b),
file('theBenchmark.p',a_subset_b) ).
cnf(c_66,plain,
subset(a,b),
inference(clausify,[status(thm)],[a_subset_b]) ).
fof(subset3,axiom,
! [VAR_0,VAR_1] :
( ~ member(f17(VAR_0,VAR_1),VAR_1)
| subset(VAR_0,VAR_1) ),
file('theBenchmark.p',subset3) ).
cnf(c_125,plain,
( ~ member(f17(A,B),B)
| subset(A,B) ),
inference(clausify,[status(thm)],[subset3]) ).
fof(subset2,axiom,
! [VAR_0,VAR_1] :
( member(f17(VAR_0,VAR_1),VAR_0)
| subset(VAR_0,VAR_1) ),
file('theBenchmark.p',subset2) ).
cnf(c_126,plain,
( member(f17(A,B),A)
| subset(A,B) ),
inference(clausify,[status(thm)],[subset2]) ).
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_127,plain,
( member(C,B)
| ~ member(C,A)
| ~ subset(A,B) ),
inference(clausify,[status(thm)],[subset1]) ).
cnf(c_391,plain,
member(f17(a,c),a),
inference(resolve,[status(thm)],[c_126,c_64]) ).
cnf(c_418,plain,
( member(A,b)
| ~ member(A,a) ),
inference(resolve,[status(thm)],[c_127,c_66]) ).
cnf(c_419,plain,
( member(A,c)
| ~ member(A,b) ),
inference(resolve,[status(thm)],[c_127,c_65]) ).
cnf(c_1890,plain,
member(f17(a,c),b),
inference(resolve,[status(thm)],[c_391,c_418]) ).
cnf(c_2575,plain,
member(f17(a,c),c),
inference(resolve,[status(thm)],[c_1890,c_419]) ).
cnf(c_2749,plain,
subset(a,c),
inference(resolve,[status(thm)],[c_2575,c_125]) ).
cnf(c_2748,plain,
$false,
inference(resolve,[status(thm)],[c_64,c_2749]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET027-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n026.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 06:57:25 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 344716 was started by sandbox on n026,
% 0.10/0.37 % Sat Sep 26 06:57:25 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 3.29/0.83
% 3.29/0.83 % SZS status Unsatisfiable for theBenchmark
% 3.29/0.83
% 3.29/0.83 % Proof 1 at 0.35 (+ 0.08) seconds.
% 3.29/0.83 % Length of proof is 12.
% 3.29/0.83 % Level of proof is 4.
% 3.29/0.83 % Maximum clause weight is 18.000.
% 3.29/0.83 % Given clauses 333.
% 3.29/0.83
% 3.29/0.83 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------