%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN067+2 : TPTP v9.2.1. Released v7.3.0.
% 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 : n013.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 05:00:49 PM UTC 2026
% Result : Theorem 0.23s 1.62s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 62 ( 28 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 78 ( 38 ~; 25 |; 15 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 42 ( 8 sgn 21 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(nonzerosexist,conjecture,
? [X39] :
! [X22] :
( ~ r1(X22)
| X39 != X22 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonzerosexist) ).
fof(axiom_7a,axiom,
! [X41,X42] :
( ! [X43] :
( ~ r1(X43)
| X43 != X42 )
| ~ r2(X41,X42) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_7a) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1) ).
fof(axiom_2,axiom,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2) ).
fof(c_0_4,negated_conjecture,
~ ? [X39] :
! [X22] :
( ~ r1(X22)
| X39 != X22 ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[nonzerosexist])]) ).
fof(c_0_5,plain,
! [X41,X42] :
( ! [X43] :
( ~ r1(X43)
| X43 != X42 )
| ~ r2(X41,X42) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
fof(c_0_6,negated_conjecture,
! [X132] :
( r1(esk21_1(X132))
& X132 = esk21_1(X132) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).
fof(c_0_7,plain,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_8,plain,
! [X129,X130,X131] :
( ~ r1(X131)
| X131 != X130
| ~ r2(X129,X130) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_5])]) ).
cnf(c_0_9,negated_conjecture,
r1(esk21_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
cnf(c_0_10,negated_conjecture,
X1 = esk21_1(X1),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
fof(c_0_11,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_12,plain,
! [X90] :
( ( r1(X90)
| ~ r1(X90) )
& ( X90 = esk1_0
| ~ r1(X90) )
& ( r1(X90)
| X90 != esk1_0 )
& ( X90 = esk1_0
| X90 != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])]) ).
cnf(c_0_13,plain,
( ~ r1(X1)
| X1 != X2
| ~ r2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,negated_conjecture,
r1(X1),
inference(rw,[status(thm)],[c_0_9,c_0_10]) ).
fof(c_0_15,plain,
! [X91,X93] :
( ( r2(X91,X93)
| ~ r2(X91,X93) )
& ( X93 = esk2_1(X91)
| ~ r2(X91,X93) )
& ( r2(X91,X93)
| X93 != esk2_1(X91) )
& ( X93 = esk2_1(X91)
| X93 != esk2_1(X91) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_11])])]) ).
cnf(c_0_16,plain,
( X1 = esk1_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,negated_conjecture,
( X1 != X2
| ~ r2(X3,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_13,c_0_14])]) ).
cnf(c_0_18,plain,
( r2(X1,X2)
| X2 != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_19,negated_conjecture,
X1 = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_14])]) ).
cnf(c_0_20,negated_conjecture,
~ r2(X1,X2),
inference(er,[status(thm)],[c_0_17]) ).
cnf(c_0_21,plain,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]),c_0_20]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : NUN067+2 : TPTP v9.2.1. Released v7.3.0.
% 0.00/0.13 % 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
% 0.14/0.33 % Computer : n013.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 : Tue May 5 01:22:26 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 0.23/1.62 % Version : CSE_E---1.7
% 0.23/1.62 % Problem : theBenchmark.p
% 0.23/1.62 % SZS status Theorem for theBenchmark.p
% 0.23/1.62 % SZS output start CNFRefutation
% See solution above
% 0.23/1.62 % Total time : 1.270s
%------------------------------------------------------------------------------