%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN085+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 : n014.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 05:00:53 PM UTC 2026
% Result : Theorem 1.26s 1.72s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 66 ( 40 unt; 0 def)
% Number of atoms : 146 ( 57 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 137 ( 57 ~; 42 |; 38 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 100 ( 6 sgn 43 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
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_4a,axiom,
! [X30] :
? [X31] :
( ? [X32] :
( r1(X32)
& r3(X30,X32,X31) )
& X31 = X30 ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4a) ).
fof(axiom_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_3) ).
fof(zeroplusoneidzero,conjecture,
! [X39] :
( ! [X22] :
( ! [X23] :
( ~ r1(X23)
| ~ r3(X23,X22,X39) )
| ! [X16] :
( ~ r1(X16)
| ~ r2(X16,X22) ) )
| ! [X17] :
( X39 != X17
| ~ r1(X17) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zeroplusoneidzero) ).
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(axiom_1a,axiom,
! [X14,X15] :
? [X16] :
( ? [X17] :
( ? [X18] :
( r2(X15,X18)
& r3(X14,X18,X17) )
& X17 = X16 )
& ? [X19] :
( r2(X19,X16)
& r3(X14,X15,X19) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_1a) ).
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(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,
! [X121] :
( r1(esk14_1(X121))
& r3(X121,esk14_1(X121),esk13_1(X121))
& esk13_1(X121) = X121 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_9,plain,
! [X93] :
( ( r1(X93)
| ~ r1(X93) )
& ( X93 = esk1_0
| ~ r1(X93) )
& ( r1(X93)
| X93 != esk1_0 )
& ( X93 = esk1_0
| X93 != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_7])])]) ).
fof(c_0_10,plain,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
inference(fof_simplification,[status(thm)],[axiom_3]) ).
cnf(c_0_11,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
esk13_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( X1 = esk1_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
fof(c_0_15,negated_conjecture,
~ ! [X39] :
( ! [X22] :
( ! [X23] :
( ~ r1(X23)
| ~ r3(X23,X22,X39) )
| ! [X16] :
( ~ r1(X16)
| ~ r2(X16,X22) ) )
| ! [X17] :
( X39 != X17
| ~ r1(X17) ) ),
inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[zeroplusoneidzero])]) ).
fof(c_0_16,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_17,plain,
! [X97,X98,X100] :
( ( r3(X97,X98,X100)
| ~ r3(X97,X98,X100) )
& ( X100 = esk3_2(X97,X98)
| ~ r3(X97,X98,X100) )
& ( r3(X97,X98,X100)
| X100 != esk3_2(X97,X98) )
& ( X100 = esk3_2(X97,X98)
| X100 != esk3_2(X97,X98) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_10])])]) ).
cnf(c_0_18,plain,
r3(X1,esk14_1(X1),X1),
inference(rw,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_19,plain,
esk14_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_20,plain,
! [X105,X106] :
( r2(X106,esk7_2(X105,X106))
& r3(X105,esk7_2(X105,X106),esk6_2(X105,X106))
& esk6_2(X105,X106) = esk5_2(X105,X106)
& r2(esk8_2(X105,X106),esk5_2(X105,X106))
& r3(X105,X106,esk8_2(X105,X106)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_21,negated_conjecture,
( r1(esk23_0)
& r3(esk23_0,esk22_0,esk21_0)
& r1(esk24_0)
& r2(esk24_0,esk22_0)
& esk21_0 = esk25_0
& r1(esk25_0) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])]) ).
fof(c_0_22,plain,
! [X94,X96] :
( ( r2(X94,X96)
| ~ r2(X94,X96) )
& ( X96 = esk2_1(X94)
| ~ r2(X94,X96) )
& ( r2(X94,X96)
| X96 != esk2_1(X94) )
& ( X96 = esk2_1(X94)
| X96 != esk2_1(X94) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_16])])]) ).
cnf(c_0_23,plain,
( X1 = esk3_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_24,plain,
r3(X1,esk1_0,X1),
inference(rw,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_25,plain,
r3(X1,X2,esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_26,negated_conjecture,
r1(esk24_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,negated_conjecture,
r1(esk25_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,negated_conjecture,
esk21_0 = esk25_0,
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_29,plain,
r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
esk6_2(X1,X2) = esk5_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_31,plain,
( X1 = esk2_1(X2)
| ~ r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_32,plain,
r2(X1,esk7_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_33,plain,
r2(esk8_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_34,plain,
esk3_2(X1,esk1_0) = X1,
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_35,plain,
esk3_2(X1,X2) = esk8_2(X1,X2),
inference(spm,[status(thm)],[c_0_23,c_0_25]) ).
