%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET018-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 08:35:20 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.65s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 12 unt; 0 def)
% Number of atoms : 20 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 13 ( 8 ~; 5 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 5 con; 0-2 aty)
% Number of variables : 8 ( 2 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_ordered_pair_determines_components2_3,axiom,
x != z,
file('theBenchmark.p',prove_ordered_pair_determines_components2_3) ).
cnf(c_33,plain,
x != z,
inference(clausify,[status(thm)],[prove_ordered_pair_determines_components2_3]) ).
cnf(c_34,plain,
z != x,
inference(copy,[status(thm)],[c_33]) ).
fof(prove_ordered_pair_determines_components2_2,axiom,
member(x,universal_class),
file('theBenchmark.p',prove_ordered_pair_determines_components2_2) ).
cnf(c_35,plain,
member(x,universal_class),
inference(clausify,[status(thm)],[prove_ordered_pair_determines_components2_2]) ).
fof(prove_ordered_pair_determines_components2_1,axiom,
ordered_pair(w,x) = ordered_pair(y,z),
file('theBenchmark.p',prove_ordered_pair_determines_components2_1) ).
cnf(c_36,plain,
ordered_pair(w,x) = ordered_pair(y,z),
inference(clausify,[status(thm)],[prove_ordered_pair_determines_components2_1]) ).
cnf(c_37,plain,
ordered_pair(y,z) = ordered_pair(w,x),
inference(copy,[status(thm)],[c_36]) ).
fof(ordered_pair_determines_components2,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( VAR_1 = VAR_3
| ~ member(VAR_1,universal_class)
| ordered_pair(VAR_0,VAR_1) != ordered_pair(VAR_2,VAR_3) ),
file('theBenchmark.p',ordered_pair_determines_components2) ).
cnf(c_49,plain,
( B = D
| ~ member(B,universal_class)
| ordered_pair(A,B) != ordered_pair(C,D) ),
inference(clausify,[status(thm)],[ordered_pair_determines_components2]) ).
cnf(c_291,plain,
ordered_pair(w,x) = ordered_pair(y,z),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_292,plain,
( x = z
| ~ member(x,universal_class) ),
inference(resolve,[status(thm)],[c_49,c_291]) ).
cnf(c_293,plain,
x = z,
inference(resolve,[status(thm)],[c_292,c_35]) ).
cnf(c_294,plain,
z = x,
inference(copy,[status(thm)],[c_293]) ).
cnf(c_290,plain,
$false,
inference(resolve,[status(thm)],[c_34,c_294]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET018-7 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n008.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Sat Sep 26 06:52:26 UTC 2026
% 0.08/0.57 % CPUTime :
% 0.08/0.57 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.57 % Process 3007461 was started by sandbox on n008,
% 0.08/0.57 % Sat Sep 26 06:52:26 2026
% 0.08/0.57 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.57
% 0.08/0.57 % From the command line: assign(max_seconds, 300).
% 0.12/0.65
% 0.12/0.65 % SZS status Unsatisfiable for theBenchmark
% 0.12/0.65
% 0.12/0.65 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.12/0.65 % Length of proof is 7.
% 0.12/0.65 % Level of proof is 2.
% 0.12/0.65 % Maximum clause weight is 23.000.
% 0.12/0.65 % Given clauses 18.
% 0.12/0.65
% 0.12/0.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------