%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL672+1.001 : TPTP v9.2.1. Released v4.0.0.
% 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 : n013.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 04:44:43 PM UTC 2026
% Result : Theorem 2.04s 1.94s
% Output : CNFRefutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 285 ( 0 equ)
% Maximal formula atoms : 90 ( 8 avg)
% Number of connectives : 480 ( 229 ~; 210 |; 40 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-3 aty)
% Number of variables : 138 ( 0 sgn 88 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(main,conjecture,
~ ? [X1] :
~ ( ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ! [X2] :
( ~ r1(X1,X2)
| ~ p1(X2) ) )
& p1(X2) ) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) )
| ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X1] :
( ~ r1(X2,X1)
| p1(X1) ) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) ) ) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) )
| ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X1] :
( ~ r1(X2,X1)
| p1(X1) ) ) )
& ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) ) ) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) )
| ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X1] :
( ~ r1(X2,X1)
| ~ $true ) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) )
| ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
| ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) )
| ! [X1] :
( ~ r1(X2,X1)
| p1(X1) ) )
| ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main) ).
fof(transitivity,axiom,
! [X1,X2,X3] :
( ( r1(X1,X2)
& r1(X2,X3) )
=> r1(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(reflexivity,axiom,
! [X1] : r1(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(c_0_3,negated_conjecture,
~ ~ ? [X1] :
~ ( ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ! [X2] :
( ~ r1(X1,X2)
| ~ p1(X2) ) )
& p1(X2) ) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) )
| ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| ~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X1] :
( ~ r1(X2,X1)
| p1(X1) ) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) ) ) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) )
| ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X1] :
( ~ r1(X2,X1)
| p1(X1) ) ) )
& ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) ) ) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) )
| ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X1] : ~ r1(X2,X1) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) )
| ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
| ! [X2] :
( ~ r1(X1,X2)
| ! [X1] :
( ~ r1(X2,X1)
| ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) )
| ! [X1] :
( ~ r1(X2,X1)
| p1(X1) ) )
| ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[main])]) ).
fof(c_0_4,plain,
! [X40,X41,X42] :
( ~ r1(X40,X41)
| ~ r1(X41,X42)
| r1(X40,X42) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity])]) ).
fof(c_0_5,negated_conjecture,
! [X44,X45,X46,X48,X49,X50,X51,X52,X54,X55,X56,X57,X58,X60,X61,X63,X64,X65,X67,X71] :
( ( r1(X46,esk2_2(X45,X46))
| ~ r1(X45,X46)
| ~ p1(X45)
| ~ r1(esk1_0,X45)
| ~ r1(esk1_0,X44)
| p2(X44)
| ~ r1(esk1_0,X48)
| p1(X48) )
& ( p1(esk2_2(X45,X46))
| ~ r1(X45,X46)
| ~ p1(X45)
| ~ r1(esk1_0,X45)
| ~ r1(esk1_0,X44)
| p2(X44)
| ~ r1(esk1_0,X48)
| p1(X48) )
& ( r1(X52,esk3_3(X50,X51,X52))
| ~ r1(X51,X52)
| ~ r1(X51,X54)
| p1(X54)
| ~ r1(X50,X51)
| ~ r1(esk1_0,X50)
| ~ r1(esk1_0,X49)
| p2(X49)
| ~ r1(esk1_0,X55)
| p1(X55) )
& ( ~ p1(esk3_3(X50,X51,X52))
| ~ r1(X51,X52)
| ~ r1(X51,X54)
| p1(X54)
| ~ r1(X50,X51)
| ~ r1(esk1_0,X50)
| ~ r1(esk1_0,X49)
| p2(X49)
| ~ r1(esk1_0,X55)
| p1(X55) )
& ( r1(X61,esk5_2(X57,X61))
| ~ r1(X57,X61)
| r1(X58,esk4_2(X57,X58))
| ~ r1(X57,X58)
| ~ r1(esk1_0,X57)
| ~ r1(esk1_0,X56)
| p2(X56)
| ~ r1(esk1_0,X63)
| p1(X63) )
& ( ~ p1(esk5_2(X57,X61))
| ~ r1(X57,X61)
| r1(X58,esk4_2(X57,X58))
| ~ r1(X57,X58)
| ~ r1(esk1_0,X57)
| ~ r1(esk1_0,X56)
| p2(X56)
| ~ r1(esk1_0,X63)
| p1(X63) )
& ( r1(X61,esk5_2(X57,X61))
| ~ r1(X57,X61)
| ~ r1(esk4_2(X57,X58),X60)
| p1(X60)
| ~ r1(X57,X58)
| ~ r1(esk1_0,X57)
| ~ r1(esk1_0,X56)
| p2(X56)
| ~ r1(esk1_0,X63)
| p1(X63) )
& ( ~ p1(esk5_2(X57,X61))
| ~ r1(X57,X61)
| ~ r1(esk4_2(X57,X58),X60)
| p1(X60)
| ~ r1(X57,X58)
| ~ r1(esk1_0,X57)
| ~ r1(esk1_0,X56)
| p2(X56)
| ~ r1(esk1_0,X63)
| p1(X63) )
& ( ~ r1(esk1_0,X64)
| p2(X64)
| ~ r1(esk1_0,X65)
| r1(X65,esk6_1(X65))
| ~ r1(esk1_0,X67)
| p1(X67) )
& r1(esk1_0,esk7_0)
& ~ p2(esk7_0)
& r1(esk1_0,esk8_0)
& r1(esk8_0,esk9_0)
& ( ~ r1(esk9_0,X71)
| p1(X71) )
& r1(esk8_0,esk10_0)
& ~ p1(esk10_0)
& r1(esk1_0,esk11_0)
& ~ p1(esk11_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_3])])])])]) ).
