%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUN054+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 01:57:36 PM UTC 2026
% Result : Theorem 1.34s 0.68s
% Output : CNFRefutation 1.34s
% 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/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_3) ).
fof(zeroplusoneidone,conjecture,
? [X63] :
( ? [X47] :
( ? [X49] :
( r2(X49,X47)
& r1(X49) )
& id(X63,X47) )
& ? [X46] :
( ? [X41] :
( r2(X41,X46)
& r1(X41) )
& ? [X40] :
( r3(X40,X46,X63)
& r1(X40) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',zeroplusoneidone) ).
fof(axiom_7,axiom,
! [X17,X18,X19] :
( ~ id(X18,X19)
| id(X17,X19)
| ~ id(X17,X18) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_7) ).
fof(axiom_6,axiom,
! [X15,X16] :
( id(X16,X15)
| ~ id(X15,X16) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_6) ).
fof(axiom_4a,axiom,
! [X54] :
? [X55] :
( ? [X56] :
( r3(X54,X56,X55)
& r1(X56) )
& id(X55,X54) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_4a) ).
fof(axiom_1a,axiom,
! [X38,X39] :
? [X40] :
( ? [X43] :
( r3(X38,X39,X43)
& r2(X43,X40) )
& ? [X41] :
( ? [X42] :
( r3(X38,X42,X41)
& r2(X39,X42) )
& id(X41,X40) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1a) ).
fof(axiom_8,axiom,
! [X20,X21] :
( ( r1(X21)
& r1(X20) )
| ( ~ r1(X21)
& ~ r1(X20) )
| ~ id(X20,X21) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/NUM009+0.ax',axiom_1) ).
fof(axiom_5,axiom,
! [X14] : id(X14,X14),
file('/export/starexec/sandbox2/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] :
( ? [X47] :
( ? [X49] :
( r2(X49,X47)
& r1(X49) )
& id(X63,X47) )
& ? [X46] :
( ? [X41] :
( r2(X41,X46)
& r1(X41) )
& ? [X40] :
( r3(X40,X46,X63)
& r1(X40) ) ) ),
inference(assume_negation,[status(cth)],[zeroplusoneidone]) ).
fof(c_0_11,plain,
! [X17,X18,X19] :
( ~ id(X18,X19)
| id(X17,X19)
| ~ id(X17,X18) ),
inference(fof_simplification,[status(thm)],[axiom_7]) ).
fof(c_0_12,plain,
! [X15,X16] :
( id(X16,X15)
| ~ id(X15,X16) ),
inference(fof_simplification,[status(thm)],[axiom_6]) ).
fof(c_0_13,plain,
! [X73,X74,X76] :
( ( r3(X73,X74,X76)
| ~ id(X76,esk3_2(X73,X74)) )
& ( r3(X73,X74,X76)
| ~ r3(X73,X74,X76) )
& ( id(X76,esk3_2(X73,X74))
| ~ id(X76,esk3_2(X73,X74)) )
& ( id(X76,esk3_2(X73,X74))
| ~ r3(X73,X74,X76) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_9])])])]) ).
fof(c_0_14,plain,
! [X121] :
( r3(X121,esk14_1(X121),esk13_1(X121))
& r1(esk14_1(X121))
& id(esk13_1(X121),X121) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_4a])]) ).
fof(c_0_15,negated_conjecture,
! [X135,X136,X137,X138,X139,X140] :
( ~ r2(X140,X139)
| ~ r1(X140)
| ~ id(X135,X139)
| ~ r2(X138,X136)
| ~ r1(X138)
| ~ r3(X137,X136,X135)
| ~ r1(X137) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])]) ).
fof(c_0_16,plain,
! [X105,X106] :
( r3(X105,X106,esk8_2(X105,X106))
& r2(esk8_2(X105,X106),esk5_2(X105,X106))
& r3(X105,esk7_2(X105,X106),esk6_2(X105,X106))
& r2(X106,esk7_2(X105,X106))
& id(esk6_2(X105,X106),esk5_2(X105,X106)) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[axiom_1a])]) ).
fof(c_0_17,plain,
! [X84,X85,X86] :
( ~ id(X85,X86)
| id(X84,X86)
| ~ id(X84,X85) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_11])]) ).
fof(c_0_18,plain,
! [X82,X83] :
( id(X83,X82)
| ~ id(X82,X83) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_12])]) ).
