%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV403+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 02:54:39 PM UTC 2026
% Result : Theorem 0.10s 0.43s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 9 unt; 0 def)
% Number of atoms : 114 ( 24 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 113 ( 42 ~; 45 |; 15 &)
% ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 99 ( 6 sgn 57 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(l39_co,conjecture,
! [X1] :
( ! [X2,X3,X4] :
( ( strictly_less_than(X3,X4)
& pair_in_list(X1,X2,X3) )
=> pair_in_list(update_slb(X1,X4),X2,X4) )
=> ! [X5,X6,X7,X8,X9] :
( ( strictly_less_than(X6,X7)
& pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6) )
=> pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X7) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l39_co) ).
fof(ax29,axiom,
! [X1,X2,X3,X4] :
( strictly_less_than(X4,X3)
=> update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X3)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax29) ).
fof(ax23,axiom,
! [X1,X2,X3,X4,X5] :
( pair_in_list(insert_slb(X1,pair(X2,X4)),X3,X5)
<=> ( ( X4 = X5
& X2 = X3 )
| pair_in_list(X1,X3,X5) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax23) ).
fof(ax30,axiom,
! [X1,X2,X3,X4] :
( less_than(X3,X4)
=> update_slb(insert_slb(X1,pair(X2,X4)),X3) = insert_slb(update_slb(X1,X3),pair(X2,X4)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax30) ).
fof(stricly_smaller_definition,axiom,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( ~ less_than(X2,X1)
& less_than(X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X2,X1)
| less_than(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( ! [X2,X3,X4] :
( ( strictly_less_than(X3,X4)
& pair_in_list(X1,X2,X3) )
=> pair_in_list(update_slb(X1,X4),X2,X4) )
=> ! [X5,X6,X7,X8,X9] :
( ( strictly_less_than(X6,X7)
& pair_in_list(insert_slb(X1,pair(X8,X9)),X5,X6) )
=> pair_in_list(update_slb(insert_slb(X1,pair(X8,X9)),X7),X5,X7) ) ),
inference(assume_negation,[status(cth)],[l39_co]) ).
fof(c_0_7,negated_conjecture,
! [X11,X12,X13] :
( ~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk4_0)
& strictly_less_than(esk3_0,esk4_0)
& pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0)
& ( pair_in_list(update_slb(esk1_0,X13),X11,X13)
| ~ strictly_less_than(X12,X13)
| ~ pair_in_list(esk1_0,X11,X12) ) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])])]) ).
fof(c_0_8,plain,
! [X27,X28,X29,X30] :
( update_slb(insert_slb(X27,pair(X28,X30)),X29) = insert_slb(update_slb(X27,X29),pair(X28,X29))
| ~ strictly_less_than(X30,X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax29])])]) ).
fof(c_0_9,plain,
! [X21,X22,X23,X24,X25] :
( ( pair_in_list(insert_slb(X21,pair(X22,X24)),X23,X25)
| X24 != X25
| X22 != X23 )
& ( pair_in_list(insert_slb(X21,pair(X22,X24)),X23,X25)
| ~ pair_in_list(X21,X23,X25) )
& ( ~ pair_in_list(insert_slb(X21,pair(X22,X24)),X23,X25)
| pair_in_list(X21,X23,X25)
| X24 = X25 )
& ( ~ pair_in_list(insert_slb(X21,pair(X22,X24)),X23,X25)
| pair_in_list(X21,X23,X25)
| X22 = X23 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax23])])])]) ).
fof(c_0_10,plain,
! [X31,X32,X33,X34] :
( update_slb(insert_slb(X31,pair(X32,X34)),X33) = insert_slb(update_slb(X31,X33),pair(X32,X34))
| ~ less_than(X33,X34) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax30])])]) ).
cnf(c_0_11,negated_conjecture,
~ pair_in_list(update_slb(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk4_0),esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
( ~ strictly_less_than(X1,X2)
| update_slb(insert_slb(X3,pair(X4,X1)),X2) = insert_slb(update_slb(X3,X2),pair(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
( ~ pair_in_list(insert_slb(X3,pair(X5,X1)),X4,X2)
| pair_in_list(X3,X4,X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,negated_conjecture,
pair_in_list(insert_slb(esk1_0,pair(esk5_0,esk6_0)),esk2_0,esk3_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
fof(c_0_15,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( ~ less_than(X2,X1)
& less_than(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).
