%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM226_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n026.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 12:11:46 PM UTC 2026
% Result : Theorem 0.14s 0.77s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 40 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 74 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 58 ( 24 ~; 18 |; 8 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-1 aty)
% Number of variables : 36 ( 0 sgn 35 !; 1 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
vOptTerm: $tType ).
tff(decl_sort2,type,
vTy: $tType ).
tff(decl_sort3,type,
vTerm: $tType ).
tff(decl_23,type,
vNat: vTy ).
tff(decl_24,type,
vSucc: vTerm > vTerm ).
tff(decl_26,type,
vsomeTerm: vTerm > vOptTerm ).
tff(decl_35,type,
vt1: vTerm ).
tff(decl_38,type,
vreduce: vTerm > vOptTerm ).
tff(decl_40,type,
visSomeTerm: vOptTerm > $o ).
tff(decl_41,type,
vptchecksimple: ( vTy * vTerm ) > $o ).
tff(decl_42,type,
vgetTerm: vOptTerm > vTerm ).
tff(decl_51,type,
esk1_0: vTy ).
tff(decl_52,type,
esk2_0: vTerm ).
tff(decl_54,type,
esk4_1: vOptTerm > vTerm ).
tff('Preservation-Succ-isSomeTerm-True',conjecture,
! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vSucc(vt1)) = vsomeTerm(X99) )
& vptchecksimple(vSucc(vt1),X98)
& visSomeTerm(vreduce(vt1)) )
=> vptchecksimple(X99,X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Succ-isSomeTerm-True') ).
tff('TSucc_inv1',axiom,
! [X14: vTerm,X98: vTy] :
( vptchecksimple(vSucc(X14),X98)
=> ( X98 = vNat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','TSucc_inv1') ).
tff('getTerm-0',axiom,
! [X10: vTerm] : ( vgetTerm(vsomeTerm(X10)) = X10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','getTerm-0') ).
tff('reduce-4',axiom,
! [X14: vTerm] :
( visSomeTerm(vreduce(X14))
=> ( vreduce(vSucc(X14)) = vsomeTerm(vSucc(vgetTerm(vreduce(X14)))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','reduce-4') ).
tff('TSucc_inv2',axiom,
! [X14: vTerm] :
( vptchecksimple(vSucc(X14),vNat)
=> vptchecksimple(X14,vNat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','TSucc_inv2') ).
tff('TSucc',axiom,
! [X14: vTerm] :
( vptchecksimple(X14,vNat)
=> vptchecksimple(vSucc(X14),vNat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','TSucc') ).
tff('Preservation-Succ-IH0',axiom,
! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vt1) = vsomeTerm(X99) )
& vptchecksimple(vt1,X98) )
=> vptchecksimple(X99,X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Succ-IH0') ).
tff('isSomeTerm-true-INV',axiom,
! [X15: vOptTerm] :
( visSomeTerm(X15)
=> ? [X12: vTerm] : ( X15 = vsomeTerm(X12) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','isSomeTerm-true-INV') ).
tff(c_0_8,negated_conjecture,
~ ! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vSucc(vt1)) = vsomeTerm(X99) )
& vptchecksimple(vSucc(vt1),X98)
& visSomeTerm(vreduce(vt1)) )
=> vptchecksimple(X99,X98) ),
inference(assume_negation,[status(cth)],['Preservation-Succ-isSomeTerm-True']) ).
tff(c_0_9,plain,
! [X120: vTerm,X121: vTy] :
( ( X121 = vNat )
| ~ vptchecksimple(vSucc(X120),X121) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TSucc_inv1'])])]) ).
tff(c_0_10,negated_conjecture,
( ~ vptchecksimple(esk2_0,esk1_0)
& ( vreduce(vSucc(vt1)) = vsomeTerm(esk2_0) )
& vptchecksimple(vSucc(vt1),esk1_0)
& visSomeTerm(vreduce(vt1)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
tff(c_0_11,plain,
! [X145: vTerm] : ( vgetTerm(vsomeTerm(X145)) = X145 ),
inference(variable_rename,[status(thm)],['getTerm-0']) ).
tff(c_0_12,plain,
! [X160: vTerm] :
( ( vreduce(vSucc(X160)) = vsomeTerm(vSucc(vgetTerm(vreduce(X160)))) )
| ~ visSomeTerm(vreduce(X160)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['reduce-4'])])]) ).
tcf(c_0_13,plain,
! [X1: vTerm,X9: vTy] :
( ~ vptchecksimple(vSucc(X1),X9)
| ( X9 = vNat ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_14,negated_conjecture,
vptchecksimple(vSucc(vt1),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_15,plain,
! [X1: vTerm] : vgetTerm(vsomeTerm(X1)) = X1,
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_16,plain,
! [X1: vTerm] :
( ~ visSomeTerm(vreduce(X1))
| ( vreduce(vSucc(X1)) = vsomeTerm(vSucc(vgetTerm(vreduce(X1)))) ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tff(c_0_17,plain,
! [X122: vTerm] :
( vptchecksimple(X122,vNat)
| ~ vptchecksimple(vSucc(X122),vNat) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TSucc_inv2'])])]) ).
