%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SEV515+1 : TPTP v9.2.1. Released v7.0.0.
% 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 : n019.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 05:15:20 PM UTC 2026
% Result : Theorem 1.46s 1.78s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 88 ( 11 unt; 0 def)
% Number of atoms : 653 ( 0 equ)
% Maximal formula atoms : 284 ( 7 avg)
% Number of connectives : 724 ( 159 ~; 490 |; 70 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 52 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-1 aty)
% Number of variables : 113 ( 3 sgn 28 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(nc1,conjecture,
( ! [X1] :
? [X2] :
( ( g_true_only(X2,X1)
& ( g_both(X2,X2)
| g_true_only(X2,X2) ) )
| ( g_both(X2,X1)
& ( g_false_only(X2,X2)
| g_true_only(X2,X2) ) )
| ( g_false_only(X2,X1)
& ( g_false_only(X2,X2)
| g_both(X2,X2) ) ) )
| ( ? [X1] :
( ? [X2] :
( g_both(X2,X1)
& g_both(X2,X2) )
& ~ ? [X2] :
( ( g_true_only(X2,X1)
& ( g_both(X2,X2)
| g_true_only(X2,X2) ) )
| ( g_both(X2,X1)
& ( g_false_only(X2,X2)
| g_true_only(X2,X2) ) )
| ( g_false_only(X2,X1)
& ( g_false_only(X2,X2)
| g_both(X2,X2) ) ) ) )
& ~ ? [X1] :
! [X2] :
( ( g_true_only(X2,X1)
& g_false_only(X2,X2) )
| ( g_false_only(X2,X1)
& g_true_only(X2,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nc1) ).
fof(exhaustion_g,axiom,
! [X3,X4] :
( g_true_only(X3,X4)
| g_both(X3,X4)
| g_false_only(X3,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exhaustion_g) ).
fof(true_only_g,axiom,
! [X3,X4] :
( g_true_only(X3,X4)
<=> ( g_true(X3,X4)
& ~ g_false(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',true_only_g) ).
fof(false_only_g,axiom,
! [X3,X4] :
( g_false_only(X3,X4)
<=> ( g_false(X3,X4)
& ~ g_true(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',false_only_g) ).
fof(both_g,axiom,
! [X3,X4] :
( g_both(X3,X4)
<=> ( g_true(X3,X4)
& g_false(X3,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',both_g) ).
fof(c_0_5,negated_conjecture,
~ ( ! [X1] :
? [X2] :
( ( g_true_only(X2,X1)
& ( g_both(X2,X2)
| g_true_only(X2,X2) ) )
| ( g_both(X2,X1)
& ( g_false_only(X2,X2)
| g_true_only(X2,X2) ) )
| ( g_false_only(X2,X1)
& ( g_false_only(X2,X2)
| g_both(X2,X2) ) ) )
| ( ? [X1] :
( ? [X2] :
( g_both(X2,X1)
& g_both(X2,X2) )
& ~ ? [X2] :
( ( g_true_only(X2,X1)
& ( g_both(X2,X2)
| g_true_only(X2,X2) ) )
| ( g_both(X2,X1)
& ( g_false_only(X2,X2)
| g_true_only(X2,X2) ) )
| ( g_false_only(X2,X1)
& ( g_false_only(X2,X2)
| g_both(X2,X2) ) ) ) )
& ~ ? [X1] :
! [X2] :
( ( g_true_only(X2,X1)
& g_false_only(X2,X2) )
| ( g_false_only(X2,X1)
& g_true_only(X2,X2) ) ) ) ),
inference(assume_negation,[status(cth)],[nc1]) ).
