%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL903+1 : TPTP v9.3.1. Released v5.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 01:17:42 PM UTC 2026
% Result : Theorem 1.24s 0.64s
% Output : CNFRefutation 1.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 12
% Syntax : Number of formulae : 61 ( 36 unt; 0 def)
% Number of atoms : 93 ( 35 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 60 ( 28 ~; 25 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 105 ( 9 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(sos_07,axiom,
! [X9,X10,X11] :
( '>='('+'(X9,X10),X11)
<=> '>='(X10,'==>'(X9,X11)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_07) ).
fof(sos_04,axiom,
! [X1] : '>='(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_04) ).
fof(sos_03,axiom,
! [X1] : '+'(X1,'0') = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_03) ).
fof(sos_02,axiom,
! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_02) ).
fof(sos_06,axiom,
! [X7,X8] :
( ( '>='(X8,X7)
& '>='(X7,X8) )
=> X7 = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(sos_10,axiom,
! [X15,X16,X17] :
( '>='(X15,X16)
=> '>='('==>'(X16,X17),'==>'(X15,X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_10) ).
fof(sos_08,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_13,axiom,
! [X1] : '==>'('==>'('==>'(X1,'1'),X1),X1) = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
fof(sos_09,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(sos_12,axiom,
! [X1] : '+'(X1,'1') = '1',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
fof(sos_11,axiom,
! [X18,X19,X20] :
( '>='(X18,X19)
=> '>='('==>'(X20,X18),'==>'(X20,X19)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_11) ).
fof(goals_14,conjecture,
! [X21] : '+'(X21,X21) = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(c_0_12,plain,
! [X34,X35,X36] :
( ( '>='('+'(X34,X35),X36)
| ~ '>='(X35,'==>'(X34,X36)) )
& ( '>='(X35,'==>'(X34,X36))
| ~ '>='('+'(X34,X35),X36) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])])]) ).
fof(c_0_13,plain,
! [X28] : '>='(X28,X28),
inference(variable_rename,[status(thm)],[sos_04]) ).
fof(c_0_14,plain,
! [X27] : '+'(X27,'0') = X27,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_15,plain,
! [X25,X26] : '+'(X25,X26) = '+'(X26,X25),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_16,plain,
! [X32,X33] :
( X32 = X33
| ~ '>='(X33,X32)
| ~ '>='(X32,X33) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])])]) ).
cnf(c_0_17,plain,
( ~ '>='(X1,'==>'(X2,X3))
| '>='('+'(X2,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_21,plain,
( ~ '>='(X2,X1)
| ~ '>='(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_22,plain,
( ~ '>='('+'(X1,X2),X3)
| '>='(X2,'==>'(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_23,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_24,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
fof(c_0_25,plain,
! [X41,X42,X43] :
( '>='('==>'(X42,X43),'==>'(X41,X43))
| ~ '>='(X41,X42) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_10])])]) ).
cnf(c_0_26,plain,
( ~ '>='('+'(X1,X3),X2)
| ~ '>='('==>'(X1,X2),X3)
| '==>'(X1,X2) = X3 ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_27,plain,
'>='('==>'('0',X1),X1),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
fof(c_0_28,plain,
! [X37] : '>='(X37,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
fof(c_0_29,plain,
! [X48] : '==>'('==>'('==>'(X48,'1'),X48),X48) = '0',
inference(variable_rename,[status(thm)],[sos_13]) ).
cnf(c_0_30,plain,
( ~ '>='(X1,X2)
| '>='('==>'(X2,X3),'==>'(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
cnf(c_0_31,plain,
'==>'('0',X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_24]),c_0_18])]) ).
cnf(c_0_32,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
fof(c_0_33,plain,
! [X38,X39,X40] :
( '>='('+'(X38,X40),'+'(X39,X40))
| ~ '>='(X38,X39) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])])]) ).
fof(c_0_34,plain,
! [X47] : '+'(X47,'1') = '1',
inference(variable_rename,[status(thm)],[sos_12]) ).
cnf(c_0_35,plain,
( ~ '>='(X2,'+'(X1,'==>'(X1,X2)))
| '+'(X1,'==>'(X1,X2)) = X2 ),
inference(spm,[status(thm)],[c_0_21,c_0_23]) ).
cnf(c_0_36,plain,
'==>'('==>'('==>'(X1,'1'),X1),X1) = '0',
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,plain,
'>='(X1,'==>'(X2,X1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32])]) ).
cnf(c_0_38,plain,
( ~ '>='(X1,X2)
| '>='('+'(X1,X3),'+'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
'+'(X1,'1') = '1',
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_40,plain,
( ~ '>='(X1,X3)
| ~ '>='('==>'(X1,X2),'==>'(X3,X2))
| '==>'(X1,X2) = '==>'(X3,X2) ),
inference(spm,[status(thm)],[c_0_21,c_0_30]) ).
