%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET792+4 : TPTP v9.2.1. Released v3.2.0.
% 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 : n016.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 05:08:30 PM UTC 2026
% Result : Theorem 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 7 unt; 0 def)
% Number of atoms : 384 ( 24 equ)
% Maximal formula atoms : 256 ( 12 avg)
% Number of connectives : 462 ( 110 ~; 242 |; 91 &)
% ( 5 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 77 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 87 ( 1 sgn 58 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(thIV4,conjecture,
! [X1,X2,X6] :
( ( order(X1,X2)
& least(X6,X1,X2) )
=> min(X6,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIV4) ).
fof(least,axiom,
! [X1,X2,X6] :
( least(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( member(X3,X2)
=> apply(X1,X6,X3) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',least) ).
fof(min,axiom,
! [X1,X2,X6] :
( min(X6,X1,X2)
<=> ( member(X6,X2)
& ! [X3] :
( ( member(X3,X2)
& apply(X1,X3,X6) )
=> X6 = X3 ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',min) ).
fof(order,axiom,
! [X1,X2] :
( order(X1,X2)
<=> ( ! [X3] :
( member(X3,X2)
=> apply(X1,X3,X3) )
& ! [X3,X4] :
( ( member(X3,X2)
& member(X4,X2) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X4,X3) )
=> X3 = X4 ) )
& ! [X3,X4,X5] :
( ( member(X3,X2)
& member(X4,X2)
& member(X5,X2) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X4,X5) )
=> apply(X1,X3,X5) ) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+3.ax',order) ).
fof(c_0_4,negated_conjecture,
~ ! [X1,X2,X6] :
( ( order(X1,X2)
& least(X6,X1,X2) )
=> min(X6,X1,X2) ),
inference(assume_negation,[status(cth)],[thIV4]) ).
fof(c_0_5,plain,
! [X2,X1] :
( epred1_2(X1,X2)
<=> ( ! [X3] :
( member(X3,X2)
=> apply(X1,X3,X3) )
& ! [X3,X4] :
( ( member(X3,X2)
& member(X4,X2) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X4,X3) )
=> X3 = X4 ) )
& ! [X3,X4,X5] :
( ( member(X3,X2)
& member(X4,X2)
& member(X5,X2) )
=> ( ( apply(X1,X3,X4)
& apply(X1,X4,X5) )
=> apply(X1,X3,X5) ) ) ) ),
introduced(definition) ).
fof(c_0_6,plain,
! [X91,X92,X93,X94,X95,X96,X97] :
( ( member(X93,X92)
| ~ least(X93,X91,X92) )
& ( ~ member(X94,X92)
| apply(X91,X93,X94)
| ~ least(X93,X91,X92) )
& ( member(esk6_3(X95,X96,X97),X96)
| ~ member(X97,X96)
| least(X97,X95,X96) )
& ( ~ apply(X95,X97,esk6_3(X95,X96,X97))
| ~ member(X97,X96)
| least(X97,X95,X96) ) ),
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)],[least])])])])])]) ).
fof(c_0_7,negated_conjecture,
( order(esk11_0,esk12_0)
& least(esk13_0,esk11_0,esk12_0)
& ~ min(esk13_0,esk11_0,esk12_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_8,plain,
! [X138,X139,X140,X141,X142,X143,X144,X145,X146,X147] :
( ( ~ member(X140,X138)
| apply(X139,X140,X140)
| ~ epred1_2(X139,X138) )
& ( ~ member(X141,X138)
| ~ member(X142,X138)
| ~ apply(X139,X141,X142)
| ~ apply(X139,X142,X141)
| X141 = X142
| ~ epred1_2(X139,X138) )
& ( ~ member(X143,X138)
| ~ member(X144,X138)
| ~ member(X145,X138)
| ~ apply(X139,X143,X144)
| ~ apply(X139,X144,X145)
| apply(X139,X143,X145)
| ~ epred1_2(X139,X138) )
& ( member(esk17_2(X146,X147),X146)
| member(esk15_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk18_2(X146,X147),X146)
| member(esk15_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk19_2(X146,X147),X146)
| member(esk15_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( apply(X147,esk17_2(X146,X147),esk18_2(X146,X147))
| member(esk15_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( apply(X147,esk18_2(X146,X147),esk19_2(X146,X147))
| member(esk15_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( ~ apply(X147,esk17_2(X146,X147),esk19_2(X146,X147))
| member(esk15_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk17_2(X146,X147),X146)
| member(esk16_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk18_2(X146,X147),X146)
| member(esk16_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk19_2(X146,X147),X146)
| member(esk16_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( apply(X147,esk17_2(X146,X147),esk18_2(X146,X147))
| member(esk16_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( apply(X147,esk18_2(X146,X147),esk19_2(X146,X147))
| member(esk16_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( ~ apply(X147,esk17_2(X146,X147),esk19_2(X146,X147))
| member(esk16_2(X146,X147),X146)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk17_2(X146,X147),X146)
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk18_2(X146,X147),X146)
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk19_2(X146,X147),X146)
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( apply(X147,esk17_2(X146,X147),esk18_2(X146,X147))
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( apply(X147,esk18_2(X146,X147),esk19_2(X146,X147))