cnf(c_0_19,plain,
( ~ r3(X1,X2,X3)
| id(X3,esk3_2(X1,X2)) ),
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,
( ~ r2(X6,X5)
| ~ r1(X6)
| ~ id(X3,X5)
| ~ r2(X4,X2)
| ~ r1(X4)
| ~ r3(X1,X2,X3)
| ~ r1(X1) ),
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] :
( ( r1(X21)
& r1(X20) )
| ( ~ r1(X21)
& ~ r1(X20) )
| ~ id(X20,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(X2,X3)
| ~ id(X1,X2)
| id(X1,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(X1,X2)
| id(X2,X1) ),
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,
( ~ id(esk6_2(X2,X3),X5)
| ~ r1(X2)
| ~ r1(X1)
| ~ r1(X4)
| ~ r2(X4,X5)
| ~ r2(X1,esk7_2(X2,X3)) ),
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,
! [X87,X88] :
( ( ~ id(X87,X88)
| ~ r1(X88)
| r1(X88) )
& ( ~ id(X87,X88)
| ~ r1(X88)
| r1(X87) )
& ( ~ id(X87,X88)
| ~ r1(X87)
| r1(X88) )
& ( ~ id(X87,X88)
| ~ r1(X87)
| r1(X87) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[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,
! [X69] :
( ( r1(X69)
| ~ id(X69,esk1_0) )
& ( r1(X69)
| ~ r1(X69) )
& ( id(X69,esk1_0)
| ~ id(X69,esk1_0) )
& ( id(X69,esk1_0)
| ~ r1(X69) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[c_0_24])])])]) ).
cnf(c_0_34,plain,
( ~ id(X1,esk13_1(X2))
| id(X1,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,
( ~ id(esk6_2(X4,X3),X2)
| ~ r1(X4)
| ~ r1(X3)
| ~ r1(X1)
| ~ r2(X1,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,
( ~ id(X1,X2)
| ~ r1(X2)
| r1(X1) ),
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,
( ~ id(X1,esk1_0)
| r1(X1) ),
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,
! [X81] : id(X81,X81),
inference(variable_rename,[status(thm)],[axiom_5]) ).
cnf(c_0_43,negated_conjecture,
( ~ r1(X2)
| ~ r1(X3)
| ~ r1(X1)
| ~ r2(X1,esk5_2(X2,X3)) ),
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(esk3_2(X1,X2))
| r1(esk8_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(X1)
| ~ r1(X2)
| ~ r1(esk8_2(X1,X2)) ),
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
% 0.00/0.03 % Problem : NUN054+1 : TPTP v9.3.1. Bugfixed v7.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n001.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 21 03:28:28 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.34/0.68 % Version: 3.5.1
% 1.34/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.34/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.34/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.34/0.68 % Starting new_bool_3 with 300s (1) cores
% 1.34/0.68 % Starting new_bool_1 with 300s (1) cores
% 1.34/0.68 % Starting sh5l with 300s (1) cores
% 1.34/0.68 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 2089330 completed with status 0
% 1.34/0.68 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.34/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.34/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.34/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.34/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.34/0.68 % No SInE strategy applied
% 1.34/0.68 % Search class: FGHNM-FFMF21-SFFFFFNN
% 1.34/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.34/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.34/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.34/0.68 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 1.34/0.68 % Starting new_bool_3 with 211s (1) cores
% 1.34/0.68 % Starting G-E--_107_C18_F1_PI_AE_Q4_CS_SP_PS_S4S with 136s (1) cores
% 1.34/0.68 % G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with pid 2089337 completed with status 0
% 1.34/0.68 % Result found by G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S
% 1.34/0.68 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.34/0.68 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.34/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.34/0.68 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.34/0.68 % No SInE strategy applied
% 1.34/0.68 % Search class: FGHNM-FFMF21-SFFFFFNN
% 1.34/0.68 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.34/0.68 % Starting SubtermCWHack with 136s (1) cores
% 1.34/0.68 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.34/0.68 % Starting G-E--_110_C45_F1_PI_SE_CS_SP_PS_S4S with 231s (1) cores
% 1.34/0.68 % Preprocessing time : 0.002 s
% 1.34/0.68 % Presaturation interreduction done
% 1.34/0.68
% 1.34/0.68 % Proof found!
