%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM855+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 01:50:51 PM UTC 2026
% Result : Theorem 1.40s 0.65s
% Output : CNFRefutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 14
% Syntax : Number of formulae : 58 ( 36 unt; 0 def)
% Number of atoms : 87 ( 22 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 66 ( 37 ~; 25 |; 1 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 87 ( 9 sgn 43 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof('ass(cond(goal(130), 0), 2)',axiom,
! [X76,X77] :
( ~ less(X76,X77)
| ~ greater(X76,X77) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 2)') ).
fof('ass(cond(140, 0), 0)',axiom,
! [X74,X75] :
( greater(X74,X75)
=> less(X75,X74) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(140, 0), 0)') ).
fof('ass(cond(189, 0), 0)',axiom,
! [X53,X54] : greater(vplus(X53,X54),X53),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(189, 0), 0)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X93,X94] : vplus(X94,X93) = vplus(X93,X94),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X98,X99,X100] : vplus(vplus(X98,X99),X100) = vplus(X98,vplus(X99,X100)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
! [X81,X82] :
( greater(X82,X81)
<=> ? [X83] : X82 = vplus(X81,X83) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).
fof('holds(conseq_conjunct2(315), 516, 0)',conjecture,
greater(vmul(vd508,vd511),vmul(vd509,vd512)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conseq_conjunct2(315), 516, 0)') ).
fof('holds(conjunct2(315), 515, 1)',axiom,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 1)') ).
fof('holds(conjunct2(315), 515, 0)',axiom,
vmul(vd509,vd511) = vmul(vd511,vd509),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 0)') ).
fof('holds(conjunct2(315), 515, 2)',axiom,
vmul(vd512,vd509) = vmul(vd509,vd512),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct2(315), 515, 2)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [X23,X24] : vmul(X23,X24) = vmul(X24,X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(147, 0), 0)',axiom,
! [X72,X73] :
( less(X72,X73)
=> greater(X73,X72) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(147, 0), 0)') ).
fof('ass(cond(goal(130), 0), 0)',axiom,
! [X76,X77] :
( less(X76,X77)
| greater(X76,X77)
| X76 = X77 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).
fof('holds(conjunct1(315), 514, 0)',axiom,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','holds(conjunct1(315), 514, 0)') ).
fof(c_0_14,plain,
! [X76,X77] :
( ~ less(X76,X77)
| ~ greater(X76,X77) ),
inference(fof_simplification,[status(thm)],['ass(cond(goal(130), 0), 2)']) ).
fof(c_0_15,plain,
! [X203,X204] :
( ~ less(X203,X204)
| ~ greater(X203,X204) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_14])]) ).
fof(c_0_16,plain,
! [X197,X198] :
( less(X198,X197)
| ~ greater(X197,X198) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(140, 0), 0)'])])]) ).
cnf(c_0_17,plain,
( ~ less(X1,X2)
| ~ greater(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_18,plain,
( ~ greater(X1,X2)
| less(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_19,plain,
! [X176,X177] : greater(vplus(X176,X177),X176),
inference(variable_rename,[status(thm)],['ass(cond(189, 0), 0)']) ).
cnf(c_0_20,plain,
( ~ greater(X2,X1)
| ~ greater(X1,X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,plain,
greater(vplus(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_22,plain,
! [X238,X239] : vplus(X239,X238) = vplus(X238,X239),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_23,plain,
~ greater(X1,vplus(X1,X2)),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
fof(c_0_25,plain,
! [X243,X244,X245] : vplus(vplus(X243,X244),X245) = vplus(X243,vplus(X244,X245)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_26,plain,
~ greater(X1,vplus(X2,X1)),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_27,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_28,plain,
~ greater(X1,vplus(X2,vplus(X3,X1))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_29,plain,
! [X213,X214,X216,X217,X218] :
( ( greater(X217,X216)
| X217 != vplus(X216,X218) )
& ( X214 = vplus(X213,esk2_2(X213,X214))
| ~ greater(X214,X213) ) ),
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)'])])])])])]) ).
cnf(c_0_30,plain,
~ greater(X1,vplus(X2,vplus(X1,X3))),
inference(spm,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_31,plain,
( ~ greater(X1,X2)
| X1 = vplus(X2,esk2_2(X2,X1)) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
fof(c_0_32,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(assume_negation,[status(cth)],['holds(conseq_conjunct2(315), 516, 0)']) ).
cnf(c_0_33,plain,
( ~ greater(X3,X1)
| ~ greater(X1,vplus(X2,X3)) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
fof(c_0_34,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(fof_simplification,[status(thm)],[c_0_32]) ).