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( ~ apply(X147,esk17_2(X146,X147),esk19_2(X146,X147))
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk17_2(X146,X147),X146)
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk18_2(X146,X147),X146)
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk19_2(X146,X147),X146)
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( apply(X147,esk17_2(X146,X147),esk18_2(X146,X147))
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( apply(X147,esk18_2(X146,X147),esk19_2(X146,X147))
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( ~ apply(X147,esk17_2(X146,X147),esk19_2(X146,X147))
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk17_2(X146,X147),X146)
| esk15_2(X146,X147) != esk16_2(X146,X147)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk18_2(X146,X147),X146)
| esk15_2(X146,X147) != esk16_2(X146,X147)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk19_2(X146,X147),X146)
| esk15_2(X146,X147) != esk16_2(X146,X147)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( apply(X147,esk17_2(X146,X147),esk18_2(X146,X147))
| esk15_2(X146,X147) != esk16_2(X146,X147)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( apply(X147,esk18_2(X146,X147),esk19_2(X146,X147))
| esk15_2(X146,X147) != esk16_2(X146,X147)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( ~ apply(X147,esk17_2(X146,X147),esk19_2(X146,X147))
| esk15_2(X146,X147) != esk16_2(X146,X147)
| member(esk14_2(X146,X147),X146)
| epred1_2(X147,X146) )
& ( member(esk17_2(X146,X147),X146)
| member(esk15_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk18_2(X146,X147),X146)
| member(esk15_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk19_2(X146,X147),X146)
| member(esk15_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( apply(X147,esk17_2(X146,X147),esk18_2(X146,X147))
| member(esk15_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( apply(X147,esk18_2(X146,X147),esk19_2(X146,X147))
| member(esk15_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( ~ apply(X147,esk17_2(X146,X147),esk19_2(X146,X147))
| member(esk15_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk17_2(X146,X147),X146)
| member(esk16_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk18_2(X146,X147),X146)
| member(esk16_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk19_2(X146,X147),X146)
| member(esk16_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( apply(X147,esk17_2(X146,X147),esk18_2(X146,X147))
| member(esk16_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( apply(X147,esk18_2(X146,X147),esk19_2(X146,X147))
| member(esk16_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( ~ apply(X147,esk17_2(X146,X147),esk19_2(X146,X147))
| member(esk16_2(X146,X147),X146)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk17_2(X146,X147),X146)
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk18_2(X146,X147),X146)
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk19_2(X146,X147),X146)
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( apply(X147,esk17_2(X146,X147),esk18_2(X146,X147))
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( apply(X147,esk18_2(X146,X147),esk19_2(X146,X147))
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( ~ apply(X147,esk17_2(X146,X147),esk19_2(X146,X147))
| apply(X147,esk15_2(X146,X147),esk16_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk17_2(X146,X147),X146)
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk18_2(X146,X147),X146)
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk19_2(X146,X147),X146)
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( apply(X147,esk17_2(X146,X147),esk18_2(X146,X147))
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( apply(X147,esk18_2(X146,X147),esk19_2(X146,X147))
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( ~ apply(X147,esk17_2(X146,X147),esk19_2(X146,X147))
| apply(X147,esk16_2(X146,X147),esk15_2(X146,X147))
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk17_2(X146,X147),X146)
| esk15_2(X146,X147) != esk16_2(X146,X147)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk18_2(X146,X147),X146)
| esk15_2(X146,X147) != esk16_2(X146,X147)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( member(esk19_2(X146,X147),X146)
| esk15_2(X146,X147) != esk16_2(X146,X147)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( apply(X147,esk17_2(X146,X147),esk18_2(X146,X147))
| esk15_2(X146,X147) != esk16_2(X146,X147)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( apply(X147,esk18_2(X146,X147),esk19_2(X146,X147))
| esk15_2(X146,X147) != esk16_2(X146,X147)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) )
& ( ~ apply(X147,esk17_2(X146,X147),esk19_2(X146,X147))
| esk15_2(X146,X147) != esk16_2(X146,X147)
| ~ apply(X147,esk14_2(X146,X147),esk14_2(X146,X147))
| epred1_2(X147,X146) ) ),
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])])])])])]) ).