cnf(c_0_41,plain,
'==>'('==>'(X1,'1'),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_19]),c_0_19]),c_0_37])]) ).
fof(c_0_42,plain,
! [X44,X45,X46] :
( '>='('==>'(X46,X44),'==>'(X46,X45))
| ~ '>='(X44,X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_11])])]) ).
cnf(c_0_43,plain,
'>='('+'(X1,X2),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_24]),c_0_32])]) ).
cnf(c_0_44,plain,
'+'('1',X1) = '1',
inference(spm,[status(thm)],[c_0_39,c_0_20]) ).
cnf(c_0_45,plain,
( ~ '>='('0',X1)
| '0' = X1 ),
inference(spm,[status(thm)],[c_0_21,c_0_32]) ).
cnf(c_0_46,plain,
( ~ '>='('==>'(X2,'1'),X1)
| '==>'(X1,X2) = X2 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_37])]) ).
cnf(c_0_47,plain,
( ~ '>='(X1,X2)
| '>='('==>'(X3,X1),'==>'(X3,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_42]) ).
cnf(c_0_48,plain,
'>='('1',X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_49,plain,
( ~ '>='(X1,X2)
| '==>'(X1,X2) = '0' ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_22]),c_0_19]) ).
cnf(c_0_50,plain,
'==>'('==>'(X1,X2),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_47]),c_0_48])]) ).
cnf(c_0_51,plain,
( ~ '>='('==>'(X1,X2),X1)
| X1 = '0' ),
inference(spm,[status(thm)],[c_0_49,c_0_50]) ).
cnf(c_0_52,plain,
( ~ '>='(X1,'==>'(X1,X2))
| '==>'(X1,X2) = '0' ),
inference(spm,[status(thm)],[c_0_51,c_0_50]) ).
fof(c_0_53,negated_conjecture,
~ ! [X21] : '+'(X21,X21) = X21,
inference(assume_negation,[status(cth)],[goals_14]) ).
cnf(c_0_54,plain,
( ~ '>='('+'(X1,X1),X2)
| '==>'(X1,X2) = '0' ),
inference(spm,[status(thm)],[c_0_52,c_0_22]) ).
fof(c_0_55,negated_conjecture,
'+'(esk1_0,esk1_0) != esk1_0,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_53])])])]) ).
cnf(c_0_56,plain,
'==>'(X1,'+'(X1,X1)) = '0',
inference(spm,[status(thm)],[c_0_54,c_0_18]) ).
cnf(c_0_57,plain,
'>='('+'(X1,X2),X1),
inference(spm,[status(thm)],[c_0_43,c_0_20]) ).
cnf(c_0_58,negated_conjecture,
'+'(esk1_0,esk1_0) != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_55]) ).
cnf(c_0_59,plain,
'+'(X1,X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_56]),c_0_19]),c_0_19]),c_0_57])]) ).
cnf(c_0_60,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_59])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL903+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 % Computer : n011.cluster.edu
% 0.13/0.38 % Model : x86_64 x86_64
% 0.13/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.38 % Memory : 8046.5625MB
% 0.13/0.38 % OS : Linux 6.8.0-71-generic
% 0.13/0.38 % CPULimit : 300
% 0.13/0.38 % WCLimit : 300
% 0.13/0.38 % DateTime : Mon Sep 21 01:10:55 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.13/0.43 Running first-order theorem proving
% 0.13/0.43 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
% 1.24/0.64 % Version: 3.5.1
% 1.24/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.24/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.24/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.24/0.64 % Starting new_bool_3 with 300s (1) cores
% 1.24/0.64 % Starting new_bool_1 with 300s (1) cores
% 1.24/0.64 % Starting sh5l with 300s (1) cores
% 1.24/0.64 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 643421 completed with status 0
% 1.24/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.24/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.24/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.24/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.24/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.24/0.64 % No SInE strategy applied
% 1.24/0.64 % Search class: FHUSM-FFSF22-MFFFFFNN
% 1.24/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.24/0.64 % Starting SubtermCWHack with 136s (1) cores
% 1.24/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.24/0.64 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 1.24/0.64 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 1.24/0.64 % Starting new_bool_3 with 136s (1) cores
% 1.24/0.64 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 643428 completed with status 0
% 1.24/0.64 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 1.24/0.64 % Preprocessing class: FSMSSMSSSSSNFFN.