cnf(c_0_35,plain,
( ~ greater(X2,X1)
| ~ greater(X1,vplus(X2,X3)) ),
inference(spm,[status(thm)],[c_0_33,c_0_24]) ).
cnf(c_0_36,plain,
greater(vmul(vd511,vd509),vmul(vd512,vd509)),
inference(split_conjunct,[status(thm)],['holds(conjunct2(315), 515, 1)']) ).
cnf(c_0_37,plain,
vmul(vd509,vd511) = vmul(vd511,vd509),
inference(split_conjunct,[status(thm)],['holds(conjunct2(315), 515, 0)']) ).
cnf(c_0_38,plain,
vmul(vd512,vd509) = vmul(vd509,vd512),
inference(split_conjunct,[status(thm)],['holds(conjunct2(315), 515, 2)']) ).
fof(c_0_39,plain,
! [X134,X135] : vmul(X134,X135) = vmul(X135,X134),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
fof(c_0_40,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(fof_nnf,[status(thm)],[c_0_34]) ).
fof(c_0_41,plain,
! [X195,X196] :
( greater(X196,X195)
| ~ less(X195,X196) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(147, 0), 0)'])])]) ).
fof(c_0_42,plain,
! [X199,X200] :
( less(X199,X200)
| greater(X199,X200)
| X199 = X200 ),
inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).
cnf(c_0_43,plain,
( ~ greater(X2,X3)
| ~ greater(X3,X1)
| ~ greater(X1,X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_31]) ).
cnf(c_0_44,plain,
greater(vmul(vd509,vd511),vmul(vd509,vd512)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_45,plain,
greater(vmul(vd508,vd511),vmul(vd509,vd511)),
inference(split_conjunct,[status(thm)],['holds(conjunct1(315), 514, 0)']) ).
cnf(c_0_46,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_39]) ).
cnf(c_0_47,negated_conjecture,
~ greater(vmul(vd508,vd511),vmul(vd509,vd512)),
inference(split_conjunct,[status(thm)],[c_0_40]) ).
cnf(c_0_48,plain,
( ~ less(X1,X2)
| greater(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_41]) ).
cnf(c_0_49,plain,
( less(X1,X2)
| greater(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_50,plain,
( ~ greater(vmul(vd509,vd512),X1)
| ~ greater(X1,vmul(vd509,vd511)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_51,plain,
greater(vmul(vd511,vd508),vmul(vd509,vd511)),
inference(rw,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_52,negated_conjecture,
~ greater(vmul(vd511,vd508),vmul(vd509,vd512)),
inference(rw,[status(thm)],[c_0_47,c_0_46]) ).
cnf(c_0_53,plain,
( greater(X2,X1)
| greater(X1,X2)
| X1 = X2 ),
inference(spm,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_54,plain,
~ greater(vmul(vd509,vd512),vmul(vd511,vd508)),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_55,plain,
~ greater(vmul(vd509,vd511),vmul(vd511,vd508)),
inference(spm,[status(thm)],[c_0_20,c_0_51]) ).
cnf(c_0_56,negated_conjecture,
vmul(vd511,vd508) = vmul(vd509,vd512),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_53]),c_0_54]) ).
cnf(c_0_57,plain,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_55,c_0_56]),c_0_44])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM855+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n018.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 03:15:44 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.12/0.43 Running first-order theorem proving
% 0.12/0.43 Running: /export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p
% 1.40/0.65 % Version: 3.5.1
% 1.40/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.40/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.40/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.40/0.65 % Starting new_bool_3 with 300s (1) cores
% 1.40/0.65 % Starting new_bool_1 with 300s (1) cores
% 1.40/0.65 % Starting sh5l with 300s (1) cores
% 1.40/0.65 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 840194 completed with status 0
% 1.40/0.65 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 1.40/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.40/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.40/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.40/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.40/0.65 % No SInE strategy applied
% 1.40/0.65 % Search class: FGHSM-FFMM21-SFFFFFNN
% 1.40/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.40/0.65 % Starting SubtermCWHack with 136s (1) cores
% 1.40/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.40/0.65 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 1.40/0.65 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 1.40/0.65 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 1.40/0.65 % G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with pid 840205 completed with status 0
% 1.40/0.65 % Result found by G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN
% 1.40/0.65 % Preprocessing class: FSLSSMSSSSSNFFN.
% 1.40/0.65 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.40/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 1.40/0.65 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.40/0.65 % No SInE strategy applied
% 1.40/0.65 % Search class: FGHSM-FFMM21-SFFFFFNN
% 1.40/0.65 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.40/0.65 % Starting SubtermCWHack with 136s (1) cores
% 1.40/0.65 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 1.40/0.65 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S04AN with 136s (1) cores
% 1.40/0.65 % Starting G-E--_301_C18_F1_URBAN_S5PRR_RG_S0Y with 136s (1) cores
% 1.40/0.65 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S5PRR_S04AN with 136s (1) cores
% 1.40/0.65 % Preprocessing time : 0.002 s
% 1.40/0.65 % Presaturation interreduction done
% 1.40/0.65
% 1.40/0.65 % Proof found!
