%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : LCL902+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 : n006.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 0.28s 0.54s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 50 ( 38 unt; 0 def)
% Number of atoms : 67 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 32 ( 15 ~; 12 |; 2 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 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 : 73 ( 7 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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_09,axiom,
! [X12,X13,X14] :
( '>='(X12,X13)
=> '>='('+'(X12,X14),'+'(X13,X14)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_09) ).
fof(sos_08,axiom,
! [X1] : '>='(X1,'0'),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_08) ).
fof(sos_12,axiom,
! [X1] : '+'(X1,'1') = '1',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_12) ).
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_06,axiom,
! [X7,X8] :
( ( '>='(X8,X7)
& '>='(X7,X8) )
=> X7 = X8 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_06) ).
fof(sos_13,axiom,
! [X1] : '==>'('==>'('==>'(X1,'1'),X1),X1) = '0',
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_13) ).
fof(goals_14,conjecture,
! [X21] : '==>'('==>'(X21,'1'),'1') = X21,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals_14) ).
fof(c_0_10,plain,
! [X27] : '+'(X27,'0') = X27,
inference(variable_rename,[status(thm)],[sos_03]) ).
fof(c_0_11,plain,
! [X25,X26] : '+'(X25,X26) = '+'(X26,X25),
inference(variable_rename,[status(thm)],[sos_02]) ).
fof(c_0_12,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])])]) ).
cnf(c_0_13,plain,
'+'(X1,'0') = X1,
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
'+'(X1,X2) = '+'(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_15,plain,
! [X37] : '>='(X37,'0'),
inference(variable_rename,[status(thm)],[sos_08]) ).
fof(c_0_16,plain,
! [X47] : '+'(X47,'1') = '1',
inference(variable_rename,[status(thm)],[sos_12]) ).
cnf(c_0_17,plain,
( ~ '>='(X1,X2)
| '>='('+'(X1,X3),'+'(X2,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_18,plain,
'+'('0',X1) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_19,plain,
'>='(X1,'0'),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_20,plain,
'+'(X1,'1') = '1',
inference(split_conjunct,[status(thm)],[c_0_16]) ).
fof(c_0_21,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_22,plain,
! [X28] : '>='(X28,X28),
inference(variable_rename,[status(thm)],[sos_04]) ).
fof(c_0_23,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_24,plain,
'>='('+'(X1,X2),X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19])]) ).
cnf(c_0_25,plain,
'+'('1',X1) = '1',
inference(spm,[status(thm)],[c_0_20,c_0_14]) ).
cnf(c_0_26,plain,
( ~ '>='('+'(X1,X2),X3)
| '>='(X2,'==>'(X1,X3)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,plain,
'>='(X1,X1),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_28,plain,
( ~ '>='(X2,X1)
| ~ '>='(X1,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_29,plain,
'>='('1',X1),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_30,plain,
( ~ '>='(X1,'==>'(X2,X3))
| '>='('+'(X2,X1),X3) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
fof(c_0_31,plain,
! [X48] : '==>'('==>'('==>'(X48,'1'),X48),X48) = '0',
inference(variable_rename,[status(thm)],[sos_13]) ).
cnf(c_0_32,plain,
'>='(X1,'==>'(X2,'+'(X2,X1))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
( ~ '>='(X1,'1')
| X1 = '1' ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
'>='('+'(X1,'==>'(X1,X2)),X2),
inference(spm,[status(thm)],[c_0_30,c_0_27]) ).
cnf(c_0_35,plain,
'==>'('==>'('==>'(X1,'1'),X1),X1) = '0',
inference(split_conjunct,[status(thm)],[c_0_31]) ).
cnf(c_0_36,plain,
'>='(X1,'==>'(X2,'+'(X1,X2))),
inference(spm,[status(thm)],[c_0_32,c_0_14]) ).
cnf(c_0_37,plain,
'+'(X1,'==>'(X1,'1')) = '1',
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_38,plain,
'>='('==>'('==>'(X1,'1'),X1),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_13]) ).
cnf(c_0_39,plain,
'>='(X1,'==>'(X2,X1)),
inference(spm,[status(thm)],[c_0_26,c_0_24]) ).
fof(c_0_40,negated_conjecture,
~ ! [X21] : '==>'('==>'(X21,'1'),'1') = X21,
inference(assume_negation,[status(cth)],[goals_14]) ).
cnf(c_0_41,plain,
'>='(X1,'==>'('==>'(X1,'1'),'1')),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,plain,
'>='('==>'(X1,'1'),'==>'(X1,X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_29])]) ).
cnf(c_0_43,plain,
'==>'('==>'(X1,'1'),X1) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_38]),c_0_39])]) ).
fof(c_0_44,negated_conjecture,
'==>'('==>'(esk1_0,'1'),'1') != esk1_0,
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_40])])])]) ).
cnf(c_0_45,plain,
( ~ '>='('==>'('==>'(X1,'1'),'1'),X1)
| '==>'('==>'(X1,'1'),'1') = X1 ),
inference(spm,[status(thm)],[c_0_28,c_0_41]) ).
cnf(c_0_46,plain,
'>='('==>'('==>'(X1,'1'),'1'),X1),
inference(spm,[status(thm)],[c_0_42,c_0_43]) ).
cnf(c_0_47,negated_conjecture,
'==>'('==>'(esk1_0,'1'),'1') != esk1_0,
inference(split_conjunct,[status(thm)],[c_0_44]) ).
cnf(c_0_48,plain,
'==>'('==>'(X1,'1'),'1') = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46])]) ).
cnf(c_0_49,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_48])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL902+1 : TPTP v9.3.1. Released v5.5.0.