fof(c_0_6,negated_conjecture,
! [X21,X22,X23,X28] :
( ( ~ g_both(X21,X21)
| ~ g_true_only(X21,esk1_0) )
& ( ~ g_true_only(X21,X21)
| ~ g_true_only(X21,esk1_0) )
& ( ~ g_false_only(X21,X21)
| ~ g_both(X21,esk1_0) )
& ( ~ g_true_only(X21,X21)
| ~ g_both(X21,esk1_0) )
& ( ~ g_false_only(X21,X21)
| ~ g_false_only(X21,esk1_0) )
& ( ~ g_both(X21,X21)
| ~ g_false_only(X21,esk1_0) )
& ( g_false_only(X28,esk5_0)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),X22)
| g_both(esk3_1(X22),X22)
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),X22)
| g_both(esk3_1(X22),X22)
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),X22)
| g_both(esk3_1(X22),X22)
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),X22)
| g_both(esk3_1(X22),X22)
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_both(esk3_1(X22),X22)
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_both(esk3_1(X22),X22)
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_both(esk3_1(X22),X22)
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_both(esk3_1(X22),X22)
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),X22)
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),X22)
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),X22)
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),X22)
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk2_1(X22),X22)
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),X22)
| g_both(esk3_1(X22),X22)
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),X22)
| g_both(esk3_1(X22),X22)
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),X22)
| g_both(esk3_1(X22),X22)
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),X22)
| g_both(esk3_1(X22),X22)
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_both(esk3_1(X22),X22)
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_both(esk3_1(X22),X22)
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_both(esk3_1(X22),X22)
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_both(esk3_1(X22),X22)
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),X22)
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),X22)
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),X22)
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),X22)
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_true_only(X28,esk5_0)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_false_only(X28,esk5_0)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) )
& ( g_true_only(X28,X28)
| g_false_only(X28,X28)
| g_false_only(esk4_1(X22),esk4_1(X22))
| g_both(esk4_1(X22),esk4_1(X22))
| g_false_only(esk3_1(X22),esk3_1(X22))
| g_true_only(esk3_1(X22),esk3_1(X22))
| g_both(esk2_1(X22),esk2_1(X22))
| g_true_only(esk2_1(X22),esk2_1(X22))
| ~ g_both(X23,X22)
| ~ g_both(X23,X23) ) ),
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)],[c_0_5])])])])])]) ).
fof(c_0_7,plain,
! [X35,X36] :
( g_true_only(X35,X36)
| g_both(X35,X36)
| g_false_only(X35,X36) ),
inference(variable_rename,[status(thm)],[exhaustion_g]) ).
cnf(c_0_8,negated_conjecture,
( ~ g_true_only(X1,X1)
| ~ g_true_only(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_9,plain,
( g_true_only(X1,X2)
| g_both(X1,X2)
| g_false_only(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_10,negated_conjecture,
( ~ g_true_only(X1,X1)
| ~ g_both(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_11,negated_conjecture,
( g_false_only(X1,esk1_0)
| ~ g_true_only(X1,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_10]) ).
cnf(c_0_12,negated_conjecture,
( g_false_only(X1,esk1_0)
| g_false_only(X1,X1)
| g_both(X1,X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_9]) ).
cnf(c_0_13,negated_conjecture,
( ~ g_false_only(X1,X1)
| ~ g_false_only(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_14,negated_conjecture,
( g_false_only(esk1_0,esk1_0)
| g_both(esk1_0,esk1_0) ),
inference(ef,[status(thm)],[c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( g_true_only(X1,X1)
| g_false_only(X1,X1)
| g_false_only(esk4_1(X2),X2)
| g_both(esk3_1(X2),X2)
| g_true_only(esk2_1(X2),X2)
| ~ g_both(X3,X2)
| ~ g_both(X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_16,negated_conjecture,
g_both(esk1_0,esk1_0),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_14]) ).
