%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL893+1 : TPTP v9.2.1. Released v5.5.0.
% 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 : n002.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 04:45:19 PM UTC 2026
% Result : Theorem 1.28s 1.72s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 28 ( 18 unt; 0 def)
% Number of atoms : 43 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 26 ( 11 ~; 8 |; 3 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 32 ( 1 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_08,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).
fof(goals_15,conjecture,
! [X21] :
( h(X21) = X21
=> X21 = '0' ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_15) ).
fof(sos_05,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_05) ).
fof(sos_14,axiom,
! [X1] : h(X1) = '==>'(h(X1),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_14) ).
fof(sos_07,axiom,
! [X7,X8] :
( ( '>='(X7,X8)
& '>='(X8,X7) )
=> X7 = X8 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).
fof(sos_09,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).
fof(c_0_7,plain,
! [X65,X66,X67] :
( ( ~ '>='('+'(X65,X66),X67)
| '>='(X66,'==>'(X65,X67)) )
& ( ~ '>='(X66,'==>'(X65,X67))
| '>='('+'(X65,X66),X67) ) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_08])]) ).
fof(c_0_8,plain,
! [X57] : '+'(X57,'0') = X57,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_9,negated_conjecture,
~ ! [X21] :
( h(X21) = X21
=> X21 = '0' ),
inference(assume_negation,[status(cth)],[goals_15]) ).
cnf(c_0_10,plain,
( '>='(X2,'==>'(X1,X3))
| ~ '>='('+'(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_12,plain,
! [X59] : '>='(X59,X59),
inference(variable_rename,[status(thm)],[sos_05]) ).
fof(c_0_13,plain,
! [X80] : h(X80) = '==>'(h(X80),X80),
inference(variable_rename,[status(thm)],[sos_14]) ).
fof(c_0_14,negated_conjecture,
( h(esk1_0) = esk1_0
& esk1_0 != '0' ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).
cnf(c_0_15,plain,
( '>='('0','==>'(X1,X2))
| ~ '>='(X1,X2) ),
inference(spm,[status(thm)],[c_0_10,c_0_11]) ).
cnf(c_0_16,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
h(X1) = '==>'(h(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,negated_conjecture,
h(esk1_0) = esk1_0,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_19,plain,
! [X63,X64] :
( ~ '>='(X63,X64)
| ~ '>='(X64,X63)
| X63 = X64 ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).
cnf(c_0_20,plain,
'>='('0','==>'(X1,X1)),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_21,negated_conjecture,
'==>'(esk1_0,esk1_0) = esk1_0,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
fof(c_0_22,plain,
! [X68] : '>='(X68,'0'),
inference(variable_rename,[status(thm)],[sos_09]) ).
cnf(c_0_23,plain,
( X1 = X2
| ~ '>='(X1,X2)
| ~ '>='(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,negated_conjecture,
'>='('0',esk1_0),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
esk1_0 != '0',
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]),c_0_26]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL893+1 : TPTP v9.2.1. Released v5.5.0.
% 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
% 0.16/0.33 % Computer : n002.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 : Mon May 4 23:16:31 EDT 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 1.28/1.72 % Version : CSE_E---1.7
% 1.28/1.72 % Problem : theBenchmark.p
% 1.28/1.72 % SZS status Theorem for theBenchmark.p
% 1.28/1.72 % SZS output start CNFRefutation
% See solution above
% 1.28/1.72 % Total time : 1.368s
%------------------------------------------------------------------------------