%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN084+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 : n016.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 1.28s 1.73s
% Output : CNFRefutation 1.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 83 ( 49 unt; 0 def)
% Number of atoms : 190 ( 72 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 169 ( 62 ~; 45 |; 62 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 1 con; 0-2 aty)
% Number of variables : 180 ( 26 sgn 45 !; 33 ?)
% 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_5a,axiom,
! [X33] :
? [X34] :
( ? [X35] :
( r1(X35)
& r4(X33,X35,X34) )
& ? [X36] :
( r1(X36)
& X34 = X36 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_5a) ).
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_4,axiom,
! [X10,X11] :
? [X12] :
! [X13] :
( ( ~ r4(X10,X11,X13)
& X13 != X12 )
| ( r4(X10,X11,X13)
& X13 = X12 ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_4) ).
fof(xtimesyeqtwo,conjecture,
? [X39,X22,X23] :
( r4(X39,X22,X23)
& ? [X16] :
( X23 = X16
& ? [X17] :
( r2(X17,X16)
& ? [X25] :
( r1(X25)
& r2(X25,X17) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',xtimesyeqtwo) ).
fof(axiom_2a,axiom,
! [X20,X21] :
? [X22] :
( ? [X23] :
( ? [X24] :
( r2(X21,X24)
& r4(X20,X24,X23) )
& X23 = X22 )
& ? [X25] :
( r3(X25,X20,X22)
& r4(X20,X21,X25) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM008+0.ax',axiom_2a) ).
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(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_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(c_0_9,plain,
? [X1] :
! [X2] :
( ( ~ r1(X2)
& X2 != X1 )
| ( r1(X2)
& X2 = X1 ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
fof(c_0_10,plain,
! [X125] :
( r1(esk16_1(X125))
& r4(X125,esk16_1(X125),esk15_1(X125))
& r1(esk17_1(X125))
& esk15_1(X125) = esk17_1(X125) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_5a])]) ).
fof(c_0_11,plain,
! [X94] :
( ( r1(X94)
| ~ r1(X94) )
& ( X94 = esk1_0
| ~ r1(X94) )
& ( r1(X94)
| X94 != esk1_0 )
& ( X94 = esk1_0
| X94 != esk1_0 ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_9])])]) ).
cnf(c_0_12,plain,
r1(esk17_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_13,plain,
esk15_1(X1) = esk17_1(X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_14,plain,
! [X3] :
? [X4] :
! [X5] :
( ( ~ r2(X3,X5)
& X5 != X4 )
| ( r2(X3,X5)
& X5 = X4 ) ),
inference(fof_simplification,[status(thm)],[axiom_2]) ).
fof(c_0_15,plain,
! [X10,X11] :
? [X12] :
! [X13] :
( ( ~ r4(X10,X11,X13)
& X13 != X12 )
| ( r4(X10,X11,X13)
& X13 = X12 ) ),
inference(fof_simplification,[status(thm)],[axiom_4]) ).
cnf(c_0_16,plain,
( X1 = esk1_0
| ~ r1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_17,plain,
r1(esk16_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
r1(esk15_1(X1)),
inference(rw,[status(thm)],[c_0_12,c_0_13]) ).
fof(c_0_19,negated_conjecture,
~ ? [X39,X22,X23] :
( r4(X39,X22,X23)
& ? [X16] :
( X23 = X16
& ? [X17] :
( r2(X17,X16)
& ? [X25] :
( r1(X25)
& r2(X25,X17) ) ) ) ),
inference(assume_negation,[status(cth)],[xtimesyeqtwo]) ).
fof(c_0_20,plain,
! [X112,X113] :
( r2(X113,esk11_2(X112,X113))
& r4(X112,esk11_2(X112,X113),esk10_2(X112,X113))
& esk10_2(X112,X113) = esk9_2(X112,X113)
& r3(esk12_2(X112,X113),X112,esk9_2(X112,X113))
& r4(X112,X113,esk12_2(X112,X113)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_2a])]) ).
fof(c_0_21,plain,
! [X95,X97] :
( ( r2(X95,X97)
| ~ r2(X95,X97) )
& ( X97 = esk2_1(X95)
| ~ r2(X95,X97) )
& ( r2(X95,X97)
| X97 != esk2_1(X95) )
& ( X97 = esk2_1(X95)
| X97 != esk2_1(X95) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_14])])]) ).