cnf(c_0_17,negated_conjecture,
( g_true_only(X1,X1)
| g_false_only(X1,X1)
| g_false_only(esk4_1(X2),X2)
| g_false_only(esk3_1(X2),esk3_1(X2))
| g_true_only(esk3_1(X2),esk3_1(X2))
| g_true_only(esk2_1(X2),X2)
| ~ g_both(X3,X2)
| ~ g_both(X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_18,negated_conjecture,
( g_false_only(esk4_1(X1),X1)
| g_false_only(X2,X2)
| g_both(esk3_1(X1),X1)
| g_true_only(esk2_1(X1),X1)
| g_true_only(X2,X2)
| ~ g_both(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( g_false_only(esk3_1(X1),esk3_1(X1))
| g_false_only(esk4_1(X1),X1)
| g_false_only(X2,X2)
| g_true_only(esk3_1(X1),esk3_1(X1))
| g_true_only(esk2_1(X1),X1)
| g_true_only(X2,X2)
| ~ g_both(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk1_0)
| g_false_only(X1,X1)
| g_both(esk3_1(esk1_0),esk1_0)
| g_true_only(esk2_1(esk1_0),esk1_0)
| g_true_only(X1,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
( ~ g_false_only(X1,X1)
| ~ g_both(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_22,negated_conjecture,
( g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_false_only(esk4_1(esk1_0),esk1_0)
| g_false_only(X1,X1)
| g_true_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_true_only(esk2_1(esk1_0),esk1_0)
| g_true_only(X1,X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_23,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk1_0)
| g_both(esk3_1(esk1_0),esk1_0)
| g_true_only(esk2_1(esk1_0),esk1_0)
| ~ g_both(X1,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_20]),c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_false_only(esk4_1(esk1_0),esk1_0)
| g_true_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_true_only(esk2_1(esk1_0),esk1_0) ),
inference(ef,[status(thm)],[c_0_22]) ).
cnf(c_0_25,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk1_0)
| g_both(esk3_1(esk1_0),esk1_0)
| g_true_only(esk2_1(esk1_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_16]) ).
fof(c_0_26,plain,
! [X3,X4] :
( g_true_only(X3,X4)
<=> ( g_true(X3,X4)
& ~ g_false(X3,X4) ) ),
inference(fof_simplification,[status(thm)],[true_only_g]) ).
cnf(c_0_27,negated_conjecture,
( g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_false_only(esk4_1(esk1_0),esk1_0)
| g_true_only(esk2_1(esk1_0),esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_24]),c_0_25]) ).
fof(c_0_28,plain,
! [X3,X4] :
( g_false_only(X3,X4)
<=> ( g_false(X3,X4)
& ~ g_true(X3,X4) ) ),
inference(fof_simplification,[status(thm)],[false_only_g]) ).
fof(c_0_29,plain,
! [X29,X30] :
( ( g_true(X29,X30)
| ~ g_true_only(X29,X30) )
& ( ~ g_false(X29,X30)
| ~ g_true_only(X29,X30) )
& ( ~ g_true(X29,X30)
| g_false(X29,X30)
| g_true_only(X29,X30) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_26])])]) ).
fof(c_0_30,plain,
! [X31,X32] :
( ( g_true(X31,X32)
| ~ g_both(X31,X32) )
& ( g_false(X31,X32)
| ~ g_both(X31,X32) )
& ( ~ g_true(X31,X32)
| ~ g_false(X31,X32)
| g_both(X31,X32) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[both_g])])]) ).
cnf(c_0_31,negated_conjecture,
( g_true_only(X1,X1)
| g_false_only(X1,X1)
| g_false_only(esk4_1(X2),X2)
| g_both(esk3_1(X2),X2)
| g_both(esk2_1(X2),esk2_1(X2))
| g_true_only(esk2_1(X2),esk2_1(X2))
| ~ g_both(X3,X2)
| ~ g_both(X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_32,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk1_0)
| g_true_only(esk2_1(esk1_0),esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_27]),c_0_25]) ).
cnf(c_0_33,negated_conjecture,
( ~ g_both(X1,X1)
| ~ g_true_only(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_34,plain,
! [X33,X34] :
( ( g_false(X33,X34)
| ~ g_false_only(X33,X34) )
& ( ~ g_true(X33,X34)
| ~ g_false_only(X33,X34) )
& ( ~ g_false(X33,X34)
| g_true(X33,X34)
| g_false_only(X33,X34) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_28])])]) ).
cnf(c_0_35,plain,
( ~ g_false(X1,X2)
| ~ g_true_only(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_36,plain,
( g_false(X1,X2)
| ~ g_both(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_37,negated_conjecture,
( g_false_only(esk4_1(X1),X1)
| g_false_only(X2,X2)
| g_both(esk2_1(X1),esk2_1(X1))
| g_both(esk3_1(X1),X1)
| g_true_only(esk2_1(X1),esk2_1(X1))
| g_true_only(X2,X2)
| ~ g_both(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_16]) ).
cnf(c_0_38,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk1_0)
| ~ g_true_only(esk2_1(esk1_0),esk2_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_8,c_0_32]) ).
