%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET788+1 : TPTP v9.2.1. Released v3.1.0.
% 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 : n027.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 05:08:29 PM UTC 2026
% Result : Theorem 0.36s 1.61s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 1
% Syntax : Number of formulae : 45 ( 7 unt; 0 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 147 ( 68 ~; 66 |; 5 &)
% ( 6 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_this,conjecture,
( ! [X1,X2] :
( equalish(X1,X2)
<=> ! [X3] :
( a_member_of(X3,X1)
<=> a_member_of(X3,X2) ) )
=> ! [X1,X2] :
( equalish(X1,X2)
<=> equalish(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(i_0_1,negated_conjecture,
~ ( ! [X1,X2] :
( equalish(X1,X2)
<=> ! [X3] :
( a_member_of(X3,X1)
<=> a_member_of(X3,X2) ) )
=> ! [X1,X2] :
( equalish(X1,X2)
<=> equalish(X2,X1) ) ),
inference(assume_negation,[status(cth)],[prove_this]) ).
fof(i_0_2,negated_conjecture,
! [X9,X10,X11,X12,X13,X14] :
( ( ~ a_member_of(X11,X9)
| a_member_of(X11,X10)
| ~ equalish(X9,X10) )
& ( ~ a_member_of(X12,X10)
| a_member_of(X12,X9)
| ~ equalish(X9,X10) )
& ( ~ a_member_of(esk1_2(X13,X14),X13)
| ~ a_member_of(esk1_2(X13,X14),X14)
| equalish(X13,X14) )
& ( a_member_of(esk1_2(X13,X14),X13)
| a_member_of(esk1_2(X13,X14),X14)
| equalish(X13,X14) )
& ( ~ equalish(esk2_0,esk3_0)
| ~ equalish(esk3_0,esk2_0) )
& ( equalish(esk2_0,esk3_0)
| equalish(esk3_0,esk2_0) ) ),
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)],[i_0_1])])])])])]) ).
cnf(i_0_3,negated_conjecture,
( equalish(X1,X2)
| ~ a_member_of(esk1_2(X1,X2),X1)
| ~ a_member_of(esk1_2(X1,X2),X2) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_4,negated_conjecture,
( a_member_of(esk1_2(X1,X2),X1)
| a_member_of(esk1_2(X1,X2),X2)
| equalish(X1,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_5,negated_conjecture,
( a_member_of(X1,X3)
| ~ a_member_of(X1,X2)
| ~ equalish(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_6,negated_conjecture,
( a_member_of(X1,X3)
| ~ a_member_of(X1,X2)
| ~ equalish(X3,X2) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_7,negated_conjecture,
( ~ equalish(esk2_0,esk3_0)
| ~ equalish(esk3_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_8,negated_conjecture,
( equalish(esk2_0,esk3_0)
| equalish(esk3_0,esk2_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_9,plain,
( ~ equalish(esk3_0,esk2_0)
| equalish(esk3_0,esk2_0) ),
inference(scs_inference,[],[i_0_7,i_0_8]) ).
cnf(i_0_10,plain,
( a_member_of(X1,esk3_0)
| ~ a_member_of(X1,esk2_0)
| equalish(esk3_0,esk2_0) ),
inference(scs_inference,[],[i_0_5,i_0_8]) ).
cnf(i_0_11,plain,
( a_member_of(X1,esk2_0)
| ~ a_member_of(X1,esk3_0)
| equalish(esk3_0,esk2_0) ),
inference(scs_inference,[],[i_0_6,i_0_8]) ).
cnf(i_0_12,plain,
( ~ a_member_of(X1,esk3_0)
| a_member_of(X1,esk3_0)
| equalish(esk3_0,esk2_0) ),
inference(scs_inference,[],[i_0_10,i_0_11]) ).
cnf(i_0_13,plain,
( ~ a_member_of(esk1_2(esk2_0,esk3_0),esk2_0)
| ~ a_member_of(esk1_2(esk2_0,esk3_0),esk3_0)
| ~ equalish(esk3_0,esk2_0) ),
inference(scs_inference,[],[i_0_3,i_0_7]) ).