% 1.24/0.64 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 1.24/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 1.24/0.64 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 1.24/0.64 % No SInE strategy applied
% 1.24/0.64 % Search class: FHUSM-FFSF22-MFFFFFNN
% 1.24/0.64 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 1.24/0.64 % Starting SubtermCWHack with 136s (1) cores
% 1.24/0.64 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 1.24/0.64 % Preprocessing time : 0.001 s
% 1.24/0.64 % Presaturation interreduction done
% 1.24/0.64
% 1.24/0.64 % Proof found!
% 1.24/0.64 % SZS status Theorem
% 1.24/0.64 % SZS output start CNFRefutation
% See solution above
% 1.24/0.64 % Parsed axioms : 14
% 1.24/0.64 % Removed by relevancy pruning/SinE : 0
% 1.24/0.64 % Initial clauses : 15
% 1.24/0.64 % Removed in clause preprocessing : 0
% 1.24/0.64 % Initial clauses in saturation : 15
% 1.24/0.65 % Processed clauses : 2444
% 1.24/0.65 % ...of these trivial : 100
% 1.24/0.65 % ...subsumed : 2070
% 1.24/0.65 % ...remaining for further processing : 274
% 1.24/0.65 % Other redundant clauses eliminated : 0
% 1.24/0.65 % Clauses deleted for lack of memory : 0
% 1.24/0.65 % Backward-subsumed : 12
% 1.24/0.65 % Backward-rewritten : 18
% 1.24/0.65 % Generated clauses : 13094
% 1.24/0.65 % ...of the previous two non-redundant : 9877
% 1.24/0.65 % ...aggressively subsumed : 0
% 1.24/0.65 % Contextual simplify-reflections : 2
% 1.24/0.65 % Paramodulations : 13094
% 1.24/0.65 % Factorizations : 0
% 1.24/0.65 % NegExts : 0
% 1.24/0.65 % Equation resolutions : 0
% 1.24/0.65 % Disequality decompositions : 0
% 1.24/0.65 % Total rewrite steps : 9935
% 1.24/0.65 % ...of those cached : 9036
% 1.24/0.65 % Propositional unsat checks : 0
% 1.24/0.65 % Propositional check models : 0
% 1.24/0.65 % Propositional check unsatisfiable : 0
% 1.24/0.65 % Propositional clauses : 0
% 1.24/0.65 % Propositional clauses after purity: 0
% 1.24/0.65 % Propositional unsat core size : 0
% 1.24/0.65 % Propositional preprocessing time : 0.000
% 1.24/0.65 % Propositional encoding time : 0.000
% 1.24/0.65 % Propositional solver time : 0.000
% 1.24/0.65 % Success case prop preproc time : 0.000
% 1.24/0.65 % Success case prop encoding time : 0.000
% 1.24/0.65 % Success case prop solver time : 0.000
% 1.24/0.65 % Current number of processed clauses : 229
% 1.24/0.65 % Positive orientable unit clauses : 53
% 1.24/0.65 % Positive unorientable unit clauses: 4
% 1.24/0.65 % Negative unit clauses : 3
% 1.24/0.65 % Non-unit-clauses : 169
% 1.24/0.65 % Current number of unprocessed clauses: 7373
% 1.24/0.65 % ...number of literals in the above : 17486
% 1.24/0.65 % Current number of archived formulas : 0
% 1.24/0.65 % Current number of archived clauses : 45
% 1.24/0.65 % Clause-clause subsumption calls (NU) : 11820
% 1.24/0.65 % Rec. Clause-clause subsumption calls : 11465
% 1.24/0.65 % Non-unit clause-clause subsumptions : 1687
% 1.24/0.65 % Unit Clause-clause subsumption calls : 263
% 1.24/0.65 % Rewrite failures with RHS unbound : 0
% 1.24/0.65 % BW rewrite match attempts : 395
% 1.24/0.65 % BW rewrite match successes : 57
% 1.24/0.65 % Condensation attempts : 0
% 1.24/0.65 % Condensation successes : 0
% 1.24/0.65 % Termbank termtop insertions : 110641
% 1.24/0.65 % Search garbage collected termcells : 111
% 1.24/0.65
% 1.24/0.65 % -------------------------------------------------
% 1.24/0.65 % User time : 0.134 s
% 1.24/0.65 % System time : 0.011 s
% 1.24/0.65 % Total time : 0.145 s
% 1.24/0.65 % Maximum resident set size: 3648 pages
% 1.24/0.65
% 1.24/0.65 % -------------------------------------------------
% 1.24/0.65 % User time : 0.711 s
% 1.24/0.65 % System time : 0.049 s
% 1.24/0.65 % Total time : 0.760 s
% 1.24/0.65 % Maximum resident set size: 4864 pages
% 1.24/0.65 % E exiting
%------------------------------------------------------------------------------