%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : MSC012+1 : TPTP v9.2.1. Released v3.2.0.
% 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 : n010.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 04:48:56 PM UTC 2026
% Result : Theorem 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 5
% Syntax : Number of formulae : 22 ( 8 unt; 0 def)
% Number of atoms : 50 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 47 ( 19 ~; 21 |; 5 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 0 con; 1-1 aty)
% Number of variables : 31 ( 1 sgn 14 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(transitive_less,axiom,
! [X1,X2,X3] :
( ( less(X1,X2)
& less(X2,X3) )
=> less(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitive_less) ).
fof(right_to_left,axiom,
! [X1] :
( p(X1)
| ? [X2] :
( less(X1,X2)
& p(X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_to_left) ).
fof(left_to_right,axiom,
! [X1,X2] :
( ( p(X1)
& less(X1,X2)
& p(X2) )
=> goal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_to_right) ).
fof(goal_to_be_proved,conjecture,
goal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goal_to_be_proved) ).
fof(serial_less,axiom,
! [X1] :
? [X2] : less(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',serial_less) ).
fof(c_0_5,plain,
! [X17,X18,X19] :
( ~ less(X17,X18)
| ~ less(X18,X19)
| less(X17,X19) ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[transitive_less])]) ).
fof(c_0_6,plain,
! [X15] :
( ( less(X15,esk1_1(X15))
| p(X15) )
& ( p(esk1_1(X15))
| p(X15) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[right_to_left])])]) ).
fof(c_0_7,plain,
! [X13,X14] :
( ~ p(X13)
| ~ less(X13,X14)
| ~ p(X14)
| goal ),
inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[left_to_right])]) ).
fof(c_0_8,negated_conjecture,
~ goal,
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[goal_to_be_proved])]) ).
cnf(c_0_9,plain,
( less(X1,X3)
| ~ less(X1,X2)
| ~ less(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_5]) ).
cnf(c_0_10,plain,
( less(X1,esk1_1(X1))
| p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,plain,
! [X20] : less(X20,esk2_1(X20)),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[serial_less])]) ).
cnf(c_0_12,plain,
( goal
| ~ p(X1)
| ~ less(X1,X2)
| ~ p(X2) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,negated_conjecture,
~ goal,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( less(X1,esk1_1(X2))
| p(X2)
| ~ less(X1,X2) ),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
less(X1,esk2_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_16,plain,
( ~ less(X1,X2)
| ~ p(X2)
| ~ p(X1) ),
inference(sr,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_17,plain,
( less(X1,esk1_1(esk2_1(X1)))
| p(esk2_1(X1)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
( p(esk1_1(X1))
| p(X1) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_19,plain,
( ~ p(esk2_1(X1))
| ~ p(X1) ),
inference(spm,[status(thm)],[c_0_16,c_0_15]) ).
cnf(c_0_20,plain,
~ p(X1),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]) ).
cnf(c_0_21,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[c_0_18,c_0_20]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : MSC012+1 : TPTP v9.2.1. Released v3.2.0.
% 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
% 0.14/0.33 % Computer : n010.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Mon May 4 23:35:51 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Theorem for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.372s
%------------------------------------------------------------------------------