cnf(i_0_14,plain,
( a_member_of(esk1_2(esk2_0,esk3_0),esk2_0)
| a_member_of(esk1_2(esk2_0,esk3_0),esk3_0)
| ~ equalish(esk3_0,esk2_0) ),
inference(scs_inference,[],[i_0_4,i_0_7]) ).
cnf(i_0_15,plain,
( ~ a_member_of(esk1_2(esk2_0,esk3_0),esk2_0)
| a_member_of(esk1_2(esk2_0,esk3_0),esk2_0)
| ~ equalish(esk3_0,esk2_0) ),
inference(scs_inference,[],[i_0_13,i_0_14]) ).
cnf(i_0_16,plain,
( ~ equalish(esk2_0,esk3_0)
| equalish(esk2_0,esk3_0) ),
inference(scs_inference,[],[i_0_7,i_0_8]) ).
cnf(i_0_17,plain,
( ~ a_member_of(esk1_2(esk3_0,esk2_0),esk3_0)
| ~ a_member_of(esk1_2(esk3_0,esk2_0),esk2_0)
| ~ equalish(esk2_0,esk3_0) ),
inference(scs_inference,[],[i_0_7,i_0_3]) ).
cnf(i_0_18,plain,
( ~ a_member_of(esk1_2(esk3_0,esk2_0),esk3_0)
| ~ equalish(esk2_0,esk3_0)
| equalish(esk3_0,esk2_0) ),
inference(scs_inference,[],[i_0_17,i_0_11]) ).
cnf(i_0_19,plain,
( ~ a_member_of(esk1_2(esk3_0,esk2_0),esk2_0)
| ~ equalish(esk2_0,esk3_0)
| equalish(esk3_0,esk2_0) ),
inference(scs_inference,[],[i_0_18,i_0_10]) ).
cnf(i_0_20,plain,
( ~ a_member_of(esk1_2(esk3_0,esk2_0),esk2_0)
| equalish(esk3_0,esk2_0) ),
inference(scs_inference,[],[i_0_19,i_0_8]) ).
cnf(i_0_21,plain,
( equalish(esk3_0,esk2_0)
| a_member_of(esk1_2(esk3_0,esk2_0),esk3_0) ),
inference(scs_inference,[],[i_0_20,i_0_4]) ).
cnf(i_0_22,plain,
( a_member_of(esk1_2(esk3_0,esk2_0),esk3_0)
| ~ equalish(esk2_0,esk3_0) ),
inference(scs_inference,[],[i_0_21,i_0_7]) ).
cnf(i_0_23,plain,
( ~ equalish(esk3_0,X1)
| a_member_of(esk1_2(esk3_0,esk2_0),X1)
| ~ equalish(esk2_0,esk3_0) ),
inference(scs_inference,[],[i_0_22,i_0_5]) ).
cnf(i_0_24,plain,
( ~ a_member_of(esk1_2(esk3_0,esk2_0),esk2_0)
| ~ equalish(esk3_0,esk3_0)
| ~ equalish(esk2_0,esk3_0) ),
inference(scs_inference,[],[i_0_23,i_0_17]) ).
cnf(i_0_25,plain,
( ~ a_member_of(esk1_2(esk3_0,esk2_0),esk2_0)
| ~ a_member_of(esk1_2(esk3_0,esk3_0),esk3_0)
| ~ equalish(esk2_0,esk3_0) ),
inference(scs_inference,[],[i_0_24,i_0_3]) ).
cnf(i_0_26,plain,
( equalish(esk3_0,esk3_0)
| ~ a_member_of(esk1_2(esk3_0,esk2_0),esk2_0)
| ~ equalish(esk2_0,esk3_0) ),
inference(scs_inference,[],[i_0_25,i_0_4]) ).
cnf(i_0_27,plain,
( ~ a_member_of(esk1_2(esk3_0,esk2_0),esk2_0)
| ~ equalish(esk2_0,esk3_0) ),
inference(scs_inference,[],[i_0_26,i_0_24]) ).
