%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET988+1 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 05:09:05 PM UTC 2026
% Result : Theorem 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 5
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 98 ( 30 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 98 ( 37 ~; 37 |; 17 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 1 con; 0-2 aty)
% Number of variables : 79 ( 4 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(t2_funct_1,conjecture,
! [X1] :
( ( ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : ordered_pair(X3,X4) != X2 )
& ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X4),X1) )
=> X3 = X4 ) )
=> ( relation(X1)
& function(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2_funct_1) ).
fof(d1_relat_1,axiom,
! [X1] :
( relation(X1)
<=> ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : X2 != ordered_pair(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_relat_1) ).
fof(d5_tarski,axiom,
! [X1,X2] : ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5_tarski) ).
fof(commutativity_k2_tarski,axiom,
! [X1,X2] : unordered_pair(X1,X2) = unordered_pair(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(d1_funct_1,axiom,
! [X1] :
( function(X1)
<=> ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X4),X1) )
=> X3 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_funct_1) ).
fof(c_0_5,negated_conjecture,
~ ! [X1] :
( ( ! [X2] :
~ ( in(X2,X1)
& ! [X3,X4] : ordered_pair(X3,X4) != X2 )
& ! [X2,X3,X4] :
( ( in(ordered_pair(X2,X3),X1)
& in(ordered_pair(X2,X4),X1) )
=> X3 = X4 ) )
=> ( relation(X1)
& function(X1) ) ),
inference(assume_negation,[status(cth)],[t2_funct_1]) ).
fof(c_0_6,plain,
! [X124,X125,X128,X130,X131] :
( ( ~ relation(X124)
| ~ in(X125,X124)
| X125 = ordered_pair(esk16_2(X124,X125),esk17_2(X124,X125)) )
& ( in(esk18_1(X128),X128)
| relation(X128) )
& ( esk18_1(X128) != ordered_pair(X130,X131)
| relation(X128) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_relat_1])])])])])]) ).
fof(c_0_7,plain,
! [X107,X108] : ordered_pair(X107,X108) = unordered_pair(unordered_pair(X107,X108),singleton(X107)),
inference(variable_rename,[status(thm)],[d5_tarski]) ).
fof(c_0_8,negated_conjecture,
! [X110,X113,X114,X115] :
( ( ~ in(X110,esk10_0)
| ordered_pair(esk11_1(X110),esk12_1(X110)) = X110 )
& ( ~ in(ordered_pair(X113,X114),esk10_0)
| ~ in(ordered_pair(X113,X115),esk10_0)
| X114 = X115 )
& ( ~ relation(esk10_0)
| ~ function(esk10_0) ) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])])]) ).
cnf(c_0_9,plain,
( relation(X1)
| esk18_1(X1) != ordered_pair(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,plain,
ordered_pair(X1,X2) = unordered_pair(unordered_pair(X1,X2),singleton(X1)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X66,X67] : unordered_pair(X66,X67) = unordered_pair(X67,X66),
inference(variable_rename,[status(thm)],[commutativity_k2_tarski]) ).
cnf(c_0_12,negated_conjecture,
( ordered_pair(esk11_1(X1),esk12_1(X1)) = X1
| ~ in(X1,esk10_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( relation(X1)
| esk18_1(X1) != unordered_pair(unordered_pair(X2,X3),singleton(X2)) ),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_14,plain,
unordered_pair(X1,X2) = unordered_pair(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,negated_conjecture,
( unordered_pair(unordered_pair(esk11_1(X1),esk12_1(X1)),singleton(esk11_1(X1))) = X1
| ~ in(X1,esk10_0) ),
inference(rw,[status(thm)],[c_0_12,c_0_10]) ).
fof(c_0_16,plain,
! [X116,X117,X118,X119,X120] :
( ( ~ function(X116)
| ~ in(ordered_pair(X117,X118),X116)
| ~ in(ordered_pair(X117,X119),X116)
| X118 = X119 )
& ( in(ordered_pair(esk13_1(X120),esk14_1(X120)),X120)
| function(X120) )
& ( in(ordered_pair(esk13_1(X120),esk15_1(X120)),X120)
| function(X120) )
& ( esk14_1(X120) != esk15_1(X120)
| function(X120) ) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[d1_funct_1])])])])])]) ).
cnf(c_0_17,plain,
( relation(X1)
| esk18_1(X1) != unordered_pair(singleton(X2),unordered_pair(X2,X3)) ),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,negated_conjecture,
( unordered_pair(singleton(esk11_1(X1)),unordered_pair(esk11_1(X1),esk12_1(X1))) = X1
| ~ in(X1,esk10_0) ),
inference(rw,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( X2 = X3
| ~ in(ordered_pair(X1,X2),esk10_0)
| ~ in(ordered_pair(X1,X3),esk10_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_20,plain,
( in(ordered_pair(esk13_1(X1),esk14_1(X1)),X1)
| function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( relation(X1)
| ~ in(esk18_1(X1),esk10_0) ),
inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18])]) ).
cnf(c_0_22,plain,
( in(esk18_1(X1),X1)
| relation(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_23,negated_conjecture,
( X2 = X3
| ~ in(unordered_pair(unordered_pair(X1,X3),singleton(X1)),esk10_0)
| ~ in(unordered_pair(unordered_pair(X1,X2),singleton(X1)),esk10_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_10]),c_0_10]) ).
cnf(c_0_24,plain,
( function(X1)
| in(unordered_pair(unordered_pair(esk13_1(X1),esk14_1(X1)),singleton(esk13_1(X1))),X1) ),
inference(rw,[status(thm)],[c_0_20,c_0_10]) ).
cnf(c_0_25,negated_conjecture,
( ~ relation(esk10_0)
| ~ function(esk10_0) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_26,negated_conjecture,
relation(esk10_0),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
( in(ordered_pair(esk13_1(X1),esk15_1(X1)),X1)
| function(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_28,negated_conjecture,
( X1 = X2
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X2)),esk10_0)
| ~ in(unordered_pair(singleton(X3),unordered_pair(X3,X1)),esk10_0) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_14]),c_0_14]) ).
cnf(c_0_29,plain,
( in(unordered_pair(singleton(esk13_1(X1)),unordered_pair(esk13_1(X1),esk14_1(X1))),X1)
| function(X1) ),
inference(rw,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_30,negated_conjecture,
~ function(esk10_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_26])]) ).
cnf(c_0_31,plain,
( function(X1)
| in(unordered_pair(unordered_pair(esk13_1(X1),esk15_1(X1)),singleton(esk13_1(X1))),X1) ),
inference(rw,[status(thm)],[c_0_27,c_0_10]) ).
cnf(c_0_32,negated_conjecture,
( X1 = esk14_1(esk10_0)
| ~ in(unordered_pair(singleton(esk13_1(esk10_0)),unordered_pair(esk13_1(esk10_0),X1)),esk10_0) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
cnf(c_0_33,plain,
( in(unordered_pair(singleton(esk13_1(X1)),unordered_pair(esk13_1(X1),esk15_1(X1))),X1)
| function(X1) ),
inference(rw,[status(thm)],[c_0_31,c_0_14]) ).
cnf(c_0_34,plain,
( function(X1)
| esk14_1(X1) != esk15_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_35,negated_conjecture,
esk15_1(esk10_0) = esk14_1(esk10_0),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_30]) ).
cnf(c_0_36,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_30]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET988+1 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.32 % Computer : n015.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 02:41:17 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Theorem for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------