%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LCL678+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 : n001.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 04:44:46 PM UTC 2026
% Result : Theorem 0.23s 1.61s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 3
% Syntax : Number of formulae : 23 ( 10 unt; 0 def)
% Number of atoms : 58 ( 0 equ)
% Maximal formula atoms : 9 ( 2 avg)
% Number of connectives : 76 ( 41 ~; 30 |; 4 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 18 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(main,conjecture,
~ ? [X1] :
~ ( ~ $true
| ~ ! [X2] :
( ~ r1(X1,X2)
| ~ $true
| ~ ! [X1] :
( ~ r1(X2,X1)
| ! [X2] :
( ~ r1(X1,X2)
| p1(X2) )
| ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',main) ).
fof(transitivity,axiom,
! [X1,X2,X3] :
( ( r1(X1,X2)
& r1(X2,X3) )
=> r1(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
fof(reflexivity,axiom,
! [X1] : r1(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(i_0_3,negated_conjecture,
~ ~ ? [X1] :
~ ~ ! [X2] :
( ~ r1(X1,X2)
| ~ ! [X1] :
( ~ r1(X2,X1)
| ! [X2] :
( ~ r1(X1,X2)
| p1(X2) )
| ~ ! [X2] :
( ~ r1(X1,X2)
| p1(X2) ) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[main])]) ).
fof(i_0_4,plain,
! [X14,X15,X16] :
( ~ r1(X14,X15)
| ~ r1(X15,X16)
| r1(X14,X16) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitivity])]) ).
fof(i_0_5,negated_conjecture,
! [X18,X21] :
( ( r1(X18,esk2_1(X18))
| ~ r1(esk1_0,X18) )
& ( r1(esk2_1(X18),esk3_1(X18))
| ~ r1(esk1_0,X18) )
& ( ~ p1(esk3_1(X18))
| ~ r1(esk1_0,X18) )
& ( ~ r1(esk2_1(X18),X21)
| p1(X21)
| ~ r1(esk1_0,X18) ) ),
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_6,plain,
! [X13] : r1(X13,X13),
inference(variable_rename,[status(thm)],[reflexivity]) ).
cnf(i_0_7,plain,
( r1(X1,X3)
| ~ r1(X1,X2)
| ~ r1(X2,X3) ),
inference(split_conjunct,[status(thm)],[i_0_4]),
[final] ).
cnf(i_0_8,negated_conjecture,
( p1(X2)
| ~ r1(esk2_1(X1),X2)
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_9,negated_conjecture,
( r1(esk2_1(X1),esk3_1(X1))
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_10,negated_conjecture,
( r1(X1,esk2_1(X1))
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_11,negated_conjecture,
( ~ p1(esk3_1(X1))
| ~ r1(esk1_0,X1) ),
inference(split_conjunct,[status(thm)],[i_0_5]),
[final] ).
cnf(i_0_12,plain,
r1(X1,X1),
inference(split_conjunct,[status(thm)],[i_0_6]),
[final] ).
cnf(i_0_13,plain,
r1(esk2_1(esk1_0),esk3_1(esk1_0)),
inference(scs_inference,[],[i_0_12,i_0_9]) ).
cnf(i_0_14,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_15,plain,
( ~ r1(esk1_0,X1)
| r1(esk2_1(X1),esk3_1(X1)) ),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_16,plain,
r1(esk1_0,esk2_1(esk1_0)),
inference(scs_inference,[],[i_0_12,i_0_14,i_0_9,i_0_10]) ).
cnf(i_0_17,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_18,plain,
( ~ r1(esk1_0,X1)
| r1(X1,esk2_1(X1)) ),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_19,plain,
p1(esk3_1(esk1_0)),
inference(scs_inference,[],[i_0_12,i_0_14,i_0_17,i_0_9,i_0_10,i_0_8]) ).
cnf(i_0_20,plain,
r1(X1,X1),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_21,plain,
( ~ r1(esk1_0,X1)
| ~ r1(esk2_1(X1),X2)
| p1(X2) ),
inference(rename_variables,[],[i_0_8]) ).
cnf(i_0_22,plain,
$false,
inference(scs_inference,[],[i_0_12,i_0_14,i_0_17,i_0_20,i_0_9,i_0_10,i_0_8,i_0_11]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LCL678+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
% 0.14/0.32 % Computer : n001.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 22:57:48 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.23/1.61 % Version : CSE_E---1.7
% 0.23/1.61 % Problem : theBenchmark.p
% 0.23/1.61 % SZS status Theorem for theBenchmark.p
% 0.23/1.61 % SZS output start CNFRefutation
% See solution above
% 0.23/1.64 % Total time : 1.270s
%------------------------------------------------------------------------------