%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL636+1.001 : TPTP v9.2.1. Released v4.0.0.
% 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 : n015.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 04:40:39 PM UTC 2026
% Result : Theorem 0.27s 1.62s
% Output : CNFRefutation 0.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 1
% Syntax : Number of formulae : 43 ( 9 unt; 0 def)
% Number of atoms : 381 ( 0 equ)
% Maximal formula atoms : 114 ( 8 avg)
% Number of connectives : 616 ( 278 ~; 254 |; 84 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 43 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 65 ( 0 sgn 38 !; 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) ) ) )
& ( ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( ~ p2(X2)
& ~ p102(X2)
& p101(X2) ) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( p2(X2)
& ~ p102(X2)
& p101(X2) ) ) )
| ~ ( ~ p101(X1)
& p100(X1) ) )
& ( ( ( ! [X2] :
( ~ r1(X1,X2)
| ~ p2(X2)
| ~ p101(X2) )
| p2(X1) )
& ( ! [X2] :
( ~ r1(X1,X2)
| p2(X2)
| ~ p101(X2) )
| ~ p2(X1) ) )
| ~ p101(X1) )
& ( ( ( ! [X2] :
( ~ r1(X1,X2)
| ~ p1(X2)
| ~ p100(X2) )
| p1(X1) )
& ( ! [X2] :
( ~ r1(X1,X2)
| p1(X2)
| ~ p100(X2) )
| ~ p1(X1) ) )
| ~ p100(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( p100(X1)
| ~ p101(X1) )
& ~ p101(X1)
& p100(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(i_0_1,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) ) ) )
& ( ( ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( ~ p2(X2)
& ~ p102(X2)
& p101(X2) ) )
& ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ( p2(X2)
& ~ p102(X2)
& p101(X2) ) ) )
| ~ ( ~ p101(X1)
& p100(X1) ) )
& ( ( ( ! [X2] :
( ~ r1(X1,X2)
| ~ p2(X2)
| ~ p101(X2) )
| p2(X1) )
& ( ! [X2] :
( ~ r1(X1,X2)
| p2(X2)
| ~ p101(X2) )
| ~ p2(X1) ) )
| ~ p101(X1) )
& ( ( ( ! [X2] :
( ~ r1(X1,X2)
| ~ p1(X2)
| ~ p100(X2) )
| p1(X1) )
& ( ! [X2] :
( ~ r1(X1,X2)
| p1(X2)
| ~ p100(X2) )
| ~ p1(X1) ) )
| ~ p100(X1) )
& ( p101(X1)
| ~ p102(X1) )
& ( p100(X1)
| ~ p101(X1) )
& ~ p101(X1)
& p100(X1) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[main])]) ).
fof(i_0_2,negated_conjecture,
! [X19,X20,X23,X24,X25,X26,X29,X30,X31,X32] :
( ( ~ r1(esk1_0,X19)
| p2(X19) )
& ( r1(X20,esk2_1(X20))
| p101(X20)
| ~ p100(X20)
| ~ r1(esk1_0,X20) )
& ( ~ p2(esk2_1(X20))
| p101(X20)
| ~ p100(X20)
| ~ r1(esk1_0,X20) )
& ( ~ p102(esk2_1(X20))
| p101(X20)
| ~ p100(X20)
| ~ r1(esk1_0,X20) )
& ( p101(esk2_1(X20))
| p101(X20)
| ~ p100(X20)
| ~ r1(esk1_0,X20) )
& ( r1(X20,esk3_1(X20))
| p101(X20)
| ~ p100(X20)
| ~ r1(esk1_0,X20) )
& ( p2(esk3_1(X20))
| p101(X20)
| ~ p100(X20)
| ~ r1(esk1_0,X20) )
& ( ~ p102(esk3_1(X20))
| p101(X20)
| ~ p100(X20)
| ~ r1(esk1_0,X20) )
& ( p101(esk3_1(X20))
| p101(X20)
| ~ p100(X20)
| ~ r1(esk1_0,X20) )
& ( ~ r1(X20,X23)
| ~ p2(X23)
| ~ p101(X23)
| p2(X20)
| ~ p101(X20)
| ~ r1(esk1_0,X20) )
& ( ~ r1(X20,X24)
| p2(X24)
| ~ p101(X24)
| ~ p2(X20)
| ~ p101(X20)
| ~ r1(esk1_0,X20) )
& ( ~ r1(X20,X25)
| ~ p1(X25)
| ~ p100(X25)
| p1(X20)
| ~ p100(X20)
