%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET020+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 05:06:53 PM UTC 2026
% Result : Theorem 1.31s 1.73s
% Output : CNFRefutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 14 unt; 0 def)
% Number of atoms : 53 ( 30 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 46 ( 17 ~; 14 |; 12 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 29 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ordered_pair_defn,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',ordered_pair_defn) ).
fof(singleton_set_defn,axiom,
! [X1] : singleton(X1) = unordered_pair(X1,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',singleton_set_defn) ).
fof(unique_1st_and_2nd_in_pair_of_sets1,conjecture,
! [X3,X4,X1] :
( ( member(X3,universal_class)
& member(X4,universal_class)
& X1 = ordered_pair(X3,X4) )
=> ( first(X1) = X3
& second(X1) = X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unique_1st_and_2nd_in_pair_of_sets1) ).
fof(first_second,axiom,
! [X1,X2] :
( ( member(X1,universal_class)
& member(X2,universal_class) )
=> ( first(ordered_pair(X1,X2)) = X1
& second(ordered_pair(X1,X2)) = X2 ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET005+0.ax',first_second) ).
fof(c_0_4,plain,
! [X114,X115] : ordered_pair(X114,X115) = unordered_pair(singleton(X114),unordered_pair(X114,singleton(X115))),
inference(variable_rename,[status(thm)],[ordered_pair_defn]) ).
fof(c_0_5,plain,
! [X113] : singleton(X113) = unordered_pair(X113,X113),
inference(variable_rename,[status(thm)],[singleton_set_defn]) ).
fof(c_0_6,negated_conjecture,
~ ! [X3,X4,X1] :
( ( member(X3,universal_class)
& member(X4,universal_class)
& X1 = ordered_pair(X3,X4) )
=> ( first(X1) = X3
& second(X1) = X4 ) ),
inference(assume_negation,[status(cth)],[unique_1st_and_2nd_in_pair_of_sets1]) ).
fof(c_0_7,plain,
! [X120,X121] :
( ( first(ordered_pair(X120,X121)) = X120
| ~ member(X120,universal_class)
| ~ member(X121,universal_class) )
& ( second(ordered_pair(X120,X121)) = X121
| ~ member(X120,universal_class)
| ~ member(X121,universal_class) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[first_second])])]) ).
cnf(c_0_8,plain,
ordered_pair(X1,X2) = unordered_pair(singleton(X1),unordered_pair(X1,singleton(X2))),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_9,plain,
singleton(X1) = unordered_pair(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_10,negated_conjecture,
( member(esk8_0,universal_class)
& member(esk9_0,universal_class)
& esk10_0 = ordered_pair(esk8_0,esk9_0)
& ( first(esk10_0) != esk8_0
| second(esk10_0) != esk9_0 ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).
cnf(c_0_11,plain,
( first(ordered_pair(X1,X2)) = X1
| ~ member(X1,universal_class)
| ~ member(X2,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).
cnf(c_0_13,negated_conjecture,
esk10_0 = ordered_pair(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( second(ordered_pair(X1,X2)) = X2
| ~ member(X1,universal_class)
| ~ member(X2,universal_class) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,plain,
( first(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))) = X1
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,negated_conjecture,
esk10_0 = unordered_pair(unordered_pair(esk8_0,esk8_0),unordered_pair(esk8_0,unordered_pair(esk9_0,esk9_0))),
inference(rw,[status(thm)],[c_0_13,c_0_12]) ).
cnf(c_0_17,negated_conjecture,
member(esk9_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,negated_conjecture,
member(esk8_0,universal_class),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_19,plain,
( second(unordered_pair(unordered_pair(X1,X1),unordered_pair(X1,unordered_pair(X2,X2)))) = X2
| ~ member(X2,universal_class)
| ~ member(X1,universal_class) ),
inference(rw,[status(thm)],[c_0_14,c_0_12]) ).
cnf(c_0_20,negated_conjecture,
( first(esk10_0) != esk8_0
| second(esk10_0) != esk9_0 ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_21,negated_conjecture,
first(esk10_0) = esk8_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_22,negated_conjecture,
second(esk10_0) = esk9_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_16]),c_0_17]),c_0_18])]) ).
cnf(c_0_23,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_21])]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET020+1 : TPTP v9.2.1. Bugfixed v5.4.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:05:11 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.31/1.73 % Version : CSE_E---1.7
% 1.31/1.73 % Problem : theBenchmark.p
% 1.31/1.73 % SZS status Theorem for theBenchmark.p
% 1.31/1.73 % SZS output start CNFRefutation
% See solution above
% 1.31/1.73 % Total time : 1.370s
%------------------------------------------------------------------------------