cnf(c_0_6,plain,
( r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_4]) ).
cnf(c_0_7,negated_conjecture,
r1(esk1_0,esk11_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
fof(c_0_8,plain,
! [X39] : r1(X39,X39),
inference(variable_rename,[status(thm)],[reflexivity]) ).
cnf(c_0_9,negated_conjecture,
( r1(X1,esk3_3(X2,X3,X1))
| p1(X4)
| p2(X5)
| p1(X6)
| ~ r1(X3,X1)
| ~ r1(X3,X4)
| ~ r1(X2,X3)
| ~ r1(esk1_0,X2)
| ~ r1(esk1_0,X5)
| ~ r1(esk1_0,X6) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,negated_conjecture,
( r1(X1,esk11_0)
| ~ r1(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_11,plain,
r1(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,negated_conjecture,
~ p1(esk11_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_13,negated_conjecture,
r1(esk1_0,esk7_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_14,negated_conjecture,
( p1(X1)
| p2(X2)
| r1(X3,esk3_3(X4,X5,X3))
| ~ r1(esk1_0,X2)
| ~ r1(esk1_0,X4)
| ~ r1(X5,X1)
| ~ r1(X5,X3)
| ~ r1(X4,X5) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]),c_0_12]) ).
cnf(c_0_15,negated_conjecture,
( r1(X1,esk7_0)
| ~ r1(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_6,c_0_13]) ).
cnf(c_0_16,negated_conjecture,
~ p2(esk7_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_17,negated_conjecture,
r1(esk1_0,esk8_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_18,negated_conjecture,
( p1(X1)
| r1(X2,esk3_3(X3,X4,X2))
| ~ r1(esk1_0,X3)
| ~ r1(X4,X1)
| ~ r1(X4,X2)
| ~ r1(X3,X4) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_11])]),c_0_16]) ).
cnf(c_0_19,negated_conjecture,
( r1(X1,esk8_0)
| ~ r1(X1,esk1_0) ),
inference(spm,[status(thm)],[c_0_6,c_0_17]) ).
cnf(c_0_20,negated_conjecture,
( p1(X1)
| r1(X2,esk3_3(esk8_0,X3,X2))
| ~ r1(esk8_0,X3)
| ~ r1(X3,X1)
| ~ r1(X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_11])]) ).
cnf(c_0_21,negated_conjecture,
r1(esk8_0,esk10_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_22,negated_conjecture,
( p1(X4)
| p2(X5)
| p1(X6)
| ~ p1(esk3_3(X1,X2,X3))
| ~ r1(X2,X3)
| ~ r1(X2,X4)
| ~ r1(X1,X2)
| ~ r1(esk1_0,X1)
| ~ r1(esk1_0,X5)
| ~ r1(esk1_0,X6) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_23,negated_conjecture,
( p1(X1)
| ~ r1(esk9_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_24,negated_conjecture,
( p1(X1)
| r1(X2,esk3_3(esk8_0,esk8_0,X2))
| ~ r1(esk8_0,X1)
| ~ r1(esk8_0,X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_11]) ).
cnf(c_0_25,negated_conjecture,
( r1(X1,esk10_0)
| ~ r1(X1,esk8_0) ),
inference(spm,[status(thm)],[c_0_6,c_0_21]) ).
cnf(c_0_26,negated_conjecture,
~ p1(esk10_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_27,negated_conjecture,
( p1(X1)
| p1(X2)
| p2(X3)
| ~ r1(esk9_0,esk3_3(X4,X5,X6))
| ~ r1(esk1_0,X2)
| ~ r1(esk1_0,X3)
| ~ r1(esk1_0,X4)
| ~ r1(X5,X1)
| ~ r1(X5,X6)
| ~ r1(X4,X5) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( r1(X1,esk3_3(esk8_0,esk8_0,X1))
| ~ r1(esk8_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11])]),c_0_26]) ).
cnf(c_0_29,negated_conjecture,
r1(esk8_0,esk9_0),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_30,negated_conjecture,
( p1(X1)
| p1(X2)
| p2(X3)
| ~ r1(esk1_0,X1)
| ~ r1(esk1_0,X3)
| ~ r1(esk8_0,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_17]),c_0_29]),c_0_11])]) ).
cnf(c_0_31,negated_conjecture,
( p1(X1)
| p2(X2)
| ~ r1(esk1_0,X2)
| ~ r1(esk8_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_10]),c_0_11])]),c_0_12]) ).
cnf(c_0_32,negated_conjecture,
( p1(X1)
| ~ r1(esk8_0,X1) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_15]),c_0_11])]),c_0_16]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_32]),c_0_21])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL672+1.001 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.16/0.32 % Computer : n013.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Mon May 4 22:54:56 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 2.04/1.94 % Version : CSE_E---1.7
% 2.04/1.94 % Problem : theBenchmark.p
% 2.04/1.94 % SZS status Theorem for theBenchmark.p
% 2.04/1.94 % SZS output start CNFRefutation
% See solution above
% 2.04/1.94 % Total time : 1.372s
%------------------------------------------------------------------------------