| ~ r1(esk1_0,X20) )
& ( ~ r1(X20,X26)
| p1(X26)
| ~ p100(X26)
| ~ p1(X20)
| ~ p100(X20)
| ~ r1(esk1_0,X20) )
& ( p101(X20)
| ~ p102(X20)
| ~ r1(esk1_0,X20) )
& ( p100(X20)
| ~ p101(X20)
| ~ r1(esk1_0,X20) )
& ( r1(esk1_0,esk4_0)
| p101(esk1_0)
| ~ p100(esk1_0) )
& ( ~ p2(esk4_0)
| p101(esk1_0)
| ~ p100(esk1_0) )
& ( ~ p102(esk4_0)
| p101(esk1_0)
| ~ p100(esk1_0) )
& ( p101(esk4_0)
| p101(esk1_0)
| ~ p100(esk1_0) )
& ( r1(esk1_0,esk5_0)
| p101(esk1_0)
| ~ p100(esk1_0) )
& ( p2(esk5_0)
| p101(esk1_0)
| ~ p100(esk1_0) )
& ( ~ p102(esk5_0)
| p101(esk1_0)
| ~ p100(esk1_0) )
& ( p101(esk5_0)
| p101(esk1_0)
| ~ p100(esk1_0) )
& ( ~ r1(esk1_0,X29)
| ~ p2(X29)
| ~ p101(X29)
| p2(esk1_0)
| ~ p101(esk1_0) )
& ( ~ r1(esk1_0,X30)
| p2(X30)
| ~ p101(X30)
| ~ p2(esk1_0)
| ~ p101(esk1_0) )
& ( ~ r1(esk1_0,X31)
| ~ p1(X31)
| ~ p100(X31)
| p1(esk1_0)
| ~ p100(esk1_0) )
& ( ~ r1(esk1_0,X32)
| p1(X32)
| ~ p100(X32)
| ~ p1(esk1_0)
| ~ p100(esk1_0) )
& ( p101(esk1_0)
| ~ p102(esk1_0) )
& ( p100(esk1_0)
| ~ p101(esk1_0) )
& ~ 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_1])])])])]) ).
cnf(i_0_3,negated_conjecture,
( p1(X1)
| ~ r1(X1,X2)
| ~ p1(X2)
| ~ p100(X2)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_4,negated_conjecture,
( p1(X2)
| ~ r1(X1,X2)
| ~ p100(X2)
| ~ p1(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_5,negated_conjecture,
( p2(X1)
| ~ r1(X1,X2)
| ~ p2(X2)
| ~ p101(X2)
| ~ p101(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_6,negated_conjecture,
( p2(X2)
| ~ r1(X1,X2)
| ~ p101(X2)
| ~ p2(X1)
| ~ p101(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_7,negated_conjecture,
( r1(X1,esk3_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_8,negated_conjecture,
( r1(X1,esk2_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_9,negated_conjecture,
( p101(X1)
| ~ p102(esk3_1(X1))
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_10,negated_conjecture,
( p101(X1)
| ~ p102(esk2_1(X1))
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_11,negated_conjecture,
( p101(X1)
| ~ p2(esk2_1(X1))
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_12,negated_conjecture,
( p101(esk3_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_13,negated_conjecture,
( p101(esk2_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_14,negated_conjecture,
( p2(esk3_1(X1))
| p101(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_15,negated_conjecture,
( p1(esk1_0)
| ~ r1(esk1_0,X1)
| ~ p1(X1)
| ~ p100(X1)
| ~ p100(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_16,negated_conjecture,
( p2(esk1_0)
| ~ r1(esk1_0,X1)
| ~ p2(X1)
| ~ p101(X1)
| ~ p101(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_17,negated_conjecture,
( p1(X1)
| ~ r1(esk1_0,X1)
| ~ p100(X1)
| ~ p1(esk1_0)
| ~ p100(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_18,negated_conjecture,
( p2(X1)
| ~ r1(esk1_0,X1)
| ~ p101(X1)
| ~ p2(esk1_0)
| ~ p101(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_19,negated_conjecture,
( p100(X1)
| ~ p101(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_20,negated_conjecture,
