%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL656+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 : n031.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 04:42:59 PM UTC 2026
% Result : Theorem 0.27s 1.61s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 47 ( 19 unt; 0 def)
% Number of atoms : 252 ( 0 equ)
% Maximal formula atoms : 66 ( 5 avg)
% Number of connectives : 380 ( 175 ~; 161 |; 44 &)
% ( 0 <=>; 0 =>; 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 : 61 ( 0 sgn 24 !; 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(reflexivity,axiom,
! [X1] : r1(X1,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(i_0_2,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_3,negated_conjecture,
! [X15,X16,X19,X20,X21,X22] :
( ( ~ r1(esk1_0,X15)
| p2(X15) )
& ( r1(X16,esk2_1(X16))
| p101(X16)
| ~ p100(X16)
| ~ r1(esk1_0,X16) )
& ( ~ p2(esk2_1(X16))
| p101(X16)
| ~ p100(X16)
| ~ r1(esk1_0,X16) )
& ( ~ p102(esk2_1(X16))
| p101(X16)
| ~ p100(X16)
| ~ r1(esk1_0,X16) )
& ( p101(esk2_1(X16))
| p101(X16)
| ~ p100(X16)
| ~ r1(esk1_0,X16) )
& ( r1(X16,esk3_1(X16))
| p101(X16)
| ~ p100(X16)
| ~ r1(esk1_0,X16) )
& ( p2(esk3_1(X16))
| p101(X16)
| ~ p100(X16)
| ~ r1(esk1_0,X16) )
& ( ~ p102(esk3_1(X16))
| p101(X16)
| ~ p100(X16)
| ~ r1(esk1_0,X16) )
& ( p101(esk3_1(X16))
| p101(X16)
| ~ p100(X16)
| ~ r1(esk1_0,X16) )
& ( ~ r1(X16,X19)
| ~ p2(X19)
| ~ p101(X19)
| p2(X16)
| ~ p101(X16)
| ~ r1(esk1_0,X16) )
& ( ~ r1(X16,X20)
| p2(X20)
| ~ p101(X20)
| ~ p2(X16)
| ~ p101(X16)
| ~ r1(esk1_0,X16) )
& ( ~ r1(X16,X21)
| ~ p1(X21)
| ~ p100(X21)
| p1(X16)
| ~ p100(X16)
| ~ r1(esk1_0,X16) )
& ( ~ r1(X16,X22)
| p1(X22)
| ~ p100(X22)
| ~ p1(X16)
| ~ p100(X16)
| ~ r1(esk1_0,X16) )
& ( p101(X16)
| ~ p102(X16)
| ~ r1(esk1_0,X16) )
& ( p100(X16)
| ~ p101(X16)
| ~ r1(esk1_0,X16) )
& ~ 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_2])])])])]) ).
fof(i_0_4,plain,
! [X13] : r1(X13,X13),
inference(variable_rename,[status(thm)],[reflexivity]) ).
cnf(i_0_5,negated_conjecture,
( p1(X1)
| ~ r1(X1,X2)
| ~ p1(X2)
| ~ p100(X2)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_6,negated_conjecture,
( p1(X2)
| ~ r1(X1,X2)
| ~ p100(X2)
| ~ p1(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_7,negated_conjecture,
( p2(X1)
| ~ r1(X1,X2)
| ~ p2(X2)
| ~ p101(X2)
| ~ p101(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_8,negated_conjecture,
( p2(X2)
| ~ r1(X1,X2)
| ~ p101(X2)
| ~ p2(X1)
| ~ p101(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_9,negated_conjecture,
( r1(X1,esk3_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_10,negated_conjecture,
( r1(X1,esk2_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_11,negated_conjecture,
( p101(X1)
| ~ p102(esk3_1(X1))
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_12,negated_conjecture,
( p101(X1)
| ~ p102(esk2_1(X1))
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_13,negated_conjecture,
( p101(X1)
| ~ p2(esk2_1(X1))
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_14,negated_conjecture,
( p101(esk3_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_15,negated_conjecture,
( p101(esk2_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_16,negated_conjecture,
( p2(esk3_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_17,negated_conjecture,
( p100(X1)
| ~ p101(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_18,negated_conjecture,
( p101(X1)
| ~ p102(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_19,negated_conjecture,
( p2(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_20,plain,
r1(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_21,negated_conjecture,
~ p101(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_22,negated_conjecture,
p100(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_3]),
[final] ).
cnf(i_0_23,plain,
p2(esk1_0),
inference(scs_inference,[],[i_0_20,i_0_19]) ).
cnf(i_0_24,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_25,plain,
( ~ r1(esk1_0,X1)
| p2(X1) ),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_26,plain,
r1(esk1_0,esk3_1(esk1_0)),
inference(scs_inference,[],[i_0_21,i_0_20,i_0_24,i_0_22,i_0_19,i_0_9]) ).
cnf(i_0_27,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_28,plain,
( ~ r1(esk1_0,X1)
| r1(X1,esk3_1(X1))
| p101(X1)
| ~ p100(X1) ),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_29,plain,
r1(esk1_0,esk2_1(esk1_0)),
inference(scs_inference,[],[i_0_21,i_0_20,i_0_24,i_0_27,i_0_22,i_0_19,i_0_9,i_0_10]) ).
cnf(i_0_30,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_31,plain,
( ~ r1(esk1_0,X1)
| r1(X1,esk2_1(X1))
| p101(X1)
| ~ p100(X1) ),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_32,plain,
( ~ p101(esk3_1(esk1_0))
| p100(esk3_1(esk1_0)) ),
inference(scs_inference,[],[i_0_21,i_0_20,i_0_24,i_0_27,i_0_22,i_0_19,i_0_9,i_0_10,i_0_17]) ).
cnf(i_0_33,plain,
( ~ r1(esk1_0,X1)
| ~ p101(X1)
| p100(X1) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_34,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_35,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_36,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_37,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_39,plain,
p2(esk3_1(esk1_0)),
inference(scs_inference,[],[i_0_26,i_0_19]) ).
cnf(i_0_40,plain,
( ~ r1(esk1_0,X1)
| p2(X1) ),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_41,plain,
( ~ p101(esk2_1(esk1_0))
| p100(esk2_1(esk1_0)) ),
inference(scs_inference,[],[i_0_26,i_0_29,i_0_19,i_0_17]) ).
cnf(i_0_42,plain,
( ~ r1(esk1_0,X1)
| ~ p101(X1)
| p100(X1) ),
inference(rename_variables,[],[i_0_17]) ).
cnf(i_0_43,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_20]) ).
cnf(i_0_44,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_21,i_0_26,i_0_29,i_0_20,i_0_22,i_0_19,i_0_17,i_0_15,i_0_5]) ).
cnf(i_0_45,plain,
p2(esk2_1(esk1_0)),
inference(scs_inference,[],[i_0_29,i_0_19]) ).
cnf(i_0_46,plain,
( ~ r1(esk1_0,X1)
| p2(X1) ),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_47,plain,
$false,
inference(scs_inference,[],[i_0_21,i_0_29,i_0_20,i_0_22,i_0_19,i_0_13]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL656+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
% 0.14/0.32 % Computer : n031.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Mon May 4 22:52:38 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % 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 : 1.270s
%------------------------------------------------------------------------------