cnf(i_0_28,plain,
( ~ equalish(esk2_0,X1)
| ~ a_member_of(esk1_2(esk3_0,esk2_0),X1)
| ~ equalish(esk2_0,esk3_0) ),
inference(scs_inference,[],[i_0_27,i_0_6]) ).
cnf(i_0_29,plain,
( ~ equalish(esk2_0,esk3_0)
| equalish(esk3_0,esk2_0) ),
inference(scs_inference,[],[i_0_28,i_0_21]) ).
cnf(i_0_30,plain,
equalish(esk3_0,esk2_0),
inference(scs_inference,[],[i_0_29,i_0_8]) ).
cnf(i_0_31,plain,
~ equalish(esk2_0,esk3_0),
inference(scs_inference,[],[i_0_30,i_0_7]) ).
cnf(i_0_32,plain,
( ~ a_member_of(esk1_2(esk2_0,esk3_0),esk2_0)
| ~ a_member_of(esk1_2(esk2_0,esk3_0),esk3_0) ),
inference(scs_inference,[],[i_0_30,i_0_13]) ).
cnf(i_0_33,plain,
( a_member_of(esk1_2(esk2_0,esk3_0),esk3_0)
| a_member_of(esk1_2(esk2_0,esk3_0),esk2_0) ),
inference(scs_inference,[],[i_0_30,i_0_14]) ).
cnf(i_0_34,plain,
( ~ a_member_of(esk1_2(esk2_0,esk3_0),esk2_0)
| a_member_of(esk1_2(esk2_0,esk3_0),esk2_0) ),
inference(scs_inference,[],[i_0_30,i_0_15]) ).
cnf(i_0_35,plain,
~ equalish(esk2_0,esk3_0),
inference(scs_inference,[],[i_0_31,i_0_16]) ).
cnf(i_0_36,plain,
( a_member_of(X1,esk2_0)
| ~ a_member_of(X1,esk3_0) ),
inference(scs_inference,[],[i_0_30,i_0_5]) ).
cnf(i_0_37,plain,
( ~ equalish(X1,X2)
| a_member_of(X3,X2)
| ~ a_member_of(X3,X1) ),
inference(rename_variables,[],[i_0_5]) ).
cnf(i_0_38,plain,
( a_member_of(X1,esk3_0)
| ~ a_member_of(X1,esk3_0) ),
inference(scs_inference,[],[i_0_30,i_0_5,i_0_6]) ).
cnf(i_0_39,plain,
( ~ equalish(X1,X2)
| a_member_of(X3,X1)
| ~ a_member_of(X3,X2) ),
inference(rename_variables,[],[i_0_6]) ).
cnf(i_0_40,plain,
~ a_member_of(esk1_2(esk2_0,esk3_0),esk3_0),
inference(scs_inference,[],[i_0_35,i_0_30,i_0_5,i_0_6,i_0_32,i_0_3]) ).
cnf(i_0_41,plain,
a_member_of(esk1_2(esk2_0,esk3_0),esk2_0),
inference(scs_inference,[],[i_0_40,i_0_33]) ).
cnf(i_0_42,plain,
~ a_member_of(esk1_2(esk2_0,esk3_0),esk2_0),
inference(scs_inference,[],[i_0_40,i_0_30,i_0_6]) ).
cnf(i_0_43,plain,
( ~ equalish(X1,X2)
| a_member_of(X3,X1)
| ~ a_member_of(X3,X2) ),
inference(rename_variables,[],[i_0_6]) ).
cnf(i_0_44,plain,
$false,
inference(scs_inference,[],[i_0_35,i_0_40,i_0_30,i_0_6,i_0_4]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET788+1 : TPTP v9.2.1. Released v3.1.0.
% 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
% 0.15/0.32 % Computer : n027.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 02:35:34 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.33 % start to proof: theBenchmark
% 0.36/1.61 % Version : CSE_E---1.7
% 0.36/1.61 % Problem : theBenchmark.p
% 0.36/1.61 % SZS status Theorem for theBenchmark.p
% 0.36/1.61 % SZS output start CNFRefutation
% See solution above
% 0.36/1.67 % Total time : 1.271s
%------------------------------------------------------------------------------