%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET018-1 : 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 : n010.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 0.18s 0.43s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 31 unt; 0 def)
% Number of atoms : 103 ( 71 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 65 ( 24 ~; 41 |; 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 : 32 ( 2 sgn 12 !; 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_2,axiom,
! [VAR_0,VAR_1] : member(VAR_0,unordered_pair(VAR_1,VAR_0)),
file('theBenchmark.p',unordered_pair_2) ).
cnf(c_4,plain,
member(A,unordered_pair(B,A)),
inference(clausify,[status(thm)],[unordered_pair_2]) ).
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_58,plain,
unordered_pair(singleton_set(m1),unordered_pair(m1,r1)) = ordered_pair(m2,r2),
inference(paramod,[status(thm)],[c_6,c_7]) ).
cnf(c_59,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_58]) ).
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_59]) ).
fof(prove_second_components_equal,axiom,
r1 != r2,
file('theBenchmark.p',prove_second_components_equal) ).
cnf(c_9,plain,
r1 != r2,
inference(clausify,[status(thm)],[prove_second_components_equal]) ).
cnf(c_10,plain,
r2 != r1,
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_13,plain,
member(unordered_pair(m2,r2),unordered_pair(singleton_set(m1),unordered_pair(m1,r1))),
inference(paramod,[status(thm)],[c_8,c_4]) ).
cnf(c_60,plain,
( A = unordered_pair(m2,r2)
| A = singleton_set(m2)
| ~ member(A,unordered_pair(singleton_set(m1),unordered_pair(m1,r1))) ),
inference(paramod,[status(thm)],[c_8,c_5]) ).
cnf(c_61,plain,
( A = unordered_pair(m2,r2)
| singleton_set(m2) = A
| ~ member(A,unordered_pair(singleton_set(m1),unordered_pair(m1,r1))) ),
inference(copy,[status(thm)],[c_60]) ).
cnf(c_14,plain,
( unordered_pair(m2,r2) = A
| singleton_set(m2) = A
| ~ member(A,unordered_pair(singleton_set(m1),unordered_pair(m1,r1))) ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_62,plain,
r1 != r2,
inference(copy,[status(thm)],[c_10]) ).
cnf(c_63,plain,
( r1 = A
| ~ member(r1,unordered_pair(r2,A)) ),
inference(resolve,[status(thm)],[c_5,c_62]) ).
cnf(c_64,plain,
r1 != r2,
inference(copy,[status(thm)],[c_10]) ).
cnf(c_17,plain,
~ member(r1,unordered_pair(r2,r2)),
inference(resolve,[status(thm)],[c_63,c_64]) ).
cnf(c_65,plain,
r1 != r2,
inference(copy,[status(thm)],[c_10]) ).
cnf(c_18,plain,
~ member(r1,singleton_set(r2)),
inference(resolve,[status(thm)],[c_2,c_65]) ).
cnf(c_66,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_66]) ).
cnf(c_20,plain,
( unordered_pair(m2,r2) = unordered_pair(m1,r1)
| unordered_pair(m2,r2) = singleton_set(m1) ),
inference(resolve,[status(thm)],[c_13,c_5]) ).
cnf(c_21,plain,
( member(m1,singleton_set(m2))
| singleton_set(m2) = singleton_set(m1) ),
inference(paramod,[status(thm)],[c_19,c_3]) ).
cnf(c_67,plain,
( m1 = m2
| singleton_set(m2) = singleton_set(m1) ),
inference(resolve,[status(thm)],[c_21,c_2]) ).
cnf(c_26,plain,
( m2 = m1
| singleton_set(m2) = singleton_set(m1) ),
inference(copy,[status(thm)],[c_67]) ).
cnf(c_68,plain,
( A = m2
| ~ member(A,singleton_set(m1))
| m2 = m1 ),
inference(paramod,[status(thm)],[c_26,c_2]) ).
cnf(c_28,plain,
( m2 = A
| ~ member(A,singleton_set(m1))
| m2 = m1 ),
inference(copy,[status(thm)],[c_68]) ).
cnf(c_69,plain,
( ~ member(m1,singleton_set(m1))
| m2 = m1 ),
inference(factor,[status(thm)],[c_28]) ).
cnf(c_31,plain,
m2 = m1,
inference(resolve,[status(thm)],[c_1,c_69]) ).
cnf(c_70,plain,
( unordered_pair(m2,r2) = unordered_pair(m1,r1)
| unordered_pair(m1,r2) = singleton_set(m1) ),
inference(paramod,[status(thm)],[c_31,c_20]) ).
