%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : NUN054+1 : TPTP v9.2.1. Bugfixed v7.3.0.
% 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 : n006.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 05:00:47 PM UTC 2026
% Result : Theorem 1.82s 1.89s
% Output : CNFRefutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 53 ( 19 unt; 0 def)
% Number of atoms : 166 ( 0 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 194 ( 81 ~; 68 |; 45 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 1 con; 0-2 aty)
% Number of variables : 123 ( 2 sgn 47 !; 22 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_3,axiom,
! [X6,X7] :
? [X8] :
! [X9] :
( ( id(X9,X8)
& r3(X6,X7,X9) )
| ( ~ r3(X6,X7,X9)
& ~ id(X9,X8) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_3) ).
fof(zeroplusoneidone,conjecture,
? [X63] :
( ? [X46] :
( ? [X40] :
( r1(X40)
& r3(X40,X46,X63) )
& ? [X41] :
( r1(X41)
& r2(X41,X46) ) )
& ? [X47] :
( id(X63,X47)
& ? [X49] :
( r1(X49)
& r2(X49,X47) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',zeroplusoneidone) ).
fof(axiom_7,axiom,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_7) ).
fof(axiom_6,axiom,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(axiom_4a,axiom,
! [X54] :
? [X55] :
( id(X55,X54)
& ? [X56] :
( r1(X56)
& r3(X54,X56,X55) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
fof(axiom_1a,axiom,
! [X38,X39] :
? [X40] :
( ? [X41] :
( id(X41,X40)
& ? [X42] :
( r2(X39,X42)
& r3(X38,X42,X41) ) )
& ? [X43] :
( r2(X43,X40)
& r3(X38,X39,X43) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).
fof(axiom_8,axiom,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_8) ).
fof(axiom_1,axiom,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox/benchmark/Axioms/NUM009+0.ax',axiom_5) ).
fof(c_0_9,plain,
! [X6,X7] :
? [X8] :
! [X9] :
( ( id(X9,X8)
& r3(X6,X7,X9) )
| ( ~ r3(X6,X7,X9)
& ~ id(X9,X8) ) ),
inference(fof_simplification,[status(thm)],[axiom_3]) ).
fof(c_0_10,negated_conjecture,
~ ? [X63] :
( ? [X46] :
( ? [X40] :
( r1(X40)
& r3(X40,X46,X63) )
& ? [X41] :
( r1(X41)
& r2(X41,X46) ) )
& ? [X47] :
( id(X63,X47)
& ? [X49] :
( r1(X49)
& r2(X49,X47) ) ) ),
inference(assume_negation,[status(cth)],[zeroplusoneidone]) ).
fof(c_0_11,plain,
! [X17,X18,X19] :
( ~ id(X17,X18)
| id(X17,X19)
| ~ id(X18,X19) ),
inference(fof_simplification,[status(thm)],[axiom_7]) ).
fof(c_0_12,plain,
! [X15,X16] :
( ~ id(X15,X16)
| id(X16,X15) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(c_0_13,plain,
! [X146,X147,X149] :
( ( ~ r3(X146,X147,X149)
| id(X149,esk3_2(X146,X147)) )
& ( ~ id(X149,esk3_2(X146,X147))
| id(X149,esk3_2(X146,X147)) )
& ( ~ r3(X146,X147,X149)
| r3(X146,X147,X149) )
& ( ~ id(X149,esk3_2(X146,X147))
| r3(X146,X147,X149) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_9])])]) ).
fof(c_0_14,plain,
! [X194] :
( id(esk13_1(X194),X194)
& r1(esk14_1(X194))
& r3(X194,esk14_1(X194),esk13_1(X194)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_15,negated_conjecture,
! [X208,X209,X210,X211,X212,X213] :
( ~ r1(X210)
| ~ r3(X210,X209,X208)
| ~ r1(X211)
| ~ r2(X211,X209)
| ~ id(X208,X212)
| ~ r1(X213)
| ~ r2(X213,X212) ),
inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
fof(c_0_16,plain,
! [X178,X179] :
( id(esk6_2(X178,X179),esk5_2(X178,X179))
& r2(X179,esk7_2(X178,X179))
& r3(X178,esk7_2(X178,X179),esk6_2(X178,X179))
& r2(esk8_2(X178,X179),esk5_2(X178,X179))
& r3(X178,X179,esk8_2(X178,X179)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_17,plain,
! [X157,X158,X159] :
( ~ id(X157,X158)
| id(X157,X159)
| ~ id(X158,X159) ),
inference(variable_rename,[status(thm)],[c_0_11]) ).
fof(c_0_18,plain,
! [X155,X156] :
( ~ id(X155,X156)
| id(X156,X155) ),
inference(variable_rename,[status(thm)],[c_0_12]) ).
