%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL674+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 : n008.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 04:44:44 PM UTC 2026
% Result : Theorem 0.27s 1.61s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 50 ( 19 unt; 0 def)
% Number of atoms : 261 ( 0 equ)
% Maximal formula atoms : 66 ( 5 avg)
% Number of connectives : 390 ( 179 ~; 165 |; 45 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 70 ( 0 sgn 30 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(main,conjecture,
~ ? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
| ~ ( ! [X2] :
( ~ r1(X1,X2)
| ( ( ( ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ( ~ p2(X1)
& ~ p102(X1)
& p101(X1) ) )
& ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ( p2(X1)
& ~ p102(X1)
& p101(X1) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X1] :
( ~ r1(X2,X1)
| ~ p2(X1)
| ~ p101(X1) )
| p2(X2) )
& ( ! [X1] :
( ~ r1(X2,X1)
| p2(X1)
| ~ p101(X1) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X1] :
( ~ r1(X2,X1)
| ~ p1(X1)
| ~ p100(X1) )
| p1(X2) )
& ( ! [X1] :
( ~ r1(X2,X1)
| p1(X1)
| ~ p100(X1) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X1)
& p100(X1) ) ),
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(i_0_3,negated_conjecture,
~ ~ ? [X1] :
~ ( ~ ! [X2] :
( ~ r1(X1,X2)
| p2(X2) )
| ~ ( ! [X2] :
( ~ r1(X1,X2)
| ( ( ( ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ( ~ p2(X1)
& ~ p102(X1)
& p101(X1) ) )
& ~ ! [X1] :
( ~ r1(X2,X1)
| ~ ( p2(X1)
& ~ p102(X1)
& p101(X1) ) ) )
| ~ ( ~ p101(X2)
& p100(X2) ) )
& ( ( ( ! [X1] :
( ~ r1(X2,X1)
| ~ p2(X1)
| ~ p101(X1) )
| p2(X2) )
& ( ! [X1] :
( ~ r1(X2,X1)
| p2(X1)
| ~ p101(X1) )
| ~ p2(X2) ) )
| ~ p101(X2) )
& ( ( ( ! [X1] :
( ~ r1(X2,X1)
| ~ p1(X1)
| ~ p100(X1) )
| p1(X2) )
& ( ! [X1] :
( ~ r1(X2,X1)
| p1(X1)
| ~ p100(X1) )
| ~ p1(X2) ) )
| ~ p100(X2) )
& ( p101(X2)
| ~ p102(X2) )
& ( p100(X2)
| ~ p101(X2) ) ) )
& ~ p101(X1)
& p100(X1) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[main])]) ).
fof(i_0_4,negated_conjecture,
! [X22,X23,X26,X27,X28,X29] :
( ( ~ r1(esk1_0,X22)
| p2(X22) )
& ( r1(X23,esk2_1(X23))
| p101(X23)
| ~ p100(X23)
| ~ r1(esk1_0,X23) )
& ( ~ p2(esk2_1(X23))
| p101(X23)
| ~ p100(X23)
| ~ r1(esk1_0,X23) )
& ( ~ p102(esk2_1(X23))
| p101(X23)
| ~ p100(X23)
| ~ r1(esk1_0,X23) )
& ( p101(esk2_1(X23))
| p101(X23)
| ~ p100(X23)
| ~ r1(esk1_0,X23) )
& ( r1(X23,esk3_1(X23))
| p101(X23)
| ~ p100(X23)
| ~ r1(esk1_0,X23) )
& ( p2(esk3_1(X23))
| p101(X23)
| ~ p100(X23)
| ~ r1(esk1_0,X23) )
& ( ~ p102(esk3_1(X23))
| p101(X23)
| ~ p100(X23)
| ~ r1(esk1_0,X23) )
& ( p101(esk3_1(X23))
| p101(X23)
| ~ p100(X23)
| ~ r1(esk1_0,X23) )
& ( ~ r1(X23,X26)
| ~ p2(X26)
| ~ p101(X26)
| p2(X23)
| ~ p101(X23)
| ~ r1(esk1_0,X23) )
& ( ~ r1(X23,X27)
| p2(X27)
| ~ p101(X27)
| ~ p2(X23)
| ~ p101(X23)
| ~ r1(esk1_0,X23) )
& ( ~ r1(X23,X28)
| ~ p1(X28)
| ~ p100(X28)
| p1(X23)
| ~ p100(X23)
| ~ r1(esk1_0,X23) )
& ( ~ r1(X23,X29)
| p1(X29)
| ~ p100(X29)
| ~ p1(X23)
| ~ p100(X23)
| ~ r1(esk1_0,X23) )
& ( p101(X23)
| ~ p102(X23)
| ~ r1(esk1_0,X23) )
& ( p100(X23)
| ~ p101(X23)
| ~ r1(esk1_0,X23) )
& ~ p101(esk1_0)
& p100(esk1_0) ),
inference(distribute,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[i_0_3])])])])]) ).
fof(i_0_5,plain,
! [X18,X19,X20] :
( ~ r1(X18,X19)
| ~ r1(X19,X20)
| r1(X18,X20) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity])]) ).