cnf(c_0_16,plain,
( ~ less_than(X1,X2)
| update_slb(insert_slb(X3,pair(X4,X2)),X1) = insert_slb(update_slb(X3,X1),pair(X4,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
( ~ strictly_less_than(esk6_0,esk4_0)
| ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk4_0)),esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_18,plain,
( ~ pair_in_list(X1,X2,X3)
| pair_in_list(insert_slb(X1,pair(X4,X5)),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_19,negated_conjecture,
( ~ strictly_less_than(X2,X3)
| ~ pair_in_list(esk1_0,X1,X2)
| pair_in_list(update_slb(esk1_0,X3),X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_20,negated_conjecture,
( pair_in_list(esk1_0,esk2_0,esk3_0)
| esk6_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
fof(c_0_21,plain,
! [X35,X36] :
( ( strictly_less_than(X35,X36)
| less_than(X36,X35)
| ~ less_than(X35,X36) )
& ( ~ strictly_less_than(X35,X36)
| ~ less_than(X36,X35) )
& ( ~ strictly_less_than(X35,X36)
| less_than(X35,X36) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_15])])])]) ).
fof(c_0_22,plain,
! [X41,X42] :
( less_than(X42,X41)
| less_than(X41,X42) ),
inference(variable_rename,[status(thm)],[totality]) ).
cnf(c_0_23,negated_conjecture,
( ~ less_than(esk4_0,esk6_0)
| ~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk6_0)),esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_11,c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( ~ strictly_less_than(esk6_0,esk4_0)
| ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_25,negated_conjecture,
( ~ strictly_less_than(esk3_0,X1)
| pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
| esk6_0 = esk3_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_26,negated_conjecture,
strictly_less_than(esk3_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_27,plain,
( ~ less_than(X1,X2)
| strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_28,plain,
( less_than(X2,X1)
| less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_29,negated_conjecture,
( ~ less_than(esk4_0,esk6_0)
| ~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0) ),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_30,negated_conjecture,
( ~ strictly_less_than(esk6_0,esk4_0)
| esk6_0 = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]) ).
cnf(c_0_31,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2) ),
inference(csr,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( ~ less_than(esk4_0,esk6_0)
| esk6_0 = esk3_0 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_25]),c_0_26])]) ).
cnf(c_0_33,plain,
( ~ pair_in_list(insert_slb(X3,pair(X1,X5)),X2,X4)
| pair_in_list(X3,X2,X4)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_34,negated_conjecture,
esk6_0 = esk3_0,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_35,negated_conjecture,
( pair_in_list(esk1_0,esk2_0,esk3_0)
| esk2_0 = esk5_0 ),
inference(spm,[status(thm)],[c_0_33,c_0_14]) ).
cnf(c_0_36,negated_conjecture,
~ pair_in_list(update_slb(esk1_0,esk4_0),esk2_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_34]),c_0_26])]) ).
cnf(c_0_37,negated_conjecture,
( ~ strictly_less_than(esk3_0,X1)
| pair_in_list(update_slb(esk1_0,X1),esk2_0,X1)
| esk2_0 = esk5_0 ),
inference(spm,[status(thm)],[c_0_19,c_0_35]) ).
cnf(c_0_38,plain,
( X3 != X4
| X1 != X2
| pair_in_list(insert_slb(X5,pair(X1,X3)),X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_39,negated_conjecture,
~ pair_in_list(insert_slb(update_slb(esk1_0,esk4_0),pair(esk5_0,esk4_0)),esk2_0,esk4_0),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_34]),c_0_26])]) ).
cnf(c_0_40,negated_conjecture,
esk2_0 = esk5_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_26])]) ).
cnf(c_0_41,plain,
pair_in_list(insert_slb(X1,pair(X2,X3)),X2,X3),
inference(er,[status(thm)],[inference(er,[status(thm)],[c_0_38])]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_41])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV403+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n016.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:49:38 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.43 % Version: 3.5.1
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % Starting sh5l with 300s (1) cores
% 0.10/0.43 % new_bool_1 with pid 2064224 completed with status 0
% 0.10/0.43 % Result found by new_bool_1
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.43 % Search class: FGHSS-FFMF22-MFFFFFNN
% 0.10/0.43 % partial match(1): FGHSM-FFMF22-MFFFFFNN
% 0.10/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.43 % SubtermCWHack with pid 2064230 completed with status 0
% 0.10/0.43 % Result found by SubtermCWHack
% 0.10/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.10/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.10/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.43 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.43 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.43 % Search class: FGHSS-FFMF22-MFFFFFNN
% 0.10/0.43 % partial match(1): FGHSM-FFMF22-MFFFFFNN
% 0.10/0.43 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.43 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.43 % Preprocessing time : 0.001 s
% 0.10/0.43
% 0.10/0.43 % Proof found!