fof(c_0_22,plain,
! [X6,X7] :
? [X8] :
! [X9] :
( ( ~ r3(X6,X7,X9)
& X9 != X8 )
| ( r3(X6,X7,X9)
& X9 = X8 ) ),
inference(fof_simplification,[status(thm)],[axiom_3]) ).
fof(c_0_23,plain,
! [X102,X103,X105] :
( ( r4(X102,X103,X105)
| ~ r4(X102,X103,X105) )
& ( X105 = esk4_2(X102,X103)
| ~ r4(X102,X103,X105) )
& ( r4(X102,X103,X105)
| X105 != esk4_2(X102,X103) )
& ( X105 = esk4_2(X102,X103)
| X105 != esk4_2(X102,X103) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_15])])]) ).
cnf(c_0_24,plain,
r4(X1,esk16_1(X1),esk15_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_25,plain,
esk16_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_26,plain,
esk15_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_16,c_0_18]) ).
fof(c_0_27,negated_conjecture,
! [X136,X137,X138,X139,X140,X141] :
( ~ r4(X136,X137,X138)
| X138 != X139
| ~ r2(X140,X139)
| ~ r1(X141)
| ~ r2(X141,X140) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_19])])]) ).
cnf(c_0_28,plain,
r4(X1,esk11_2(X1,X2),esk10_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_29,plain,
esk10_2(X1,X2) = esk9_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_30,plain,
( X1 = esk2_1(X2)
| ~ r2(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_31,plain,
r2(X1,esk11_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_32,plain,
! [X98,X99,X101] :
( ( r3(X98,X99,X101)
| ~ r3(X98,X99,X101) )
& ( X101 = esk3_2(X98,X99)
| ~ r3(X98,X99,X101) )
& ( r3(X98,X99,X101)
| X101 != esk3_2(X98,X99) )
& ( X101 = esk3_2(X98,X99)
| X101 != esk3_2(X98,X99) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_22])])]) ).
fof(c_0_33,plain,
! [X106,X107] :
( r2(X107,esk7_2(X106,X107))
& r3(X106,esk7_2(X106,X107),esk6_2(X106,X107))
& esk6_2(X106,X107) = esk5_2(X106,X107)
& r2(esk8_2(X106,X107),esk5_2(X106,X107))
& r3(X106,X107,esk8_2(X106,X107)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
cnf(c_0_34,plain,
( X1 = esk4_2(X2,X3)
| ~ r4(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_35,plain,
r4(X1,esk1_0,esk1_0),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_36,plain,
r4(X1,X2,esk12_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_37,negated_conjecture,
( ~ r4(X1,X2,X3)
| X3 != X4
| ~ r2(X5,X4)
| ~ r1(X6)
| ~ r2(X6,X5) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
cnf(c_0_38,plain,
r4(X1,esk11_2(X1,X2),esk9_2(X1,X2)),
inference(rw,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_39,plain,
esk11_2(X1,X2) = esk2_1(X2),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_40,plain,
( X1 = esk3_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_41,plain,
r3(X1,X2,esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_42,plain,
r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_43,plain,
esk6_2(X1,X2) = esk5_2(X1,X2),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_44,plain,
r2(X1,esk7_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_45,plain,
esk4_2(X1,esk1_0) = esk1_0,
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_46,plain,
esk4_2(X1,X2) = esk12_2(X1,X2),
inference(spm,[status(thm)],[c_0_34,c_0_36]) ).
fof(c_0_47,plain,
! [X122] :
( r1(esk14_1(X122))
& r3(X122,esk14_1(X122),esk13_1(X122))
& esk13_1(X122) = X122 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
cnf(c_0_48,negated_conjecture,
( ~ r4(X1,X2,X3)
| ~ r2(X4,X5)
| ~ r2(X5,X3)
| ~ r1(X4) ),
inference(er,[status(thm)],[c_0_37]) ).