cnf(c_0_39,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk1_0)
| ~ g_both(esk2_1(esk1_0),esk2_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_32]) ).
cnf(c_0_40,plain,
( ~ g_true(X1,X2)
| ~ g_false_only(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
( g_true(X1,X2)
| ~ g_both(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_42,negated_conjecture,
( g_true_only(X1,X1)
| g_false_only(X1,X1)
| g_false_only(esk4_1(X2),esk4_1(X2))
| g_both(esk4_1(X2),esk4_1(X2))
| g_both(esk3_1(X2),X2)
| g_true_only(esk2_1(X2),X2)
| ~ g_both(X3,X2)
| ~ g_both(X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_43,plain,
( ~ g_both(X1,X2)
| ~ g_true_only(X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_44,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk1_0)
| g_false_only(X1,X1)
| g_both(esk3_1(esk1_0),esk1_0)
| g_true_only(X1,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_16]),c_0_38]),c_0_39]) ).
cnf(c_0_45,plain,
( ~ g_false_only(X1,X2)
| ~ g_both(X1,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_46,negated_conjecture,
( g_false_only(esk4_1(X1),esk4_1(X1))
| g_false_only(X2,X2)
| g_both(esk4_1(X1),esk4_1(X1))
| g_both(esk3_1(X1),X1)
| g_true_only(esk2_1(X1),X1)
| g_true_only(X2,X2)
| ~ g_both(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_42,c_0_16]) ).
cnf(c_0_47,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk1_0)
| g_both(esk3_1(esk1_0),esk1_0)
| ~ g_both(X1,X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_48,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk4_1(esk1_0))
| g_false_only(X1,X1)
| g_both(esk4_1(esk1_0),esk4_1(esk1_0))
| g_both(esk3_1(esk1_0),esk1_0)
| g_true_only(esk2_1(esk1_0),esk1_0)
| g_true_only(X1,X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_16]) ).
cnf(c_0_49,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk1_0)
| g_both(esk3_1(esk1_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_47,c_0_16]) ).
cnf(c_0_50,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk4_1(esk1_0))
| g_both(esk4_1(esk1_0),esk4_1(esk1_0))
| g_both(esk3_1(esk1_0),esk1_0)
| g_true_only(esk2_1(esk1_0),esk1_0)
| ~ g_both(X1,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_48]),c_0_21]) ).
cnf(c_0_51,negated_conjecture,
( ~ g_both(X1,X1)
| ~ g_false_only(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_52,negated_conjecture,
( g_both(esk3_1(esk1_0),esk1_0)
| ~ g_false_only(esk4_1(esk1_0),esk4_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_13,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk4_1(esk1_0))
| g_both(esk4_1(esk1_0),esk4_1(esk1_0))
| g_both(esk3_1(esk1_0),esk1_0)
| g_true_only(esk2_1(esk1_0),esk1_0) ),
inference(spm,[status(thm)],[c_0_50,c_0_16]) ).
cnf(c_0_54,negated_conjecture,
( g_both(esk3_1(esk1_0),esk1_0)
| ~ g_both(esk4_1(esk1_0),esk4_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_51,c_0_49]) ).
cnf(c_0_55,negated_conjecture,
( g_true_only(X1,X1)
| g_false_only(X1,X1)
| g_false_only(esk4_1(X2),esk4_1(X2))
| g_both(esk4_1(X2),esk4_1(X2))
| g_both(esk3_1(X2),X2)
| g_both(esk2_1(X2),esk2_1(X2))
| g_true_only(esk2_1(X2),esk2_1(X2))
| ~ g_both(X3,X2)
| ~ g_both(X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_56,negated_conjecture,
( g_both(esk3_1(esk1_0),esk1_0)
| g_true_only(esk2_1(esk1_0),esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_57,negated_conjecture,
( g_false_only(esk4_1(X1),esk4_1(X1))
| g_false_only(X2,X2)
| g_both(esk4_1(X1),esk4_1(X1))
| g_both(esk2_1(X1),esk2_1(X1))
| g_both(esk3_1(X1),X1)
| g_true_only(esk2_1(X1),esk2_1(X1))
| g_true_only(X2,X2)
| ~ g_both(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_16]) ).