tcf(c_0_18,negated_conjecture,
esk1_0 = vNat,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
tff(c_0_19,plain,
! [X119: vTerm] :
( vptchecksimple(vSucc(X119),vNat)
| ~ vptchecksimple(X119,vNat) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TSucc'])])]) ).
tcf(c_0_20,plain,
! [X1: vTerm] :
( ~ visSomeTerm(vreduce(X1))
| ( vgetTerm(vreduce(vSucc(X1))) = vSucc(vgetTerm(vreduce(X1))) ) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
tcf(c_0_21,negated_conjecture,
vreduce(vSucc(vt1)) = vsomeTerm(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_22,negated_conjecture,
visSomeTerm(vreduce(vt1)),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_23,negated_conjecture,
~ vptchecksimple(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tff(c_0_24,plain,
! [X261: vTy,X262: vTerm] :
( vptchecksimple(X262,X261)
| ( vreduce(vt1) != vsomeTerm(X262) )
| ~ vptchecksimple(vt1,X261) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Preservation-Succ-IH0'])])]) ).
tcf(c_0_25,plain,
! [X1: vTerm] :
( ~ vptchecksimple(vSucc(X1),vNat)
| vptchecksimple(X1,vNat) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_26,negated_conjecture,
vptchecksimple(vSucc(vt1),vNat),
inference(rw,[status(thm)],[c_0_14,c_0_18]) ).
tff(c_0_27,plain,
! [X147: vOptTerm] :
( ( X147 = vsomeTerm(esk4_1(X147)) )
| ~ visSomeTerm(X147) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['isSomeTerm-true-INV'])])])]) ).
tcf(c_0_28,plain,
! [X1: vTerm] :
( ~ vptchecksimple(X1,vNat)
| vptchecksimple(vSucc(X1),vNat) ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
tcf(c_0_29,negated_conjecture,
vSucc(vgetTerm(vreduce(vt1))) = esk2_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15]),c_0_22])]) ).
tcf(c_0_30,negated_conjecture,
~ vptchecksimple(esk2_0,vNat),
inference(rw,[status(thm)],[c_0_23,c_0_18]) ).
tcf(c_0_31,plain,
! [X9: vTy,X1: vTerm] :
( ( vreduce(vt1) != vsomeTerm(X1) )
| ~ vptchecksimple(vt1,X9)
| vptchecksimple(X1,X9) ),
inference(split_conjunct,[status(thm)],[c_0_24]) ).
tcf(c_0_32,negated_conjecture,
vptchecksimple(vt1,vNat),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
tcf(c_0_33,plain,
! [X8: vOptTerm] :
( ~ visSomeTerm(X8)
| ( X8 = vsomeTerm(esk4_1(X8)) ) ),
inference(split_conjunct,[status(thm)],[c_0_27]) ).
tcf(c_0_34,negated_conjecture,
~ vptchecksimple(vgetTerm(vreduce(vt1)),vNat),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_30]) ).
tcf(c_0_35,negated_conjecture,
! [X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vt1) )
| vptchecksimple(X1,vNat) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
tcf(c_0_36,plain,
! [X8: vOptTerm] :
( ~ visSomeTerm(X8)
| ( esk4_1(X8) = vgetTerm(X8) ) ),
inference(spm,[status(thm)],[c_0_15,c_0_33]) ).
tcf(c_0_37,negated_conjecture,
vsomeTerm(vgetTerm(vreduce(vt1))) != vreduce(vt1),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
tcf(c_0_38,plain,
! [X8: vOptTerm] :
( ~ visSomeTerm(X8)
| ( vsomeTerm(vgetTerm(X8)) = X8 ) ),
inference(spm,[status(thm)],[c_0_33,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM226_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.57 % Computer : n026.cluster.edu
% 0.10/0.57 % Model : x86_64 x86_64
% 0.10/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.57 % Memory : 8046.5625MB
% 0.10/0.57 % OS : Linux 6.8.0-71-generic
% 0.10/0.57 % CPULimit : 300
% 0.10/0.57 % WCLimit : 300
% 0.10/0.57 % DateTime : Mon Sep 21 14:23:07 UTC 2026
% 0.10/0.58 % CPUTime :
% 0.10/0.58 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.62 Running first-order theorem proving
% 0.10/0.62 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
% 0.14/0.77 % Version: 3.5.1
% 0.14/0.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.77 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.77 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.77 % Starting sh5l with 300s (1) cores
% 0.14/0.77 % sh5l with pid 2500753 completed with status 0
% 0.14/0.77 % Result found by sh5l
% 0.14/0.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.77 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.77 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.77 % Starting sh5l with 300s (1) cores
% 0.14/0.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.77 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.77 % Search class: FGUSM-FSLM31-MFFFFFNN
% 0.14/0.77 % partial match(1): FGHSM-FSLM31-MFFFFFNN
% 0.14/0.77 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.77 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.77 % SubtermCWHack with pid 2500773 completed with status 0
% 0.14/0.77 % Result found by SubtermCWHack
% 0.14/0.77 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.77 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.77 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.77 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.77 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.77 % Starting sh5l with 300s (1) cores
% 0.14/0.77 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = gf500_gu_R04_F100_L20000)
% 0.14/0.77 % SinE strategy is gf500_gu_R04_F100_L20000
% 0.14/0.77 % Search class: FGUSM-FSLM31-MFFFFFNN
% 0.14/0.77 % partial match(1): FGHSM-FSLM31-MFFFFFNN
% 0.14/0.77 % Scheduled 8 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.77 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.77 % Preprocessing time : 0.009 s
% 0.14/0.77
% 0.14/0.77 % Proof found!