cnf(c_0_19,plain,
( id(X3,esk3_2(X1,X2))
| ~ r3(X1,X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_20,plain,
r3(X1,esk14_1(X1),esk13_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_21,negated_conjecture,
( ~ r1(X1)
| ~ r3(X1,X2,X3)
| ~ r1(X4)
| ~ r2(X4,X2)
| ~ id(X3,X5)
| ~ r1(X6)
| ~ r2(X6,X5) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_22,plain,
r3(X1,esk7_2(X1,X2),esk6_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_23,plain,
! [X20,X21] :
( ~ id(X20,X21)
| ( ~ r1(X20)
& ~ r1(X21) )
| ( r1(X20)
& r1(X21) ) ),
inference(fof_simplification,[status(thm)],[axiom_8]) ).
fof(c_0_24,plain,
? [X1] :
! [X2] :
( ( id(X2,X1)
& r1(X2) )
| ( ~ r1(X2)
& ~ id(X2,X1) ) ),
inference(fof_simplification,[status(thm)],[axiom_1]) ).
cnf(c_0_25,plain,
( id(X1,X3)
| ~ id(X1,X2)
| ~ id(X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_26,plain,
id(esk13_1(X1),X1),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_27,plain,
( id(X2,X1)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_28,plain,
id(esk13_1(X1),esk3_2(X1,esk14_1(X1))),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_29,negated_conjecture,
( ~ r2(X1,esk7_2(X2,X3))
| ~ r2(X4,X5)
| ~ r1(X4)
| ~ r1(X1)
| ~ r1(X2)
| ~ id(esk6_2(X2,X3),X5) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_30,plain,
r2(X1,esk7_2(X2,X1)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_31,plain,
! [X160,X161] :
( ( r1(X160)
| ~ r1(X160)
| ~ id(X160,X161) )
& ( r1(X161)
| ~ r1(X160)
| ~ id(X160,X161) )
& ( r1(X160)
| ~ r1(X161)
| ~ id(X160,X161) )
& ( r1(X161)
| ~ r1(X161)
| ~ id(X160,X161) ) ),
inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_23])]) ).
cnf(c_0_32,plain,
r3(X1,X2,esk8_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_33,plain,
! [X142] :
( ( ~ r1(X142)
| id(X142,esk1_0) )
& ( ~ id(X142,esk1_0)
| id(X142,esk1_0) )
& ( ~ r1(X142)
| r1(X142) )
& ( ~ id(X142,esk1_0)
| r1(X142) ) ),
inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_24])])]) ).
cnf(c_0_34,plain,
( id(X1,X2)
| ~ id(X1,esk13_1(X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_35,plain,
id(esk3_2(X1,esk14_1(X1)),esk13_1(X1)),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,negated_conjecture,
( ~ r2(X1,X2)
| ~ r1(X1)
| ~ r1(X3)
| ~ r1(X4)
| ~ id(esk6_2(X4,X3),X2) ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
id(esk6_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_38,plain,
( r1(X1)
| ~ r1(X2)
| ~ id(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
id(esk8_2(X1,X2),esk3_2(X1,X2)),
inference(spm,[status(thm)],[c_0_19,c_0_32]) ).
cnf(c_0_40,plain,
( r1(X1)
| ~ id(X1,esk1_0) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_41,plain,
id(esk3_2(X1,esk14_1(X1)),X1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
fof(c_0_42,plain,
! [X154] : id(X154,X154),
inference(variable_rename,[status(thm)],[axiom_5]) ).
cnf(c_0_43,negated_conjecture,
( ~ r2(X1,esk5_2(X2,X3))
| ~ r1(X1)
| ~ r1(X3)
| ~ r1(X2) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
r2(esk8_2(X1,X2),esk5_2(X1,X2)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_45,plain,
( r1(esk8_2(X1,X2))
| ~ r1(esk3_2(X1,X2)) ),
inference(spm,[status(thm)],[c_0_38,c_0_39]) ).
cnf(c_0_46,plain,
r1(esk3_2(esk1_0,esk14_1(esk1_0))),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
id(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( ~ r1(esk8_2(X1,X2))
| ~ r1(X2)
| ~ r1(X1) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
r1(esk8_2(esk1_0,esk14_1(esk1_0))),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_50,plain,
r1(esk14_1(X1)),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_51,plain,
r1(esk1_0),
inference(spm,[status(thm)],[c_0_40,c_0_47]) ).
cnf(c_0_52,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN054+1 : TPTP v9.2.1. Bugfixed v7.3.0.
% 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
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 01:21:31 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.82/1.89 % Version : CSE_E---1.7
% 1.82/1.89 % Problem : theBenchmark.p
% 1.82/1.89 % SZS status Theorem for theBenchmark.p
% 1.82/1.89 % SZS output start CNFRefutation
% See solution above
% 1.82/1.89 % Total time : 1.368s
%------------------------------------------------------------------------------