% 1.40/0.65 % SZS status Theorem
% 1.40/0.65 % SZS output start CNFRefutation
% See solution above
% 1.40/0.65 % Parsed axioms : 63
% 1.40/0.65 % Removed by relevancy pruning/SinE : 0
% 1.40/0.65 % Initial clauses : 73
% 1.40/0.65 % Removed in clause preprocessing : 3
% 1.40/0.65 % Initial clauses in saturation : 70
% 1.40/0.65 % Processed clauses : 1910
% 1.40/0.65 % ...of these trivial : 46
% 1.40/0.65 % ...subsumed : 1327
% 1.40/0.65 % ...remaining for further processing : 537
% 1.40/0.65 % Other redundant clauses eliminated : 66
% 1.40/0.65 % Clauses deleted for lack of memory : 0
% 1.40/0.65 % Backward-subsumed : 30
% 1.40/0.65 % Backward-rewritten : 25
% 1.40/0.65 % Generated clauses : 12998
% 1.40/0.65 % ...of the previous two non-redundant : 12163
% 1.40/0.65 % ...aggressively subsumed : 0
% 1.40/0.65 % Contextual simplify-reflections : 1
% 1.40/0.65 % Paramodulations : 12925
% 1.40/0.65 % Factorizations : 2
% 1.40/0.65 % NegExts : 0
% 1.40/0.65 % Equation resolutions : 71
% 1.40/0.65 % Disequality decompositions : 0
% 1.40/0.65 % Total rewrite steps : 4072
% 1.40/0.65 % ...of those cached : 2816
% 1.40/0.65 % Propositional unsat checks : 0
% 1.40/0.65 % Propositional check models : 0
% 1.40/0.65 % Propositional check unsatisfiable : 0
% 1.40/0.65 % Propositional clauses : 0
% 1.40/0.65 % Propositional clauses after purity: 0
% 1.40/0.65 % Propositional unsat core size : 0
% 1.40/0.65 % Propositional preprocessing time : 0.000
% 1.40/0.65 % Propositional encoding time : 0.000
% 1.40/0.65 % Propositional solver time : 0.000
% 1.40/0.65 % Success case prop preproc time : 0.000
% 1.40/0.65 % Success case prop encoding time : 0.000
% 1.40/0.65 % Success case prop solver time : 0.000
% 1.40/0.65 % Current number of processed clauses : 415
% 1.40/0.65 % Positive orientable unit clauses : 79
% 1.40/0.65 % Positive unorientable unit clauses: 22
% 1.40/0.65 % Negative unit clauses : 140
% 1.40/0.65 % Non-unit-clauses : 174
% 1.40/0.65 % Current number of unprocessed clauses: 10325
% 1.40/0.65 % ...number of literals in the above : 15169
% 1.40/0.65 % Current number of archived formulas : 0
% 1.40/0.65 % Current number of archived clauses : 114
% 1.40/0.65 % Clause-clause subsumption calls (NU) : 4618
% 1.40/0.65 % Rec. Clause-clause subsumption calls : 4371
% 1.40/0.65 % Non-unit clause-clause subsumptions : 289
% 1.40/0.65 % Unit Clause-clause subsumption calls : 2095
% 1.40/0.65 % Rewrite failures with RHS unbound : 0
% 1.40/0.65 % BW rewrite match attempts : 411
% 1.40/0.65 % BW rewrite match successes : 128
% 1.40/0.65 % Condensation attempts : 0
% 1.40/0.65 % Condensation successes : 0
% 1.40/0.65 % Termbank termtop insertions : 112500
% 1.40/0.65 % Search garbage collected termcells : 745
% 1.40/0.65
% 1.40/0.65 % -------------------------------------------------
% 1.40/0.65 % User time : 0.178 s
% 1.40/0.65 % System time : 0.015 s
% 1.40/0.65 % Total time : 0.193 s
% 1.40/0.65 % Maximum resident set size: 3736 pages
% 1.40/0.65
% 1.40/0.65 % -------------------------------------------------
% 1.40/0.65 % User time : 0.819 s
% 1.40/0.65 % System time : 0.063 s
% 1.40/0.65 % Total time : 0.882 s
% 1.40/0.65 % Maximum resident set size: 4864 pages
% 1.40/0.65 % E exiting
%------------------------------------------------------------------------------