%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : SWV408+2 : 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 : n020.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 02:54:40 PM UTC 2026
% Result : Theorem 0.10s 0.44s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 29 ( 4 unt; 0 def)
% Number of atoms : 79 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 80 ( 30 ~; 30 |; 13 &)
% ( 2 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 67 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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(l48_li3839,lemma,
! [X1,X2,X3,X4] :
( ( strictly_less_than(X3,X4)
& pair_in_list(X1,X2,X3) )
=> pair_in_list(update_slb(X1,X4),X2,X4) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l48_li3839) ).
fof(l45_li4647,lemma,
! [X1,X2] :
( contains_slb(X1,X2)
=> ? [X3] : pair_in_list(X1,X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_li4647) ).
fof(totality,axiom,
! [X1,X2] :
( less_than(X2,X1)
| less_than(X1,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(l44_co,conjecture,
! [X1,X2,X3,X4] :
( ( strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3)))
& contains_slb(X2,X4) )
=> ( ? [X5] :
( less_than(findmin_pqp_res(X1),X5)
& pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5) )
| pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_co) ).
fof(l49_li3637,lemma,
! [X1,X2,X3,X4] :
( ( less_than(X4,X3)
& pair_in_list(X1,X2,X3) )
=> pair_in_list(update_slb(X1,X4),X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l49_li3637) ).
fof(c_0_6,plain,
! [X1,X2] :
( strictly_less_than(X1,X2)
<=> ( ~ less_than(X2,X1)
& less_than(X1,X2) ) ),
inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).
fof(c_0_7,lemma,
! [X43,X44,X45,X46] :
( pair_in_list(update_slb(X43,X46),X44,X46)
| ~ strictly_less_than(X45,X46)
| ~ pair_in_list(X43,X44,X45) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l48_li3839])])]) ).
fof(c_0_8,lemma,
! [X40,X41] :
( pair_in_list(X40,X41,esk5_2(X40,X41))
| ~ contains_slb(X40,X41) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l45_li4647])])])]) ).
fof(c_0_9,plain,
! [X56,X57] :
( ( strictly_less_than(X56,X57)
| less_than(X57,X56)
| ~ less_than(X56,X57) )
& ( ~ strictly_less_than(X56,X57)
| ~ less_than(X57,X56) )
& ( ~ strictly_less_than(X56,X57)
| less_than(X56,X57) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_10,plain,
! [X14,X15] :
( less_than(X15,X14)
| less_than(X14,X15) ),
inference(variable_rename,[status(thm)],[totality]) ).
fof(c_0_11,negated_conjecture,
~ ! [X1,X2,X3,X4] :
( ( strictly_less_than(X4,findmin_cpq_res(triple(X1,X2,X3)))
& contains_slb(X2,X4) )
=> ( ? [X5] :
( less_than(findmin_pqp_res(X1),X5)
& pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,X5) )
| pair_in_list(update_slb(X2,findmin_pqp_res(X1)),X4,findmin_pqp_res(X1)) ) ),
inference(assume_negation,[status(cth)],[l44_co]) ).
cnf(c_0_12,lemma,
( ~ strictly_less_than(X3,X4)
| ~ pair_in_list(X1,X2,X3)
| pair_in_list(update_slb(X1,X4),X2,X4) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_13,lemma,
( ~ contains_slb(X1,X2)
| pair_in_list(X1,X2,esk5_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
( ~ less_than(X1,X2)
| strictly_less_than(X1,X2)
| less_than(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_15,plain,
( less_than(X2,X1)
| less_than(X1,X2) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
fof(c_0_16,negated_conjecture,
! [X10] :
( ( ~ less_than(findmin_pqp_res(esk1_0),X10)
| ~ pair_in_list(update_slb(esk2_0,findmin_pqp_res(esk1_0)),esk4_0,X10) )
& ~ pair_in_list(update_slb(esk2_0,findmin_pqp_res(esk1_0)),esk4_0,findmin_pqp_res(esk1_0))
& strictly_less_than(esk4_0,findmin_cpq_res(triple(esk1_0,esk2_0,esk3_0)))
& contains_slb(esk2_0,esk4_0) ),
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_11])])])])]) ).
fof(c_0_17,lemma,
! [X47,X48,X49,X50] :
( pair_in_list(update_slb(X47,X50),X48,X49)
| ~ less_than(X50,X49)
| ~ pair_in_list(X47,X48,X49) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l49_li3637])])]) ).