fof(i_0_6,plain,
! [X17] : r1(X17,X17),
inference(variable_rename,[status(thm)],[reflexivity]) ).
cnf(i_0_7,negated_conjecture,
( p1(X1)
| ~ r1(X1,X2)
| ~ p1(X2)
| ~ p100(X2)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_8,negated_conjecture,
( p1(X2)
| ~ r1(X1,X2)
| ~ p100(X2)
| ~ p1(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_9,negated_conjecture,
( p2(X1)
| ~ r1(X1,X2)
| ~ p2(X2)
| ~ p101(X2)
| ~ p101(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_10,negated_conjecture,
( p2(X2)
| ~ r1(X1,X2)
| ~ p101(X2)
| ~ p2(X1)
| ~ p101(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_11,plain,
( r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_12,negated_conjecture,
( r1(X1,esk3_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_13,negated_conjecture,
( r1(X1,esk2_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_14,negated_conjecture,
( p101(X1)
| ~ p102(esk3_1(X1))
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_15,negated_conjecture,
( p101(X1)
| ~ p102(esk2_1(X1))
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_16,negated_conjecture,
( p101(X1)
| ~ p2(esk2_1(X1))
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_17,negated_conjecture,
( p101(esk3_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_18,negated_conjecture,
( p101(esk2_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_19,negated_conjecture,
( p2(esk3_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_20,negated_conjecture,
( p100(X1)
| ~ p101(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_21,negated_conjecture,
( p101(X1)
| ~ p102(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_22,negated_conjecture,
( p2(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_23,plain,
r1(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_24,negated_conjecture,
~ p101(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_25,negated_conjecture,
p100(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_26,plain,
p2(esk1_0),
inference(scs_inference,[],[i_0_23,i_0_22]) ).
cnf(i_0_27,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_28,plain,
( ~ r1(esk1_0,X1)
| p2(X1) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_29,plain,
r1(esk1_0,esk3_1(esk1_0)),
inference(scs_inference,[],[i_0_24,i_0_23,i_0_27,i_0_25,i_0_22,i_0_12]) ).
cnf(i_0_30,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_31,plain,
( ~ r1(esk1_0,X1)
| r1(X1,esk3_1(X1))
| p101(X1)
| ~ p100(X1) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_32,plain,
r1(esk1_0,esk2_1(esk1_0)),
inference(scs_inference,[],[i_0_24,i_0_23,i_0_27,i_0_30,i_0_25,i_0_22,i_0_12,i_0_13]) ).
cnf(i_0_33,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_34,plain,
( ~ r1(esk1_0,X1)
| r1(X1,esk2_1(X1))
| p101(X1)
| ~ p100(X1) ),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_35,plain,
( ~ p101(esk3_1(esk1_0))
| p100(esk3_1(esk1_0)) ),
inference(scs_inference,[],[i_0_24,i_0_23,i_0_27,i_0_30,i_0_25,i_0_22,i_0_12,i_0_13,i_0_20]) ).
cnf(i_0_36,plain,
( ~ r1(esk1_0,X1)
| ~ p101(X1)
| p100(X1) ),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_37,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_38,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_39,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_40,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_42,plain,
p2(esk3_1(esk1_0)),
inference(scs_inference,[],[i_0_29,i_0_22]) ).
cnf(i_0_43,plain,
( ~ r1(esk1_0,X1)
| p2(X1) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_44,plain,
( ~ p101(esk2_1(esk1_0))
| p100(esk2_1(esk1_0)) ),
inference(scs_inference,[],[i_0_29,i_0_32,i_0_22,i_0_20]) ).
cnf(i_0_45,plain,
( ~ r1(esk1_0,X1)
| ~ p101(X1)
| p100(X1) ),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_46,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_23]) ).
cnf(i_0_47,plain,
( ~ p1(esk1_0)
| ~ p100(esk3_1(esk1_0))
| p100(esk2_1(esk1_0))
| ~ r1(esk3_1(esk1_0),esk1_0)
| p1(esk3_1(esk1_0)) ),
inference(scs_inference,[],[i_0_24,i_0_29,i_0_32,i_0_23,i_0_25,i_0_22,i_0_20,i_0_18,i_0_7]) ).
cnf(i_0_48,plain,
p2(esk2_1(esk1_0)),
inference(scs_inference,[],[i_0_32,i_0_22]) ).
cnf(i_0_49,plain,
( ~ r1(esk1_0,X1)
| p2(X1) ),
inference(rename_variables,[],[i_0_22]) ).
cnf(i_0_50,plain,
$false,
inference(scs_inference,[],[i_0_24,i_0_32,i_0_23,i_0_25,i_0_22,i_0_16]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL674+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
% 0.13/0.33 % Computer : n008.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Mon May 4 22:58:43 EDT 2026
% 0.13/0.33 % CPUTime :
% 0.13/0.34 % start to proof: theBenchmark
% 0.27/1.61 % Version : CSE_E---1.7
% 0.27/1.61 % Problem : theBenchmark.p
% 0.27/1.61 % SZS status Theorem for theBenchmark.p
% 0.27/1.61 % SZS output start CNFRefutation
% See solution above
% 0.27/1.66 % Total time : 1.273s
%------------------------------------------------------------------------------