%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM840+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:50:48 PM UTC 2026
% Result : Theorem 0.23s 0.56s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 53 ( 31 unt; 0 def)
% Number of atoms : 87 ( 62 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 71 ( 37 ~; 28 |; 2 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 105 ( 12 sgn 54 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(73, 0), 0)',axiom,
! [X23,X24] : X24 != vplus(X23,X24),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X30,X31,X32] : vplus(vplus(X30,X31),X32) = vplus(X30,vplus(X31,X32)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X25,X26] : vplus(X26,X25) = vplus(X25,X26),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
! [X10,X11] :
( less(X11,X10)
<=> ? [X12] : X10 = vplus(X11,X12) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).
fof('holds(antec(conjunct2(conjunct2(204))), 335, 0)',axiom,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(conjunct2(conjunct2(204))), 335, 0)') ).
fof('ass(cond(goal(88), 0), 1)',axiom,
! [X16,X17] :
( ~ ? [X19] : X17 = vplus(X16,X19)
| X16 != X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).
fof('ass(cond(81, 0), 0)',axiom,
! [X20,X21] :
( X20 != X21
=> ! [X22] : vplus(X22,X20) != vplus(X22,X21) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(81, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X13,X14] :
( greater(X14,X13)
<=> ? [X15] : X14 = vplus(X13,X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X8,X9] :
( less(X8,X9)
| greater(X8,X9)
| X8 = X9 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof('ass(cond(goal(88), 0), 0)',axiom,
! [X16,X17] :
( ? [X19] : X17 = vplus(X16,X19)
| ? [X18] : X16 = vplus(X17,X18)
| X16 = X17 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 0)') ).
fof('holds(conseq(conjunct2(conjunct2(204))), 336, 0)',conjecture,
less(vd328,vd329),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(conjunct2(conjunct2(204))), 336, 0)') ).
fof(c_0_11,plain,
! [X23,X24] : X24 != vplus(X23,X24),
inference(fof_simplification,[status(thm)],['ass(cond(73, 0), 0)']) ).
fof(c_0_12,plain,
! [X85,X86] : X86 != vplus(X85,X86),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_11])]) ).
fof(c_0_13,plain,
! [X92,X93,X94] : vplus(vplus(X92,X93),X94) = vplus(X92,vplus(X93,X94)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_14,plain,
X1 != vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_15,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_16,plain,
! [X87,X88] : vplus(X88,X87) = vplus(X87,X88),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_17,plain,
vplus(X1,vplus(X2,X3)) != X3,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X56,X57,X59,X60,X61] :
( ( less(X60,X59)
| X59 != vplus(X60,X61) )
& ( X56 = vplus(X57,esk1_2(X56,X57))
| ~ less(X57,X56) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 12), 1)'])])])])])]) ).
cnf(c_0_20,plain,
less(vplus(vd328,vd330),vplus(vd329,vd330)),
inference(split_conjunct,[status(thm)],['holds(antec(conjunct2(conjunct2(204))), 335, 0)']) ).
fof(c_0_21,plain,
! [X16,X17] :
( ~ ? [X19] : X17 = vplus(X16,X19)
| X16 != X17 ),
inference(fof_simplification,[status(thm)],['ass(cond(goal(88), 0), 1)']) ).
cnf(c_0_22,plain,
vplus(X1,vplus(X2,X3)) != X2,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,plain,
( ~ less(X1,X2)
| X2 = vplus(X1,esk1_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_24,plain,
less(vplus(vd328,vd330),vplus(vd330,vd329)),
inference(rw,[status(thm)],[c_0_20,c_0_18]) ).
fof(c_0_25,plain,
! [X20,X21] :
( X20 != X21
=> ! [X22] : vplus(X22,X20) != vplus(X22,X21) ),
inference(fof_simplification,[status(thm)],['ass(cond(81, 0), 0)']) ).
fof(c_0_26,plain,
! [X72,X73,X74] :
( X73 != vplus(X72,X74)
| X72 != X73 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])]) ).
cnf(c_0_27,plain,
vplus(X1,vplus(X2,vplus(X3,X4))) != vplus(X2,X3),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_28,plain,
vplus(vd328,vplus(vd330,esk1_2(vplus(vd330,vd329),vplus(vd328,vd330)))) = vplus(vd330,vd329),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_15]) ).
fof(c_0_29,plain,
! [X62,X63,X65,X66,X67] :
( ( greater(X66,X65)
| X66 != vplus(X65,X67) )
& ( X63 = vplus(X62,esk2_2(X62,X63))
| ~ greater(X63,X62) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 11), 1)'])])])])])]) ).