cnf(c_0_18,lemma,
( ~ strictly_less_than(esk5_2(X1,X3),X2)
| ~ contains_slb(X1,X3)
| pair_in_list(update_slb(X1,X2),X3,X2) ),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_19,plain,
( less_than(X2,X1)
| strictly_less_than(X1,X2) ),
inference(csr,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( ~ less_than(findmin_pqp_res(esk1_0),X1)
| ~ pair_in_list(update_slb(esk2_0,findmin_pqp_res(esk1_0)),esk4_0,X1) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_21,lemma,
( ~ less_than(X4,X3)
| ~ pair_in_list(X1,X2,X3)
| pair_in_list(update_slb(X1,X4),X2,X3) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
cnf(c_0_22,lemma,
( ~ contains_slb(X1,X3)
| less_than(X2,esk5_2(X1,X3))
| pair_in_list(update_slb(X1,X2),X3,X2) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
contains_slb(esk2_0,esk4_0),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,negated_conjecture,
( ~ less_than(findmin_pqp_res(esk1_0),X1)
| ~ pair_in_list(esk2_0,esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( less_than(X1,esk5_2(esk2_0,esk4_0))
| pair_in_list(update_slb(esk2_0,X1),esk4_0,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_26,negated_conjecture,
~ pair_in_list(update_slb(esk2_0,findmin_pqp_res(esk1_0)),esk4_0,findmin_pqp_res(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_27,negated_conjecture,
~ pair_in_list(esk2_0,esk4_0,esk5_2(esk2_0,esk4_0)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_28,lemma,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_13]),c_0_23])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV408+2 : 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 : n020.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 08:46:02 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.40 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
% 0.10/0.44 % Version: 3.5.1
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.44 % Starting sh5l with 300s (1) cores
% 0.10/0.44 % new_bool_3 with pid 2532628 completed with status 0
% 0.10/0.44 % Result found by new_bool_3
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGHSM-FFMF31-MFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % SubtermCWHack with pid 2532631 completed with status 0
% 0.10/0.44 % Result found by SubtermCWHack
% 0.10/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.44 % Search class: FGHSM-FFMF31-MFFFFFNN
% 0.10/0.44 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.44 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.44 % Preprocessing time : 0.002 s
% 0.10/0.44
% 0.10/0.44 % Proof found!
% 0.10/0.44 % SZS status Theorem
% 0.10/0.44 % SZS output start CNFRefutation
% See solution above
% 0.10/0.44 % Parsed axioms : 45
% 0.10/0.44 % Removed by relevancy pruning/SinE : 19
% 0.10/0.44 % Initial clauses : 36
% 0.10/0.44 % Removed in clause preprocessing : 0
% 0.10/0.44 % Initial clauses in saturation : 36
% 0.10/0.44 % Processed clauses : 174
% 0.10/0.44 % ...of these trivial : 0
% 0.10/0.44 % ...subsumed : 94
% 0.10/0.44 % ...remaining for further processing : 80
% 0.10/0.44 % Other redundant clauses eliminated : 3
% 0.10/0.44 % Clauses deleted for lack of memory : 0
% 0.10/0.44 % Backward-subsumed : 0
% 0.10/0.44 % Backward-rewritten : 0
% 0.10/0.44 % Generated clauses : 418
% 0.10/0.44 % ...of the previous two non-redundant : 365
% 0.10/0.44 % ...aggressively subsumed : 0
% 0.10/0.44 % Contextual simplify-reflections : 2
% 0.10/0.44 % Paramodulations : 388
% 0.10/0.44 % Factorizations : 28
% 0.10/0.44 % NegExts : 0
% 0.10/0.44 % Equation resolutions : 3
% 0.10/0.44 % Disequality decompositions : 0
% 0.10/0.44 % Total rewrite steps : 54
% 0.10/0.44 % ...of those cached : 29
% 0.10/0.44 % Propositional unsat checks : 0
% 0.10/0.44 % Propositional check models : 0
% 0.10/0.44 % Propositional check unsatisfiable : 0
% 0.10/0.44 % Propositional clauses : 0
% 0.10/0.44 % Propositional clauses after purity: 0
% 0.10/0.44 % Propositional unsat core size : 0
% 0.10/0.44 % Propositional preprocessing time : 0.000
% 0.10/0.44 % Propositional encoding time : 0.000
% 0.10/0.44 % Propositional solver time : 0.000
% 0.10/0.44 % Success case prop preproc time : 0.000
% 0.10/0.44 % Success case prop encoding time : 0.000
% 0.10/0.44 % Success case prop solver time : 0.000
% 0.10/0.44 % Current number of processed clauses : 78
% 0.10/0.44 % Positive orientable unit clauses : 11
% 0.10/0.44 % Positive unorientable unit clauses: 0
% 0.10/0.44 % Negative unit clauses : 6
% 0.10/0.44 % Non-unit-clauses : 61
% 0.10/0.44 % Current number of unprocessed clauses: 227
% 0.10/0.44 % ...number of literals in the above : 1001
% 0.10/0.44 % Current number of archived formulas : 0
% 0.10/0.44 % Current number of archived clauses : 0
% 0.10/0.44 % Clause-clause subsumption calls (NU) : 976
% 0.10/0.44 % Rec. Clause-clause subsumption calls : 697
% 0.10/0.44 % Non-unit clause-clause subsumptions : 87
% 0.10/0.44 % Unit Clause-clause subsumption calls : 7
% 0.10/0.44 % Rewrite failures with RHS unbound : 0
% 0.10/0.44 % BW rewrite match attempts : 1
% 0.10/0.44 % BW rewrite match successes : 0
% 0.10/0.44 % Condensation attempts : 0
% 0.10/0.44 % Condensation successes : 0
% 0.10/0.44 % Termbank termtop insertions : 8064
% 0.10/0.44 % Search garbage collected termcells : 610
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.014 s
% 0.10/0.44 % System time : 0.002 s
% 0.10/0.44 % Total time : 0.016 s
% 0.10/0.44 % Maximum resident set size: 3692 pages
% 0.10/0.44
% 0.10/0.44 % -------------------------------------------------
% 0.10/0.44 % User time : 0.015 s
% 0.10/0.44 % System time : 0.008 s
% 0.10/0.44 % Total time : 0.023 s
% 0.10/0.44 % Maximum resident set size: 4608 pages
% 0.10/0.44 % E exiting
%------------------------------------------------------------------------------