%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM225_1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 12:11:45 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 39 ( 16 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 50 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 105 ( 45 ~; 25 |; 25 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 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 : 12 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 46 !; 0 ?; 46 :)
% 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_25,type,
vPred: vTerm > vTerm ).
tff(decl_26,type,
vsomeTerm: vTerm > vOptTerm ).
tff(decl_27,type,
vZero: vTerm ).
tff(decl_31,type,
vnoTerm: 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_43,type,
esk1_0: vTy ).
tff(decl_44,type,
esk2_0: vTerm ).
tff(decl_54,type,
esk12_2: ( vTerm * vTy ) > vTerm ).
tff(decl_80,type,
esk38_1: vTerm > vTerm ).
tff('Preservation-Pred-t1',conjecture,
! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X99) )
& vptchecksimple(vPred(vt1),X98)
& ! [X13: vTerm] : ( vt1 != vSucc(X13) )
& ( vt1 != vZero ) )
=> vptchecksimple(X99,X98) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Preservation-Pred-t1') ).
tff('DIFF-noTerm-someTerm',axiom,
! [X2: vTerm] : ( vnoTerm != vsomeTerm(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noTerm-someTerm') ).
tff('reduce-11',axiom,
! [X14: vTerm] :
( ( ~ visSomeTerm(vreduce(X14))
& ! [X28: vTerm] : ( X14 != vSucc(X28) )
& ( X14 != vZero ) )
=> ( vreduce(vPred(X14)) = vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-11') ).
tff('TPred_inv2',axiom,
! [X14: vTerm,X98: vTy] :
( vptchecksimple(vPred(X14),X98)
=> ( X98 = vNat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPred_inv2') ).
tff('Preservation-Pred-t1-isSomeTerm-True',axiom,
! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X99) )
& vptchecksimple(vPred(vt1),X98)
& ! [X28: vTerm] : ( vt1 != vSucc(X28) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> vptchecksimple(X99,X98) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Preservation-Pred-t1-isSomeTerm-True') ).
tff('TPred_inv1',axiom,
! [X14: vTerm] :
( vptchecksimple(vPred(X14),vNat)
=> vptchecksimple(X14,vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPred_inv1') ).
tff('TPred',axiom,
! [X14: vTerm] :
( vptchecksimple(X14,vNat)
=> vptchecksimple(vPred(X14),vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPred') ).
tff(c_0_7,negated_conjecture,
~ ! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X99) )
& vptchecksimple(vPred(vt1),X98)
& ! [X13: vTerm] : ( vt1 != vSucc(X13) )
& ( vt1 != vZero ) )
=> vptchecksimple(X99,X98) ),
inference(assume_negation,[status(cth)],['Preservation-Pred-t1']) ).
tff(c_0_8,plain,
! [X2: vTerm] : ( vnoTerm != vsomeTerm(X2) ),
inference(fof_simplification,[status(thm)],['DIFF-noTerm-someTerm']) ).
tff(c_0_9,negated_conjecture,
~ ! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X99) )
& vptchecksimple(vPred(vt1),X98)
& ! [X13: vTerm] : ( vt1 != vSucc(X13) )
& ( vt1 != vZero ) )
=> vptchecksimple(X99,X98) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
tff(c_0_10,plain,
! [X14: vTerm] :
( ( ~ visSomeTerm(vreduce(X14))
& ! [X28: vTerm] : ( X14 != vSucc(X28) )
& ( X14 != vZero ) )
=> ( vreduce(vPred(X14)) = vnoTerm ) ),
inference(fof_simplification,[status(thm)],['reduce-11']) ).
tff(c_0_11,plain,
! [X270: vTerm] : ( vnoTerm != vsomeTerm(X270) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_8])]) ).
tff(c_0_12,negated_conjecture,
! [X102: vTerm] :
( ~ vptchecksimple(esk2_0,esk1_0)
& ( vreduce(vPred(vt1)) = vsomeTerm(esk2_0) )
& vptchecksimple(vPred(vt1),esk1_0)
& ( vt1 != vSucc(X102) )
& ( vt1 != vZero ) ),
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_9])])])])]) ).