cnf(c_0_9,plain,
( apply(X3,X4,X1)
| ~ member(X1,X2)
| ~ least(X4,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
least(esk13_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_11,plain,
! [X107,X108,X109,X110,X111,X112,X113] :
( ( member(X109,X108)
| ~ min(X109,X107,X108) )
& ( ~ member(X110,X108)
| ~ apply(X107,X110,X109)
| X109 = X110
| ~ min(X109,X107,X108) )
& ( member(esk8_3(X111,X112,X113),X112)
| ~ member(X113,X112)
| min(X113,X111,X112) )
& ( apply(X111,esk8_3(X111,X112,X113),X113)
| ~ member(X113,X112)
| min(X113,X111,X112) )
& ( X113 != esk8_3(X111,X112,X113)
| ~ member(X113,X112)
| min(X113,X111,X112) ) ),
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)],[min])])])])])]) ).
cnf(c_0_12,plain,
( member(X1,X2)
| ~ least(X1,X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_13,plain,
( X1 = X3
| ~ member(X1,X2)
| ~ member(X3,X2)
| ~ apply(X4,X1,X3)
| ~ apply(X4,X3,X1)
| ~ epred1_2(X4,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
( apply(esk11_0,esk13_0,X1)
| ~ member(X1,esk12_0) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
( apply(X1,esk8_3(X1,X2,X3),X3)
| min(X3,X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,negated_conjecture,
member(esk13_0,esk12_0),
inference(spm,[status(thm)],[c_0_12,c_0_10]) ).
fof(c_0_17,axiom,
! [X1,X2] :
( order(X1,X2)
<=> epred1_2(X1,X2) ),
inference(apply_def,[status(thm)],[order,c_0_5]) ).
cnf(c_0_18,negated_conjecture,
( X1 = esk13_0
| ~ epred1_2(esk11_0,X2)
| ~ apply(esk11_0,X1,esk13_0)
| ~ member(esk13_0,X2)
| ~ member(X1,esk12_0)
| ~ member(X1,X2) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,negated_conjecture,
( min(esk13_0,X1,esk12_0)
| apply(X1,esk8_3(X1,esk12_0,esk13_0),esk13_0) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_20,negated_conjecture,
~ min(esk13_0,esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_21,plain,
( member(esk8_3(X1,X2,X3),X2)
| min(X3,X1,X2)
| ~ member(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_22,plain,
! [X57,X58] :
( ( ~ order(X57,X58)
| epred1_2(X57,X58) )
& ( ~ epred1_2(X57,X58)
| order(X57,X58) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])]) ).
cnf(c_0_23,negated_conjecture,
( esk8_3(esk11_0,esk12_0,esk13_0) = esk13_0
| ~ epred1_2(esk11_0,X1)
| ~ member(esk8_3(esk11_0,esk12_0,esk13_0),esk12_0)
| ~ member(esk8_3(esk11_0,esk12_0,esk13_0),X1)
| ~ member(esk13_0,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_24,negated_conjecture,
( min(esk13_0,X1,esk12_0)
| member(esk8_3(X1,esk12_0,esk13_0),esk12_0) ),
inference(spm,[status(thm)],[c_0_21,c_0_16]) ).
cnf(c_0_25,plain,
( epred1_2(X1,X2)
| ~ order(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
order(esk11_0,esk12_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,negated_conjecture,
( esk8_3(esk11_0,esk12_0,esk13_0) = esk13_0
| ~ epred1_2(esk11_0,X1)
| ~ member(esk8_3(esk11_0,esk12_0,esk13_0),X1)
| ~ member(esk13_0,X1) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_20]) ).
cnf(c_0_28,negated_conjecture,
epred1_2(esk11_0,esk12_0),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,plain,
( min(X1,X2,X3)
| X1 != esk8_3(X2,X3,X1)
| ~ member(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_30,negated_conjecture,
esk8_3(esk11_0,esk12_0,esk13_0) = esk13_0,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_24]),c_0_28]),c_0_16])]),c_0_20]) ).
cnf(c_0_31,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_16])]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET792+4 : TPTP v9.2.1. Released v3.2.0.
% 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 : n016.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 02:35:51 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Theorem for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.371s
%------------------------------------------------------------------------------