fof(c_0_30,plain,
! [X48,X49] :
( less(X48,X49)
| greater(X48,X49)
| X48 = X49 ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
fof(c_0_31,plain,
! [X82,X83,X84] :
( vplus(X84,X82) != vplus(X84,X83)
| X82 = X83 ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_25])])])]) ).
fof(c_0_32,plain,
! [X68,X69] :
( X69 = vplus(X68,esk4_2(X68,X69))
| X68 = vplus(X69,esk3_2(X68,X69))
| X68 = X69 ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],['ass(cond(goal(88), 0), 0)'])]) ).
cnf(c_0_33,plain,
( X2 != vplus(X1,X3)
| X1 != X2 ),
inference(split_conjunct,[status(thm)],[c_0_26]) ).
fof(c_0_34,negated_conjecture,
~ less(vd328,vd329),
inference(assume_negation,[status(cth)],['holds(conseq(conjunct2(conjunct2(204))), 336, 0)']) ).
cnf(c_0_35,plain,
vplus(X1,vplus(vd330,vd329)) != vplus(vd328,vd330),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_36,plain,
( ~ greater(X1,X2)
| X1 = vplus(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
( less(X1,X2)
| greater(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,plain,
( vplus(X3,X1) != vplus(X3,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_39,plain,
( X2 = vplus(X1,esk4_2(X1,X2))
| X1 = vplus(X2,esk3_2(X1,X2))
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_32]) ).
cnf(c_0_40,plain,
vplus(X1,X2) != X1,
inference(er,[status(thm)],[c_0_33]) ).
fof(c_0_41,negated_conjecture,
~ less(vd328,vd329),
inference(fof_simplification,[status(thm)],[c_0_34]) ).
cnf(c_0_42,plain,
vplus(vd330,vplus(vd329,X1)) != vplus(vd328,vd330),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_18]),c_0_15]) ).
cnf(c_0_43,plain,
( less(X2,X1)
| X2 = X1
| vplus(X1,esk2_2(X1,X2)) = X2 ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_44,plain,
esk4_2(X1,vplus(X1,X2)) = X2,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39])]),c_0_15]),c_0_40]),c_0_40]) ).
fof(c_0_45,negated_conjecture,
~ less(vd328,vd329),
inference(fof_nnf,[status(thm)],[c_0_41]) ).
cnf(c_0_46,plain,
vplus(X1,vplus(X2,X3)) != vplus(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_15]) ).
cnf(c_0_47,plain,
( vplus(vd330,X1) != vplus(vd328,vd330)
| less(X1,vd329)
| X1 = vd329 ),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_48,plain,
esk4_2(X1,vplus(X2,X1)) = X2,
inference(spm,[status(thm)],[c_0_44,c_0_18]) ).
cnf(c_0_49,negated_conjecture,
~ less(vd328,vd329),
inference(split_conjunct,[status(thm)],[c_0_45]) ).
cnf(c_0_50,plain,
vplus(vd330,vd329) != vplus(vd328,vd330),
inference(spm,[status(thm)],[c_0_46,c_0_28]) ).
cnf(c_0_51,plain,
vd329 = vd328,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_39])]),c_0_48]),c_0_48]),c_0_15]),c_0_49]),c_0_22]),c_0_14]) ).
cnf(c_0_52,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM840+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.41 % Computer : n015.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Mon Sep 21 03:15:50 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.23/0.48 Running first-order theorem proving
% 0.23/0.48 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
% 0.23/0.56 % Version: 3.5.1
% 0.23/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56 % Starting new_bool_3 with 300s (1) cores
% 0.23/0.56 % Starting new_bool_1 with 300s (1) cores
% 0.23/0.56 % Starting sh5l with 300s (1) cores
% 0.23/0.56 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 431863 completed with status 0
% 0.23/0.56 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.23/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.56 % No SInE strategy applied
% 0.23/0.56 % Search class: FGHSM-FFMF22-SFFFFFNN
% 0.23/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.56 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_CO_S0Y with 136s (1) cores
% 0.23/0.56 % Starting new_bool_3 with 136s (1) cores
% 0.23/0.56 % Starting new_bool_1 with 136s (1) cores
% 0.23/0.56 % new_bool_1 with pid 431872 completed with status 0
% 0.23/0.56 % Result found by new_bool_1
% 0.23/0.56 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.23/0.56 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.23/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.23/0.56 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.23/0.56 % No SInE strategy applied
% 0.23/0.56 % Search class: FGHSM-FFMF22-SFFFFFNN
% 0.23/0.56 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.23/0.56 % Starting SubtermCWHack with 136s (1) cores
% 0.23/0.56 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.23/0.56 % Starting G-E--_107_C18_F1_AE_Q4_CS_SP_CO_S0Y with 136s (1) cores
% 0.23/0.56 % Starting new_bool_3 with 136s (1) cores
% 0.23/0.56 % Starting new_bool_1 with 136s (1) cores
% 0.23/0.56 % Preprocessing time : 0.001 s
% 0.23/0.56 % Presaturation interreduction done
% 0.23/0.56
% 0.23/0.56 % Proof found!