cnf(c_0_58,negated_conjecture,
( g_both(esk3_1(esk1_0),esk1_0)
| ~ g_true_only(esk2_1(esk1_0),esk2_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_8,c_0_56]) ).
cnf(c_0_59,negated_conjecture,
( g_both(esk3_1(esk1_0),esk1_0)
| ~ g_both(esk2_1(esk1_0),esk2_1(esk1_0)) ),
inference(spm,[status(thm)],[c_0_33,c_0_56]) ).
cnf(c_0_60,negated_conjecture,
( g_true_only(X1,X1)
| g_false_only(X1,X1)
| g_false_only(esk4_1(X2),X2)
| g_false_only(esk3_1(X2),esk3_1(X2))
| g_true_only(esk3_1(X2),esk3_1(X2))
| g_both(esk2_1(X2),esk2_1(X2))
| g_true_only(esk2_1(X2),esk2_1(X2))
| ~ g_both(X3,X2)
| ~ g_both(X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_61,negated_conjecture,
( g_false_only(X1,X1)
| g_both(esk3_1(esk1_0),esk1_0)
| g_true_only(X1,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_16]),c_0_58]),c_0_59]),c_0_54]),c_0_52]) ).
cnf(c_0_62,negated_conjecture,
( g_false_only(esk3_1(X1),esk3_1(X1))
| g_false_only(esk4_1(X1),X1)
| g_false_only(X2,X2)
| g_both(esk2_1(X1),esk2_1(X1))
| g_true_only(esk3_1(X1),esk3_1(X1))
| g_true_only(esk2_1(X1),esk2_1(X1))
| g_true_only(X2,X2)
| ~ g_both(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_60,c_0_16]) ).
cnf(c_0_63,negated_conjecture,
( g_both(esk3_1(esk1_0),esk1_0)
| ~ g_both(X1,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_61]),c_0_21]) ).
cnf(c_0_64,negated_conjecture,
( g_true_only(X1,X1)
| g_false_only(X1,X1)
| g_false_only(esk4_1(X2),esk4_1(X2))
| g_both(esk4_1(X2),esk4_1(X2))
| g_false_only(esk3_1(X2),esk3_1(X2))
| g_true_only(esk3_1(X2),esk3_1(X2))
| g_true_only(esk2_1(X2),X2)
| ~ g_both(X3,X2)
| ~ g_both(X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_65,negated_conjecture,
( g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_false_only(esk4_1(esk1_0),esk1_0)
| g_false_only(X1,X1)
| g_true_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_true_only(X1,X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_16]),c_0_38]),c_0_39]) ).
cnf(c_0_66,negated_conjecture,
( g_both(X1,X1)
| ~ g_both(X1,esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_9]),c_0_21]) ).
cnf(c_0_67,negated_conjecture,
g_both(esk3_1(esk1_0),esk1_0),
inference(spm,[status(thm)],[c_0_63,c_0_16]) ).
cnf(c_0_68,negated_conjecture,
( g_false_only(esk4_1(X1),esk4_1(X1))
| g_false_only(esk3_1(X1),esk3_1(X1))
| g_false_only(X2,X2)
| g_both(esk4_1(X1),esk4_1(X1))
| g_true_only(esk3_1(X1),esk3_1(X1))
| g_true_only(esk2_1(X1),X1)
| g_true_only(X2,X2)
| ~ g_both(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_16]) ).
cnf(c_0_69,negated_conjecture,
( g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_false_only(esk4_1(esk1_0),esk1_0)
| g_true_only(esk3_1(esk1_0),esk3_1(esk1_0)) ),
inference(ef,[status(thm)],[c_0_65]) ).
cnf(c_0_70,negated_conjecture,
g_both(esk3_1(esk1_0),esk3_1(esk1_0)),
inference(spm,[status(thm)],[c_0_66,c_0_67]) ).
cnf(c_0_71,negated_conjecture,
( g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_false_only(esk4_1(esk1_0),esk4_1(esk1_0))
| g_false_only(X1,X1)
| g_both(esk4_1(esk1_0),esk4_1(esk1_0))
| g_true_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_true_only(esk2_1(esk1_0),esk1_0)
| g_true_only(X1,X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_16]) ).
cnf(c_0_72,negated_conjecture,
( g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_false_only(esk4_1(esk1_0),esk1_0) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_69]),c_0_70])]) ).