tff(c_0_13,plain,
! [X149: vTerm,X150: vTy] :
( ( X150 = vNat )
| ~ vptchecksimple(vPred(X149),X150) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TPred_inv2'])])]) ).
tff(c_0_14,plain,
! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X99) )
& vptchecksimple(vPred(vt1),X98)
& ! [X28: vTerm] : ( vt1 != vSucc(X28) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> vptchecksimple(X99,X98) ),
inference(fof_simplification,[status(thm)],['Preservation-Pred-t1-isSomeTerm-True']) ).
tff(c_0_15,plain,
! [X273: vTerm] :
( ( vreduce(vPred(X273)) = vnoTerm )
| visSomeTerm(vreduce(X273))
| ( X273 = vSucc(esk38_1(X273)) )
| ( X273 = vZero ) ),
inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
tcf(c_0_16,plain,
! [X1: vTerm] : vnoTerm != vsomeTerm(X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tcf(c_0_17,negated_conjecture,
vreduce(vPred(vt1)) = vsomeTerm(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_18,plain,
! [X1: vTerm,X9: vTy] :
( ~ vptchecksimple(vPred(X1),X9)
| ( X9 = vNat ) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_19,negated_conjecture,
vptchecksimple(vPred(vt1),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tff(c_0_20,plain,
! [X153: vTy,X154: vTerm] :
( vptchecksimple(X154,X153)
| ( vreduce(vPred(vt1)) != vsomeTerm(X154) )
| ~ vptchecksimple(vPred(vt1),X153)
| ( vt1 = vSucc(esk12_2(X153,X154)) )
| ( vt1 = vZero )
| ~ visSomeTerm(vreduce(vt1)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_14])])])]) ).
tcf(c_0_21,negated_conjecture,
! [X1: vTerm] : vt1 != vSucc(X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_22,plain,
! [X1: vTerm] :
( ( vreduce(vPred(X1)) = vnoTerm )
| visSomeTerm(vreduce(X1))
| ( X1 = vSucc(esk38_1(X1)) )
| ( X1 = vZero ) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
tcf(c_0_23,negated_conjecture,
vreduce(vPred(vt1)) != vnoTerm,
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
tcf(c_0_24,negated_conjecture,
vt1 != vZero,
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tff(c_0_25,plain,
! [X148: vTerm] :
( vptchecksimple(X148,vNat)
| ~ vptchecksimple(vPred(X148),vNat) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TPred_inv1'])])]) ).
tcf(c_0_26,negated_conjecture,
esk1_0 = vNat,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
tcf(c_0_27,plain,
! [X9: vTy,X1: vTerm] :
( ( vreduce(vPred(vt1)) != vsomeTerm(X1) )
| ~ vptchecksimple(vPred(vt1),X9)
| ~ visSomeTerm(vreduce(vt1))
| vptchecksimple(X1,X9)
| ( vt1 = vSucc(esk12_2(X9,X1)) )
| ( vt1 = vZero ) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
tcf(c_0_28,negated_conjecture,
visSomeTerm(vreduce(vt1)),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22])]),c_0_23]),c_0_24]) ).
tff(c_0_29,plain,
! [X147: vTerm] :
( vptchecksimple(vPred(X147),vNat)
| ~ vptchecksimple(X147,vNat) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TPred'])])]) ).
tcf(c_0_30,plain,
! [X1: vTerm] :
( ~ vptchecksimple(vPred(X1),vNat)
| vptchecksimple(X1,vNat) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
tcf(c_0_31,negated_conjecture,
vptchecksimple(vPred(vt1),vNat),
inference(rw,[status(thm)],[c_0_19,c_0_26]) ).
tcf(c_0_32,plain,
! [X1: vTerm,X9: vTy] :
( ~ vptchecksimple(vPred(vt1),X9)
| ( vsomeTerm(X1) != vreduce(vPred(vt1)) )
| vptchecksimple(X1,X9) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_28])]),c_0_24]),c_0_21]) ).
tcf(c_0_33,plain,
! [X1: vTerm] :
( ~ vptchecksimple(X1,vNat)
| vptchecksimple(vPred(X1),vNat) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
tcf(c_0_34,negated_conjecture,
vptchecksimple(vt1,vNat),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
tcf(c_0_35,negated_conjecture,
~ vptchecksimple(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_36,plain,
! [X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vPred(vt1)) )
| vptchecksimple(X1,vNat) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34])]) ).