( p101(X1)
| ~ p102(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_21,negated_conjecture,
( p2(X1)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_22,negated_conjecture,
( r1(esk1_0,esk5_0)
| p101(esk1_0)
| ~ p100(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_23,negated_conjecture,
( r1(esk1_0,esk4_0)
| p101(esk1_0)
| ~ p100(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_24,negated_conjecture,
( p101(esk1_0)
| ~ p102(esk5_0)
| ~ p100(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_25,negated_conjecture,
( p101(esk1_0)
| ~ p102(esk4_0)
| ~ p100(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_26,negated_conjecture,
( p101(esk1_0)
| ~ p2(esk4_0)
| ~ p100(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_27,negated_conjecture,
( p101(esk5_0)
| p101(esk1_0)
| ~ p100(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_28,negated_conjecture,
( p101(esk4_0)
| p101(esk1_0)
| ~ p100(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_29,negated_conjecture,
( p2(esk5_0)
| p101(esk1_0)
| ~ p100(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_30,negated_conjecture,
( p100(esk1_0)
| ~ p101(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_31,negated_conjecture,
( p101(esk1_0)
| ~ p102(esk1_0) ),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_32,negated_conjecture,
~ p101(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_33,negated_conjecture,
p100(esk1_0),
inference(split_conjunct,[status(thm)],[i_0_2]),
[final] ).
cnf(i_0_34,plain,
( ~ p1(X1)
| ~ p100(X1)
| ~ r1(esk1_0,X1)
| p1(esk1_0) ),
inference(scs_inference,[],[i_0_33,i_0_15]) ).
cnf(i_0_35,plain,
( ~ p100(X1)
| p1(X1)
| ~ r1(esk1_0,X1)
| ~ p1(esk1_0) ),
inference(scs_inference,[],[i_0_33,i_0_17]) ).
cnf(i_0_36,plain,
r1(esk1_0,esk5_0),
inference(scs_inference,[],[i_0_32,i_0_33,i_0_22]) ).
cnf(i_0_37,plain,
r1(esk1_0,esk4_0),
inference(scs_inference,[],[i_0_32,i_0_33,i_0_23]) ).
cnf(i_0_38,plain,
~ p2(esk4_0),
inference(scs_inference,[],[i_0_32,i_0_33,i_0_26]) ).
cnf(i_0_39,plain,
p101(esk5_0),
inference(scs_inference,[],[i_0_32,i_0_33,i_0_27]) ).
cnf(i_0_40,plain,
p101(esk4_0),
inference(scs_inference,[],[i_0_32,i_0_33,i_0_28]) ).
cnf(i_0_41,plain,
p2(esk5_0),
inference(scs_inference,[],[i_0_32,i_0_33,i_0_29]) ).
cnf(i_0_42,plain,
$false,
inference(scs_inference,[],[i_0_37,i_0_38,i_0_21]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL636+1.001 : TPTP v9.2.1. Released v4.0.0.
% 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
% 0.17/0.34 % Computer : n015.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon May 4 22:46:32 EDT 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % start to proof: theBenchmark
% 0.27/1.62 % Version : CSE_E---1.7
% 0.27/1.62 % Problem : theBenchmark.p
% 0.27/1.62 % SZS status Theorem for theBenchmark.p
% 0.27/1.62 % SZS output start CNFRefutation
% See solution above
% 0.27/1.65 % Total time : 1.272s
%------------------------------------------------------------------------------