cnf(c_0_73,negated_conjecture,
( g_false_only(esk4_1(esk1_0),esk4_1(esk1_0))
| g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_both(esk4_1(esk1_0),esk4_1(esk1_0))
| g_true_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_true_only(esk2_1(esk1_0),esk1_0) ),
inference(ef,[status(thm)],[c_0_71]) ).
cnf(c_0_74,negated_conjecture,
g_false_only(esk4_1(esk1_0),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_72]),c_0_70])]) ).
cnf(c_0_75,negated_conjecture,
( g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_false_only(esk4_1(esk1_0),esk4_1(esk1_0))
| g_both(esk4_1(esk1_0),esk4_1(esk1_0))
| g_true_only(esk2_1(esk1_0),esk1_0) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_73]),c_0_56]) ).
cnf(c_0_76,negated_conjecture,
~ g_both(esk4_1(esk1_0),esk4_1(esk1_0)),
inference(spm,[status(thm)],[c_0_51,c_0_74]) ).
cnf(c_0_77,negated_conjecture,
~ g_false_only(esk4_1(esk1_0),esk4_1(esk1_0)),
inference(spm,[status(thm)],[c_0_13,c_0_74]) ).
cnf(c_0_78,negated_conjecture,
( g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_true_only(esk2_1(esk1_0),esk1_0) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_75,c_0_76]),c_0_77]) ).
cnf(c_0_79,negated_conjecture,
( g_true_only(X1,X1)
| g_false_only(X1,X1)
| g_false_only(esk4_1(X2),esk4_1(X2))
| g_both(esk4_1(X2),esk4_1(X2))
| g_false_only(esk3_1(X2),esk3_1(X2))
| g_true_only(esk3_1(X2),esk3_1(X2))
| g_both(esk2_1(X2),esk2_1(X2))
| g_true_only(esk2_1(X2),esk2_1(X2))
| ~ g_both(X3,X2)
| ~ g_both(X3,X3) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_80,negated_conjecture,
g_true_only(esk2_1(esk1_0),esk1_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_78]),c_0_70])]) ).
cnf(c_0_81,negated_conjecture,
( g_false_only(esk4_1(X1),esk4_1(X1))
| g_false_only(esk3_1(X1),esk3_1(X1))
| g_false_only(X2,X2)
| g_both(esk4_1(X1),esk4_1(X1))
| g_both(esk2_1(X1),esk2_1(X1))
| g_true_only(esk3_1(X1),esk3_1(X1))
| g_true_only(esk2_1(X1),esk2_1(X1))
| g_true_only(X2,X2)
| ~ g_both(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_79,c_0_16]) ).
cnf(c_0_82,negated_conjecture,
~ g_both(esk2_1(esk1_0),esk2_1(esk1_0)),
inference(spm,[status(thm)],[c_0_33,c_0_80]) ).
cnf(c_0_83,negated_conjecture,
~ g_true_only(esk2_1(esk1_0),esk2_1(esk1_0)),
inference(spm,[status(thm)],[c_0_8,c_0_80]) ).
cnf(c_0_84,negated_conjecture,
( g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_false_only(X1,X1)
| g_true_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_true_only(X1,X1) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_16]),c_0_77]),c_0_76]),c_0_82]),c_0_83]) ).
cnf(c_0_85,negated_conjecture,
( g_false_only(esk3_1(esk1_0),esk3_1(esk1_0))
| g_true_only(esk3_1(esk1_0),esk3_1(esk1_0)) ),
inference(ef,[status(thm)],[c_0_84]) ).
cnf(c_0_86,negated_conjecture,
g_false_only(esk3_1(esk1_0),esk3_1(esk1_0)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_85]),c_0_70])]) ).
cnf(c_0_87,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_86]),c_0_70])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV515+1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n019.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 03:59:14 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.46/1.78 % Version : CSE_E---1.7
% 1.46/1.78 % Problem : theBenchmark.p
% 1.46/1.78 % SZS status Theorem for theBenchmark.p
% 1.46/1.78 % SZS output start CNFRefutation
% See solution above
% 1.46/1.79 % Total time : 1.369s
%------------------------------------------------------------------------------