% 0.14/0.77 % SZS status Theorem
% 0.14/0.77 % SZS output start CNFRefutation
% See solution above
% 0.14/0.77 % Parsed axioms : 129
% 0.14/0.77 % Removed by relevancy pruning/SinE : 23
% 0.14/0.77 % Initial clauses : 771
% 0.14/0.77 % Removed in clause preprocessing : 0
% 0.14/0.77 % Initial clauses in saturation : 771
% 0.14/0.77 % Processed clauses : 1061
% 0.14/0.77 % ...of these trivial : 2
% 0.14/0.77 % ...subsumed : 453
% 0.14/0.77 % ...remaining for further processing : 606
% 0.14/0.77 % Other redundant clauses eliminated : 509
% 0.14/0.77 % Clauses deleted for lack of memory : 0
% 0.14/0.77 % Backward-subsumed : 55
% 0.14/0.77 % Backward-rewritten : 12
% 0.14/0.77 % Generated clauses : 3673
% 0.14/0.77 % ...of the previous two non-redundant : 2952
% 0.14/0.77 % ...aggressively subsumed : 0
% 0.14/0.77 % Contextual simplify-reflections : 3
% 0.14/0.77 % Paramodulations : 3111
% 0.14/0.77 % Factorizations : 44
% 0.14/0.77 % NegExts : 0
% 0.14/0.77 % Equation resolutions : 518
% 0.14/0.77 % Disequality decompositions : 0
% 0.14/0.77 % Total rewrite steps : 345
% 0.14/0.77 % ...of those cached : 269
% 0.14/0.77 % Propositional unsat checks : 0
% 0.14/0.77 % Propositional check models : 0
% 0.14/0.77 % Propositional check unsatisfiable : 0
% 0.14/0.77 % Propositional clauses : 0
% 0.14/0.77 % Propositional clauses after purity: 0
% 0.14/0.77 % Propositional unsat core size : 0
% 0.14/0.77 % Propositional preprocessing time : 0.000
% 0.14/0.77 % Propositional encoding time : 0.000
% 0.14/0.77 % Propositional solver time : 0.000
% 0.14/0.77 % Success case prop preproc time : 0.000
% 0.14/0.77 % Success case prop encoding time : 0.000
% 0.14/0.77 % Success case prop solver time : 0.000
% 0.14/0.77 % Current number of processed clauses : 539
% 0.14/0.77 % Positive orientable unit clauses : 43
% 0.14/0.77 % Positive unorientable unit clauses: 0
% 0.14/0.77 % Negative unit clauses : 89
% 0.14/0.77 % Non-unit-clauses : 407
% 0.14/0.77 % Current number of unprocessed clauses: 2593
% 0.14/0.77 % ...number of literals in the above : 11586
% 0.14/0.77 % Current number of archived formulas : 0
% 0.14/0.77 % Current number of archived clauses : 67
% 0.14/0.77 % Clause-clause subsumption calls (NU) : 31182
% 0.14/0.77 % Rec. Clause-clause subsumption calls : 17663
% 0.14/0.77 % Non-unit clause-clause subsumptions : 284
% 0.14/0.77 % Unit Clause-clause subsumption calls : 4139
% 0.14/0.77 % Rewrite failures with RHS unbound : 0
% 0.14/0.77 % BW rewrite match attempts : 46
% 0.14/0.77 % BW rewrite match successes : 11
% 0.14/0.77 % Condensation attempts : 0
% 0.14/0.77 % Condensation successes : 0
% 0.14/0.77 % Termbank termtop insertions : 72682
% 0.14/0.77 % Search garbage collected termcells : 6022
% 0.14/0.77
% 0.14/0.77 % -------------------------------------------------
% 0.14/0.77 % User time : 0.122 s
% 0.14/0.77 % System time : 0.008 s
% 0.14/0.77 % Total time : 0.130 s
% 0.14/0.77 % Maximum resident set size: 5376 pages
% 0.14/0.77
% 0.14/0.77 % -------------------------------------------------
% 0.14/0.77 % User time : 0.127 s
% 0.14/0.77 % System time : 0.013 s
% 0.14/0.77 % Total time : 0.140 s
% 0.14/0.77 % Maximum resident set size: 5120 pages
% 0.14/0.77 % E exiting
%------------------------------------------------------------------------------