%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SET016-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 : Fri Sep 25 02:41:29 PM UTC 2026
% Result : Unsatisfiable 0.15s 15.83s
% Output : Proof 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 23 unt; 0 def)
% Number of atoms : 58 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 14 ~; 20 |; 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 : 45 ( 3 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ordered_pair) ).
fof(f5_nnf,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] : ordered_pair(X,Y) = unordered_pair(singleton_set(X),unordered_pair(X,Y)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
ordered_pair(X0,X1) = unordered_pair(singleton_set(X0),unordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f4,axiom,
( X = Z
| X = Y
| ~ member(X,unordered_pair(Y,Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_3) ).
fof(f4_nnf,plain,
! [X,Y,Z] :
( X = Z
| X = Y
| ~ member(X,unordered_pair(Y,Z)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y,Z] :
( X = Z
| X = Y
| ~ member(X,unordered_pair(Y,Z)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( X0 = X2
| X0 = X1
| ~ member(X0,unordered_pair(X1,X2)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p15,plain,
( X0 = unordered_pair(X1,X2)
| X0 = singleton_set(X1)
| ~ member(X0,ordered_pair(X1,X2)) ),
inference(superposition,[status(thm)],[c5,c4]) ).
cnf(f6,hypothesis,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equal_ordered_pairs) ).
fof(f6_nnf,plain,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
ordered_pair(m1,r1) = ordered_pair(m2,r2),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(f2,axiom,
member(X,unordered_pair(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unordered_pair_1) ).
fof(f2_nnf,plain,
! [X,Y] : member(X,unordered_pair(X,Y)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : member(X,unordered_pair(X,Y)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
member(X0,unordered_pair(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p8,plain,
member(singleton_set(X0),ordered_pair(X0,X1)),
inference(superposition,[status(thm)],[c5,c2]) ).
cnf(p11,plain,
member(singleton_set(m2),ordered_pair(m1,r1)),
inference(superposition,[status(thm)],[c6,p8]) ).
cnf(p34,plain,
( singleton_set(m2) = unordered_pair(m1,r1)
| singleton_set(m2) = singleton_set(m1) ),
inference(resolution,[status(thm)],[p15,p11]) ).
cnf(p39,plain,
( member(m1,singleton_set(m2))
| singleton_set(m2) = singleton_set(m1) ),
inference(superposition,[status(thm)],[p34,c2]) ).
cnf(f0,axiom,
member(X,singleton_set(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_1) ).
fof(f0_nnf,plain,
! [X] : member(X,singleton_set(X)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : member(X,singleton_set(X)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
member(X0,singleton_set(X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p48,plain,
( member(m2,singleton_set(m1))
| member(m1,singleton_set(m2)) ),
inference(superposition,[status(thm)],[p39,c0]) ).
cnf(f1,axiom,
( X = Y
| ~ member(X,singleton_set(Y)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton_2) ).
fof(f1_nnf,plain,
! [X,Y] :
( X = Y
| ~ member(X,singleton_set(Y)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] :
( X = Y
| ~ member(X,singleton_set(Y)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( X0 = X1
| ~ member(X0,singleton_set(X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p57,plain,
( m2 = m1
| member(m1,singleton_set(m2)) ),
inference(resolution,[status(thm)],[p48,c1]) ).
cnf(p58,plain,
( m1 = m2
| m2 = m1 ),
inference(resolution,[status(thm)],[p57,c1]) ).
cnf(f7,negated_conjecture,
m1 != m2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_first_components_equal) ).
fof(f7_nnf,plain,
m1 != m2,
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
m1 != m2,
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
m1 != m2,
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(p62,plain,
( m1 != m1
| m1 = m2 ),
inference(superposition,[status(thm)],[p58,c7]) ).
cnf(p70,plain,
m1 = m2,
inference(equality_resolution,[status(thm)],[p62]) ).
cnf(p71,plain,
$false,
inference(resolution,[status(thm)],[p70,c7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET016-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/15.40 % Computer : n013.cluster.edu
% 0.03/15.40 % Model : x86_64 x86_64
% 0.03/15.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/15.40 % Memory : 8046.5625MB
% 0.03/15.40 % OS : Linux 6.8.0-71-generic
% 0.03/15.40 % CPULimit : 300
% 0.03/15.40 % WCLimit : 300
% 0.03/15.40 % DateTime : Thu Sep 24 09:08:28 UTC 2026
% 0.03/15.40 % CPUTime :
% 0.03/15.40 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/15.83 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/15.83 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------