cnf(c_0_49,plain,
r4(X1,esk2_1(X2),esk9_2(X1,X2)),
inference(rw,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_50,plain,
( r1(X1)
| X1 != esk1_0 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_51,plain,
esk3_2(X1,X2) = esk8_2(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_52,plain,
r3(X1,esk7_2(X1,X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_53,plain,
esk7_2(X1,X2) = esk2_1(X2),
inference(spm,[status(thm)],[c_0_30,c_0_44]) ).
cnf(c_0_54,plain,
r3(esk12_2(X1,X2),X1,esk9_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_55,plain,
esk12_2(X1,esk1_0) = esk1_0,
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_56,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_57,plain,
esk13_1(X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_58,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_47]) ).
cnf(c_0_59,negated_conjecture,
( ~ r2(X1,esk9_2(X2,X3))
| ~ r2(X4,X1)
| ~ r1(X4) ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_60,plain,
r1(esk1_0),
inference(er,[status(thm)],[c_0_50]) ).
cnf(c_0_61,plain,
( r2(X1,X2)
| X2 != esk2_1(X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_62,plain,
( X1 = esk8_2(X2,X3)
| ~ r3(X2,X3,X1) ),
inference(rw,[status(thm)],[c_0_40,c_0_51]) ).
cnf(c_0_63,plain,
r3(X1,esk2_1(X2),esk5_2(X1,X2)),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_64,plain,
r3(esk1_0,X1,esk9_2(X1,esk1_0)),
inference(spm,[status(thm)],[c_0_54,c_0_55]) ).
cnf(c_0_65,plain,
r3(X1,esk14_1(X1),X1),
inference(rw,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_66,plain,
esk14_1(X1) = esk1_0,
inference(spm,[status(thm)],[c_0_16,c_0_58]) ).
cnf(c_0_67,negated_conjecture,
( ~ r2(X1,esk9_2(X2,X3))
| ~ r2(esk1_0,X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_68,plain,
r2(X1,esk2_1(X1)),
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_69,plain,
esk8_2(X1,esk2_1(X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_70,plain,
esk8_2(esk1_0,X1) = esk9_2(X1,esk1_0),
inference(spm,[status(thm)],[c_0_62,c_0_64]) ).
cnf(c_0_71,plain,
r2(esk8_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_72,plain,
r3(X1,esk1_0,X1),
inference(rw,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_73,negated_conjecture,
~ r2(esk2_1(esk1_0),esk9_2(X1,X2)),
inference(spm,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_74,plain,
esk9_2(esk2_1(X1),esk1_0) = esk5_2(esk1_0,X1),
inference(spm,[status(thm)],[c_0_69,c_0_70]) ).
cnf(c_0_75,plain,
esk2_1(esk8_2(X1,X2)) = esk5_2(X1,X2),
inference(spm,[status(thm)],[c_0_30,c_0_71]) ).
cnf(c_0_76,plain,
esk3_2(X1,esk1_0) = X1,
inference(spm,[status(thm)],[c_0_40,c_0_72]) ).
cnf(c_0_77,negated_conjecture,
~ r2(esk2_1(esk1_0),esk5_2(esk1_0,X1)),
inference(spm,[status(thm)],[c_0_73,c_0_74]) ).
cnf(c_0_78,plain,
esk5_2(X1,esk2_1(X2)) = esk2_1(esk5_2(X1,X2)),
inference(spm,[status(thm)],[c_0_75,c_0_69]) ).
cnf(c_0_79,plain,
esk8_2(X1,esk1_0) = X1,
inference(rw,[status(thm)],[c_0_76,c_0_51]) ).
cnf(c_0_80,negated_conjecture,
~ r2(esk2_1(esk1_0),esk2_1(esk5_2(esk1_0,X1))),
inference(spm,[status(thm)],[c_0_77,c_0_78]) ).
cnf(c_0_81,plain,
esk5_2(X1,esk1_0) = esk2_1(X1),
inference(spm,[status(thm)],[c_0_75,c_0_79]) ).
cnf(c_0_82,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_81]),c_0_68])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN084+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
% 0.15/0.34 % Computer : n016.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue May 5 01:23:21 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.28/1.73 % Version : CSE_E---1.7
% 1.28/1.73 % Problem : theBenchmark.p
% 1.28/1.73 % SZS status Theorem for theBenchmark.p
% 1.28/1.73 % SZS output start CNFRefutation
% See solution above
% 1.28/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------