% 0.10/0.43 % SZS status Theorem
% 0.10/0.43 % SZS output start CNFRefutation
% See solution above
% 0.10/0.43 % Parsed axioms : 19
% 0.10/0.43 % Removed by relevancy pruning/SinE : 7
% 0.10/0.43 % Initial clauses : 22
% 0.10/0.43 % Removed in clause preprocessing : 0
% 0.10/0.43 % Initial clauses in saturation : 22
% 0.10/0.43 % Processed clauses : 122
% 0.10/0.43 % ...of these trivial : 0
% 0.10/0.43 % ...subsumed : 65
% 0.10/0.43 % ...remaining for further processing : 57
% 0.10/0.43 % Other redundant clauses eliminated : 3
% 0.10/0.43 % Clauses deleted for lack of memory : 0
% 0.10/0.43 % Backward-subsumed : 0
% 0.10/0.43 % Backward-rewritten : 16
% 0.10/0.43 % Generated clauses : 249
% 0.10/0.43 % ...of the previous two non-redundant : 193
% 0.10/0.43 % ...aggressively subsumed : 0
% 0.10/0.43 % Contextual simplify-reflections : 2
% 0.10/0.43 % Paramodulations : 213
% 0.10/0.43 % Factorizations : 34
% 0.10/0.43 % NegExts : 0
% 0.10/0.43 % Equation resolutions : 3
% 0.10/0.43 % Disequality decompositions : 0
% 0.10/0.43 % Total rewrite steps : 85
% 0.10/0.43 % ...of those cached : 61
% 0.10/0.43 % Propositional unsat checks : 0
% 0.10/0.43 % Propositional check models : 0
% 0.10/0.43 % Propositional check unsatisfiable : 0
% 0.10/0.43 % Propositional clauses : 0
% 0.10/0.43 % Propositional clauses after purity: 0
% 0.10/0.43 % Propositional unsat core size : 0
% 0.10/0.43 % Propositional preprocessing time : 0.000
% 0.10/0.43 % Propositional encoding time : 0.000
% 0.10/0.43 % Propositional solver time : 0.000
% 0.10/0.43 % Success case prop preproc time : 0.000
% 0.10/0.43 % Success case prop encoding time : 0.000
% 0.10/0.43 % Success case prop solver time : 0.000
% 0.10/0.43 % Current number of processed clauses : 39
% 0.10/0.43 % Positive orientable unit clauses : 8
% 0.10/0.43 % Positive unorientable unit clauses: 0
% 0.10/0.43 % Negative unit clauses : 3
% 0.10/0.43 % Non-unit-clauses : 28
% 0.10/0.43 % Current number of unprocessed clauses: 92
% 0.10/0.43 % ...number of literals in the above : 454
% 0.10/0.43 % Current number of archived formulas : 0
% 0.10/0.43 % Current number of archived clauses : 16
% 0.10/0.43 % Clause-clause subsumption calls (NU) : 693
% 0.10/0.43 % Rec. Clause-clause subsumption calls : 503
% 0.10/0.43 % Non-unit clause-clause subsumptions : 64
% 0.10/0.43 % Unit Clause-clause subsumption calls : 50
% 0.10/0.43 % Rewrite failures with RHS unbound : 0
% 0.10/0.43 % BW rewrite match attempts : 5
% 0.10/0.43 % BW rewrite match successes : 2
% 0.10/0.43 % Condensation attempts : 0
% 0.10/0.43 % Condensation successes : 0
% 0.10/0.43 % Termbank termtop insertions : 4041
% 0.10/0.43 % Search garbage collected termcells : 357
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.008 s
% 0.10/0.43 % System time : 0.003 s
% 0.10/0.43 % Total time : 0.010 s
% 0.10/0.43 % Maximum resident set size: 3604 pages
% 0.10/0.43
% 0.10/0.43 % -------------------------------------------------
% 0.10/0.43 % User time : 0.009 s
% 0.10/0.43 % System time : 0.008 s
% 0.10/0.43 % Total time : 0.016 s
% 0.10/0.43 % Maximum resident set size: 4608 pages
% 0.10/0.43 % E exiting
%------------------------------------------------------------------------------