% 0.00/0.08 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.43 % Computer : n006.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Mon Sep 21 01:10:43 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.43 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.50 Running first-order theorem proving
% 0.18/0.50 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
% 0.28/0.54 % Version: 3.5.1
% 0.28/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.54 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.54 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.54 % Starting sh5l with 300s (1) cores
% 0.28/0.54 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1690423 completed with status 0
% 0.28/0.54 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.28/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.54 % No SInE strategy applied
% 0.28/0.54 % Search class: FHUSM-FFSF22-MFFFFFNN
% 0.28/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.28/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.28/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.28/0.54 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.28/0.54 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S4d with 136s (1) cores
% 0.28/0.54 % Starting new_bool_3 with 136s (1) cores
% 0.28/0.54 % U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 1690431 completed with status 0
% 0.28/0.54 % Result found by U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.28/0.54 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.28/0.54 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.28/0.54 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.28/0.54 % No SInE strategy applied
% 0.28/0.54 % Search class: FHUSM-FFSF22-MFFFFFNN
% 0.28/0.54 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.28/0.54 % Starting SubtermCWHack with 136s (1) cores
% 0.28/0.54 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.28/0.54 % Starting U----_212g_01_B11_00_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.28/0.54 % Preprocessing time : 0.001 s
% 0.28/0.54 % Presaturation interreduction done
% 0.28/0.54
% 0.28/0.54 % Proof found!
% 0.28/0.54 % SZS status Theorem
% 0.28/0.54 % SZS output start CNFRefutation
% See solution above
% 0.28/0.54 % Parsed axioms : 14
% 0.28/0.54 % Removed by relevancy pruning/SinE : 0
% 0.28/0.54 % Initial clauses : 15
% 0.28/0.54 % Removed in clause preprocessing : 0
% 0.28/0.54 % Initial clauses in saturation : 15
% 0.28/0.54 % Processed clauses : 161
% 0.28/0.54 % ...of these trivial : 15
% 0.28/0.54 % ...subsumed : 57
% 0.28/0.54 % ...remaining for further processing : 89
% 0.28/0.54 % Other redundant clauses eliminated : 0
% 0.28/0.54 % Clauses deleted for lack of memory : 0
% 0.28/0.54 % Backward-subsumed : 1
% 0.28/0.54 % Backward-rewritten : 18
% 0.28/0.54 % Generated clauses : 691
% 0.28/0.54 % ...of the previous two non-redundant : 403
% 0.28/0.54 % ...aggressively subsumed : 0
% 0.28/0.54 % Contextual simplify-reflections : 1
% 0.28/0.54 % Paramodulations : 691
% 0.28/0.54 % Factorizations : 0
% 0.28/0.54 % NegExts : 0
% 0.28/0.54 % Equation resolutions : 0
% 0.28/0.54 % Disequality decompositions : 0
% 0.28/0.54 % Total rewrite steps : 555
% 0.28/0.54 % ...of those cached : 451
% 0.28/0.54 % Propositional unsat checks : 0
% 0.28/0.54 % Propositional check models : 0
% 0.28/0.54 % Propositional check unsatisfiable : 0
% 0.28/0.54 % Propositional clauses : 0
% 0.28/0.54 % Propositional clauses after purity: 0
% 0.28/0.54 % Propositional unsat core size : 0
% 0.28/0.54 % Propositional preprocessing time : 0.000
% 0.28/0.54 % Propositional encoding time : 0.000
% 0.28/0.54 % Propositional solver time : 0.000
% 0.28/0.54 % Success case prop preproc time : 0.000
% 0.28/0.54 % Success case prop encoding time : 0.000
% 0.28/0.54 % Success case prop solver time : 0.000
% 0.28/0.54 % Current number of processed clauses : 55
% 0.28/0.54 % Positive orientable unit clauses : 24
% 0.28/0.54 % Positive unorientable unit clauses: 1
% 0.28/0.54 % Negative unit clauses : 1
% 0.28/0.54 % Non-unit-clauses : 29
% 0.28/0.54 % Current number of unprocessed clauses: 261
% 0.28/0.54 % ...number of literals in the above : 533
% 0.28/0.54 % Current number of archived formulas : 0
% 0.28/0.54 % Current number of archived clauses : 34
% 0.28/0.54 % Clause-clause subsumption calls (NU) : 224
% 0.28/0.54 % Rec. Clause-clause subsumption calls : 218
% 0.28/0.54 % Non-unit clause-clause subsumptions : 58
% 0.28/0.54 % Unit Clause-clause subsumption calls : 11
% 0.28/0.54 % Rewrite failures with RHS unbound : 0
% 0.28/0.54 % BW rewrite match attempts : 58
% 0.28/0.54 % BW rewrite match successes : 22
% 0.28/0.54 % Condensation attempts : 0
% 0.28/0.54 % Condensation successes : 0
% 0.28/0.54 % Termbank termtop insertions : 6286
% 0.28/0.54 % Search garbage collected termcells : 112
% 0.28/0.54
% 0.28/0.54 % -------------------------------------------------
% 0.28/0.54 % User time : 0.015 s
% 0.28/0.54 % System time : 0.003 s
% 0.28/0.54 % Total time : 0.018 s
% 0.28/0.54 % Maximum resident set size: 3596 pages
% 0.28/0.54
% 0.28/0.54 % -------------------------------------------------
% 0.28/0.54 % User time : 0.062 s
% 0.28/0.54 % System time : 0.015 s
% 0.28/0.54 % Total time : 0.076 s
% 0.28/0.54 % Maximum resident set size: 4608 pages
% 0.28/0.54 % E exiting
%------------------------------------------------------------------------------