%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET016-1 : 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 : n001.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 08:35:19 AM UTC 2026
% Result : Unsatisfiable 0.19s 5.68s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 27 ( 20 unt; 0 def)
% Number of atoms : 36 ( 23 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 19 ( 10 ~; 9 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 20 ( 1 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(singleton_1,axiom,
! [VAR_0] : member(VAR_0,singleton_set(VAR_0)),
file('theBenchmark.p',singleton_1) ).
cnf(c_1,plain,
member(A,singleton_set(A)),
inference(clausify,[status(thm)],[singleton_1]) ).
fof(singleton_2,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ member(VAR_0,singleton_set(VAR_1)) ),
file('theBenchmark.p',singleton_2) ).
cnf(c_2,plain,
( A = B
| ~ member(A,singleton_set(B)) ),
inference(clausify,[status(thm)],[singleton_2]) ).
fof(unordered_pair_1,axiom,
! [VAR_0,VAR_1] : member(VAR_0,unordered_pair(VAR_0,VAR_1)),
file('theBenchmark.p',unordered_pair_1) ).
cnf(c_3,plain,
member(A,unordered_pair(A,B)),
inference(clausify,[status(thm)],[unordered_pair_1]) ).
fof(unordered_pair_3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| VAR_0 = VAR_1
| ~ member(VAR_0,unordered_pair(VAR_1,VAR_2)) ),
file('theBenchmark.p',unordered_pair_3) ).
cnf(c_5,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_3]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : ordered_pair(VAR_0,VAR_1) = unordered_pair(singleton_set(VAR_0),unordered_pair(VAR_0,VAR_1)),
file('theBenchmark.p',ordered_pair) ).
cnf(c_6,plain,
ordered_pair(A,B) = unordered_pair(singleton_set(A),unordered_pair(A,B)),
inference(clausify,[status(thm)],[ordered_pair]) ).
fof(equal_ordered_pairs,axiom,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('theBenchmark.p',equal_ordered_pairs) ).
cnf(c_7,plain,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
inference(clausify,[status(thm)],[equal_ordered_pairs]) ).
cnf(c_23,plain,
unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = ordered_pair(m2,r2),
inference(paramod,[status(thm)],[c_6,c_7]) ).
cnf(c_24,plain,
unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = unordered_pair(singleton_set(m2),unordered_pair(m2,r2)),
inference(paramod,[status(thm)],[c_6,c_23]) ).
cnf(c_8,plain,
unordered_pair(singleton_set(m2),unordered_pair(m2,r2)) = unordered_pair(singleton_set(m1),unordered_pair(m1,r1)),
inference(copy,[status(thm)],[c_24]) ).
fof(prove_first_components_equal,axiom,
m1 != m2,
file('theBenchmark.p',prove_first_components_equal) ).
cnf(c_9,plain,
m1 != m2,
inference(clausify,[status(thm)],[prove_first_components_equal]) ).
cnf(c_10,plain,
m2 != m1,
inference(copy,[status(thm)],[c_9]) ).
cnf(c_12,plain,
member(singleton_set(m2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1))),
inference(paramod,[status(thm)],[c_8,c_3]) ).
cnf(c_25,plain,
m1 != m2,
inference(copy,[status(thm)],[c_10]) ).
cnf(c_18,plain,
~ member(m1,singleton_set(m2)),
inference(resolve,[status(thm)],[c_2,c_25]) ).
cnf(c_26,plain,
( singleton_set(m2) = unordered_pair(m1,r1)
| singleton_set(m2) = singleton_set(m1) ),
inference(resolve,[status(thm)],[c_12,c_5]) ).
cnf(c_19,plain,
( unordered_pair(m1,r1) = singleton_set(m2)
| singleton_set(m2) = singleton_set(m1) ),
inference(copy,[status(thm)],[c_26]) ).
cnf(c_27,plain,
( member(m1,singleton_set(m2))
| singleton_set(m2) = singleton_set(m1) ),
inference(paramod,[status(thm)],[c_19,c_3]) ).
cnf(c_21,plain,
singleton_set(m2) = singleton_set(m1),
inference(resolve,[status(thm)],[c_18,c_27]) ).
cnf(c_28,plain,
~ member(m1,singleton_set(m1)),
inference(paramod,[status(thm)],[c_21,c_18]) ).
cnf(c_22,plain,
$false,
inference(resolve,[status(thm)],[c_1,c_28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/5.65 % Computer : n001.cluster.edu
% 0.19/5.65 % Model : x86_64 x86_64
% 0.19/5.65 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/5.65 % Memory : 8046.5625MB
% 0.19/5.65 % OS : Linux 6.8.0-71-generic
% 0.19/5.65 % CPULimit : 300
% 0.19/5.65 % WCLimit : 300
% 0.19/5.65 % DateTime : Sat Sep 26 06:56:33 UTC 2026
% 0.19/5.66 % CPUTime :
% 0.19/5.66 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/5.66 % Process 1163391 was started by sandbox on n001,
% 0.19/5.66 % Sat Sep 26 06:56:33 2026
% 0.19/5.66 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.19/5.66
% 0.19/5.66 % From the command line: assign(max_seconds, 300).
% 0.19/5.68
% 0.19/5.68 % SZS status Unsatisfiable for theBenchmark
% 0.19/5.68
% 0.19/5.68 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.19/5.68 % Length of proof is 14.
% 0.19/5.68 % Level of proof is 5.
% 0.19/5.68 % Maximum clause weight is 13.000.
% 0.19/5.68 % Given clauses 16.
% 0.19/5.68
% 0.19/5.68 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------