cnf(c_32,plain,
( unordered_pair(m1,r2) = unordered_pair(m1,r1)
| unordered_pair(m1,r2) = singleton_set(m1) ),
inference(paramod,[status(thm)],[c_31,c_70]) ).
cnf(c_71,plain,
( unordered_pair(m2,r2) = A
| singleton_set(m1) = A
| ~ member(A,unordered_pair(singleton_set(m1),unordered_pair(m1,r1))) ),
inference(paramod,[status(thm)],[c_31,c_14]) ).
cnf(c_33,plain,
( unordered_pair(m1,r2) = A
| singleton_set(m1) = A
| ~ member(A,unordered_pair(singleton_set(m1),unordered_pair(m1,r1))) ),
inference(paramod,[status(thm)],[c_31,c_71]) ).
cnf(c_36,plain,
( member(r2,unordered_pair(m1,r1))
| unordered_pair(m1,r2) = singleton_set(m1) ),
inference(paramod,[status(thm)],[c_32,c_4]) ).
cnf(c_72,plain,
( r2 = r1
| r2 = m1
| unordered_pair(m1,r2) = singleton_set(m1) ),
inference(resolve,[status(thm)],[c_36,c_5]) ).
cnf(c_38,plain,
( r2 = m1
| unordered_pair(m1,r2) = singleton_set(m1) ),
inference(resolve,[status(thm)],[c_10,c_72]) ).
cnf(c_39,plain,
( member(r2,singleton_set(m1))
| r2 = m1 ),
inference(paramod,[status(thm)],[c_38,c_4]) ).
cnf(c_73,plain,
( unordered_pair(m1,r2) = unordered_pair(m1,r1)
| singleton_set(m1) = unordered_pair(m1,r1) ),
inference(resolve,[status(thm)],[c_33,c_4]) ).
cnf(c_42,plain,
( unordered_pair(m1,r2) = unordered_pair(m1,r1)
| unordered_pair(m1,r1) = singleton_set(m1) ),
inference(copy,[status(thm)],[c_73]) ).
cnf(c_74,plain,
( r2 = m1
| r2 = m1 ),
inference(resolve,[status(thm)],[c_39,c_2]) ).
cnf(c_43,plain,
r2 = m1,
inference(copy,[status(thm)],[c_74]) ).
cnf(c_75,plain,
( unordered_pair(m1,m1) = unordered_pair(m1,r1)
| unordered_pair(m1,r1) = singleton_set(m1) ),
inference(paramod,[status(thm)],[c_43,c_42]) ).
cnf(c_44,plain,
( unordered_pair(m1,r1) = unordered_pair(m1,m1)
| unordered_pair(m1,r1) = singleton_set(m1) ),
inference(copy,[status(thm)],[c_75]) ).
cnf(c_49,plain,
~ member(r1,singleton_set(m1)),
inference(paramod,[status(thm)],[c_43,c_18]) ).
cnf(c_76,plain,
~ member(r1,unordered_pair(m1,r2)),
inference(paramod,[status(thm)],[c_43,c_17]) ).
cnf(c_50,plain,
~ member(r1,unordered_pair(m1,m1)),
inference(paramod,[status(thm)],[c_43,c_76]) ).
cnf(c_77,plain,
( member(r1,unordered_pair(m1,m1))
| unordered_pair(m1,r1) = singleton_set(m1) ),
inference(paramod,[status(thm)],[c_44,c_4]) ).
cnf(c_54,plain,
unordered_pair(m1,r1) = singleton_set(m1),
inference(resolve,[status(thm)],[c_50,c_77]) ).
cnf(c_78,plain,
member(r1,singleton_set(m1)),
inference(paramod,[status(thm)],[c_54,c_4]) ).
cnf(c_57,plain,
$false,
inference(resolve,[status(thm)],[c_49,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SET018-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.05 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40 % Computer : n010.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 06:52:17 UTC 2026
% 0.18/0.41 % CPUTime :
% 0.18/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.41 % Process 2721619 was started by sandbox2 on n010,
% 0.18/0.41 % Sat Sep 26 06:52:17 2026
% 0.18/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.41
% 0.18/0.41 % From the command line: assign(max_seconds, 300).
% 0.18/0.43
% 0.18/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.18/0.43
% 0.18/0.43 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.18/0.43 % Length of proof is 33.
% 0.18/0.43 % Level of proof is 15.
% 0.18/0.43 % Maximum clause weight is 17.000.
% 0.18/0.43 % Given clauses 28.
% 0.18/0.43
% 0.18/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------