cnf(c_0_36,negated_conjecture,
r2(esk24_0,esk22_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_37,negated_conjecture,
esk24_0 = esk1_0,
inference(spm,[status(thm)],[c_0_13,c_0_26]) ).
cnf(c_0_38,negated_conjecture,
r1(esk23_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_39,negated_conjecture,
r1(esk21_0),
inference(rw,[status(thm)],[c_0_27,c_0_28]) ).
fof(c_0_40,plain,
! [X41,X42] :
( ! [X43] :
( ~ r1(X43)
| X43 != X42 )
| ~ r2(X41,X42) ),
inference(fof_simplification,[status(thm)],[axiom_7a]) ).
cnf(c_0_41,plain,
r3(X1,esk7_2(X1,X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_42,plain,
esk7_2(X1,X2) = esk2_1(X2),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_43,plain,
esk2_1(esk8_2(X1,X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_33]) ).
cnf(c_0_44,plain,
esk8_2(X1,esk1_0) = X1,
inference(rw,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_45,negated_conjecture,
r2(esk1_0,esk22_0),
inference(rw,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_46,negated_conjecture,
r3(esk23_0,esk22_0,esk21_0),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_47,negated_conjecture,
esk23_0 = esk1_0,
inference(spm,[status(thm)],[c_0_13,c_0_38]) ).
cnf(c_0_48,negated_conjecture,
esk21_0 = esk1_0,
inference(spm,[status(thm)],[c_0_13,c_0_39]) ).
fof(c_0_49,plain,
! [X132,X133,X134] :
( ~ r1(X134)
| X134 != X133
| ~ r2(X132,X133) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_40])]) ).
cnf(c_0_50,plain,
r3(X1,esk2_1(X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_51,plain,
esk5_2(X1,esk1_0) = esk2_1(X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_52,negated_conjecture,
esk2_1(esk1_0) = esk22_0,
inference(spm,[status(thm)],[c_0_31,c_0_45]) ).
cnf(c_0_53,negated_conjecture,
r3(esk1_0,esk22_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_47]),c_0_48]) ).
cnf(c_0_54,plain,
( ~ r1(X1)
| X1 != X2
| ~ r2(X3,X2) ),
inference(split_conjunct,[status(thm)],[c_0_49]) ).
cnf(c_0_55,plain,
r3(X1,esk22_0,esk2_1(X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_56,negated_conjecture,
esk3_2(esk1_0,esk22_0) = esk1_0,
inference(spm,[status(thm)],[c_0_23,c_0_53]) ).
cnf(c_0_57,plain,
( ~ r2(X1,X2)
| ~ r1(X2) ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_58,plain,
( X1 = esk8_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(rw,[status(thm)],[c_0_23,c_0_35]) ).
cnf(c_0_59,negated_conjecture,
r3(esk1_0,esk22_0,esk22_0),
inference(spm,[status(thm)],[c_0_55,c_0_52]) ).
cnf(c_0_60,negated_conjecture,
esk8_2(esk1_0,esk22_0) = esk1_0,
inference(rw,[status(thm)],[c_0_56,c_0_35]) ).
cnf(c_0_61,plain,
( r1(X1)
| X1 != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_62,negated_conjecture,
~ r1(esk22_0),
inference(spm,[status(thm)],[c_0_57,c_0_36]) ).
cnf(c_0_63,negated_conjecture,
esk22_0 = esk1_0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]) ).
cnf(c_0_64,plain,
r1(esk1_0),
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_65,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_62,c_0_63]),c_0_64])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN085+2 : TPTP v9.2.1. Released v7.3.0.
% 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
% 0.15/0.33 % Computer : n014.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 01:24:07 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.26/1.72 % Version : CSE_E---1.7
% 1.26/1.72 % Problem : theBenchmark.p
% 1.26/1.72 % SZS status Theorem for theBenchmark.p
% 1.26/1.72 % SZS output start CNFRefutation
% See solution above
% 1.26/1.72 % Total time : 1.370s
%------------------------------------------------------------------------------