% 1.34/0.68 % SZS status Theorem
% 1.34/0.68 % SZS output start CNFRefutation
% See solution above
% 1.34/0.68 % Parsed axioms : 19
% 1.34/0.68 % Removed by relevancy pruning/SinE : 0
% 1.34/0.68 % Initial clauses : 59
% 1.34/0.68 % Removed in clause preprocessing : 16
% 1.34/0.68 % Initial clauses in saturation : 43
% 1.34/0.68 % Processed clauses : 1880
% 1.34/0.68 % ...of these trivial : 45
% 1.34/0.68 % ...subsumed : 888
% 1.34/0.68 % ...remaining for further processing : 947
% 1.34/0.68 % Other redundant clauses eliminated : 0
% 1.34/0.68 % Clauses deleted for lack of memory : 0
% 1.34/0.68 % Backward-subsumed : 4
% 1.34/0.68 % Backward-rewritten : 2
% 1.34/0.68 % Generated clauses : 14042
% 1.34/0.68 % ...of the previous two non-redundant : 11646
% 1.34/0.68 % ...aggressively subsumed : 0
% 1.34/0.68 % Contextual simplify-reflections : 0
% 1.34/0.68 % Paramodulations : 14042
% 1.34/0.68 % Factorizations : 0
% 1.34/0.68 % NegExts : 0
% 1.34/0.68 % Equation resolutions : 0
% 1.34/0.68 % Disequality decompositions : 0
% 1.34/0.68 % Total rewrite steps : 4293
% 1.34/0.68 % ...of those cached : 3969
% 1.34/0.68 % Propositional unsat checks : 0
% 1.34/0.68 % Propositional check models : 0
% 1.34/0.68 % Propositional check unsatisfiable : 0
% 1.34/0.68 % Propositional clauses : 0
% 1.34/0.68 % Propositional clauses after purity: 0
% 1.34/0.68 % Propositional unsat core size : 0
% 1.34/0.68 % Propositional preprocessing time : 0.000
% 1.34/0.68 % Propositional encoding time : 0.000
% 1.34/0.68 % Propositional solver time : 0.000
% 1.34/0.68 % Success case prop preproc time : 0.000
% 1.34/0.68 % Success case prop encoding time : 0.000
% 1.34/0.68 % Success case prop solver time : 0.000
% 1.34/0.68 % Current number of processed clauses : 898
% 1.34/0.68 % Positive orientable unit clauses : 271
% 1.34/0.68 % Positive unorientable unit clauses: 0
% 1.34/0.68 % Negative unit clauses : 25
% 1.34/0.68 % Non-unit-clauses : 602
% 1.34/0.68 % Current number of unprocessed clauses: 9826
% 1.34/0.68 % ...number of literals in the above : 18643
% 1.34/0.68 % Current number of archived formulas : 0
% 1.34/0.68 % Current number of archived clauses : 49
% 1.34/0.68 % Clause-clause subsumption calls (NU) : 55125
% 1.34/0.68 % Rec. Clause-clause subsumption calls : 10431
% 1.34/0.68 % Non-unit clause-clause subsumptions : 499
% 1.34/0.68 % Unit Clause-clause subsumption calls : 1289
% 1.34/0.68 % Rewrite failures with RHS unbound : 0
% 1.34/0.68 % BW rewrite match attempts : 167
% 1.34/0.68 % BW rewrite match successes : 2
% 1.34/0.68 % Condensation attempts : 0
% 1.34/0.68 % Condensation successes : 0
% 1.34/0.68 % Termbank termtop insertions : 148995
% 1.34/0.68 % Search garbage collected termcells : 430
% 1.34/0.68
% 1.34/0.68 % -------------------------------------------------
% 1.34/0.68 % User time : 0.200 s
% 1.34/0.68 % System time : 0.012 s
% 1.34/0.68 % Total time : 0.212 s
% 1.34/0.68 % Maximum resident set size: 3696 pages
% 1.34/0.68
% 1.34/0.68 % -------------------------------------------------
% 1.34/0.68 % User time : 0.945 s
% 1.34/0.68 % System time : 0.072 s
% 1.34/0.68 % Total time : 1.017 s
% 1.34/0.68 % Maximum resident set size: 4864 pages
% 1.34/0.68 % E exiting
%------------------------------------------------------------------------------