% 0.23/0.56 % SZS status Theorem
% 0.23/0.56 % SZS output start CNFRefutation
% See solution above
% 0.23/0.56 % Parsed axioms : 26
% 0.23/0.56 % Removed by relevancy pruning/SinE : 0
% 0.23/0.56 % Initial clauses : 29
% 0.23/0.56 % Removed in clause preprocessing : 2
% 0.23/0.56 % Initial clauses in saturation : 27
% 0.23/0.56 % Processed clauses : 695
% 0.23/0.56 % ...of these trivial : 47
% 0.23/0.56 % ...subsumed : 446
% 0.23/0.56 % ...remaining for further processing : 202
% 0.23/0.56 % Other redundant clauses eliminated : 73
% 0.23/0.56 % Clauses deleted for lack of memory : 0
% 0.23/0.56 % Backward-subsumed : 2
% 0.23/0.56 % Backward-rewritten : 31
% 0.23/0.56 % Generated clauses : 3478
% 0.23/0.56 % ...of the previous two non-redundant : 3231
% 0.23/0.56 % ...aggressively subsumed : 0
% 0.23/0.56 % Contextual simplify-reflections : 0
% 0.23/0.56 % Paramodulations : 3399
% 0.23/0.56 % Factorizations : 2
% 0.23/0.56 % NegExts : 0
% 0.23/0.56 % Equation resolutions : 77
% 0.23/0.56 % Disequality decompositions : 0
% 0.23/0.56 % Total rewrite steps : 1012
% 0.23/0.56 % ...of those cached : 768
% 0.23/0.56 % Propositional unsat checks : 0
% 0.23/0.56 % Propositional check models : 0
% 0.23/0.56 % Propositional check unsatisfiable : 0
% 0.23/0.56 % Propositional clauses : 0
% 0.23/0.56 % Propositional clauses after purity: 0
% 0.23/0.56 % Propositional unsat core size : 0
% 0.23/0.56 % Propositional preprocessing time : 0.000
% 0.23/0.56 % Propositional encoding time : 0.000
% 0.23/0.56 % Propositional solver time : 0.000
% 0.23/0.56 % Success case prop preproc time : 0.000
% 0.23/0.56 % Success case prop encoding time : 0.000
% 0.23/0.56 % Success case prop solver time : 0.000
% 0.23/0.56 % Current number of processed clauses : 140
% 0.23/0.56 % Positive orientable unit clauses : 35
% 0.23/0.56 % Positive unorientable unit clauses: 3
% 0.23/0.56 % Negative unit clauses : 69
% 0.23/0.56 % Non-unit-clauses : 33
% 0.23/0.56 % Current number of unprocessed clauses: 2528
% 0.23/0.56 % ...number of literals in the above : 5208
% 0.23/0.56 % Current number of archived formulas : 0
% 0.23/0.56 % Current number of archived clauses : 56
% 0.23/0.56 % Clause-clause subsumption calls (NU) : 316
% 0.23/0.56 % Rec. Clause-clause subsumption calls : 260
% 0.23/0.56 % Non-unit clause-clause subsumptions : 36
% 0.23/0.56 % Unit Clause-clause subsumption calls : 345
% 0.23/0.56 % Rewrite failures with RHS unbound : 0
% 0.23/0.56 % BW rewrite match attempts : 72
% 0.23/0.56 % BW rewrite match successes : 51
% 0.23/0.56 % Condensation attempts : 0
% 0.23/0.56 % Condensation successes : 0
% 0.23/0.56 % Termbank termtop insertions : 28167
% 0.23/0.56 % Search garbage collected termcells : 301
% 0.23/0.56
% 0.23/0.56 % -------------------------------------------------
% 0.23/0.56 % User time : 0.050 s
% 0.23/0.56 % System time : 0.004 s
% 0.23/0.56 % Total time : 0.054 s
% 0.23/0.56 % Maximum resident set size: 3612 pages
% 0.23/0.56
% 0.23/0.56 % -------------------------------------------------
% 0.23/0.56 % User time : 0.241 s
% 0.23/0.56 % System time : 0.025 s
% 0.23/0.56 % Total time : 0.266 s
% 0.23/0.56 % Maximum resident set size: 4864 pages
% 0.23/0.56 % E exiting
%------------------------------------------------------------------------------