tcf(c_0_37,negated_conjecture,
~ vptchecksimple(esk2_0,vNat),
inference(rw,[status(thm)],[c_0_35,c_0_26]) ).
cnf(c_0_38,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_17]),c_0_37]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COM225_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 14:18:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p
% 0.10/0.46 % Version: 3.5.1
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.46 % Starting sh5l with 300s (1) cores
% 0.10/0.46 % new_bool_3 with pid 1316809 completed with status 0
% 0.10/0.46 % Result found by new_bool_3
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.46 % Search class: FGUSS-FFMM31-MFFFFFNN
% 0.10/0.46 % partial match(2): FGHSM-FFMM31-MFFFFFNN
% 0.10/0.46 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.46 % SubtermCWHack with pid 1316816 completed with status 0
% 0.10/0.46 % Result found by SubtermCWHack
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.46 % Search class: FGUSS-FFMM31-MFFFFFNN
% 0.10/0.46 % partial match(2): FGHSM-FFMM31-MFFFFFNN
% 0.10/0.46 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.46 % Preprocessing time : 0.002 s
% 0.10/0.46
% 0.10/0.46 % Proof found!
% 0.10/0.46 % SZS status Theorem
% 0.10/0.46 % SZS output start CNFRefutation
% See solution above
% 0.10/0.46 % Parsed axioms : 131
% 0.10/0.46 % Removed by relevancy pruning/SinE : 52
% 0.10/0.46 % Initial clauses : 101
% 0.10/0.46 % Removed in clause preprocessing : 0
% 0.10/0.46 % Initial clauses in saturation : 101
% 0.10/0.46 % Processed clauses : 276
% 0.10/0.46 % ...of these trivial : 4
% 0.10/0.46 % ...subsumed : 89
% 0.10/0.46 % ...remaining for further processing : 183
% 0.10/0.46 % Other redundant clauses eliminated : 89
% 0.10/0.46 % Clauses deleted for lack of memory : 0
% 0.10/0.46 % Backward-subsumed : 0
% 0.10/0.46 % Backward-rewritten : 5
% 0.10/0.46 % Generated clauses : 592
% 0.10/0.46 % ...of the previous two non-redundant : 357
% 0.10/0.46 % ...aggressively subsumed : 0
% 0.10/0.46 % Contextual simplify-reflections : 0
% 0.10/0.46 % Paramodulations : 497
% 0.10/0.46 % Factorizations : 0
% 0.10/0.46 % NegExts : 0
% 0.10/0.46 % Equation resolutions : 95
% 0.10/0.46 % Disequality decompositions : 0
% 0.10/0.46 % Total rewrite steps : 181
% 0.10/0.46 % ...of those cached : 133
% 0.10/0.46 % Propositional unsat checks : 0
% 0.10/0.46 % Propositional check models : 0
% 0.10/0.46 % Propositional check unsatisfiable : 0
% 0.10/0.46 % Propositional clauses : 0
% 0.10/0.46 % Propositional clauses after purity: 0
% 0.10/0.46 % Propositional unsat core size : 0
% 0.10/0.46 % Propositional preprocessing time : 0.000
% 0.10/0.46 % Propositional encoding time : 0.000
% 0.10/0.46 % Propositional solver time : 0.000
% 0.10/0.46 % Success case prop preproc time : 0.000
% 0.10/0.46 % Success case prop encoding time : 0.000
% 0.10/0.46 % Success case prop solver time : 0.000
% 0.10/0.46 % Current number of processed clauses : 178
% 0.10/0.46 % Positive orientable unit clauses : 41
% 0.10/0.46 % Positive unorientable unit clauses: 4
% 0.10/0.46 % Negative unit clauses : 49
% 0.10/0.46 % Non-unit-clauses : 84
% 0.10/0.46 % Current number of unprocessed clauses: 181
% 0.10/0.46 % ...number of literals in the above : 603
% 0.10/0.46 % Current number of archived formulas : 0
% 0.10/0.46 % Current number of archived clauses : 5
% 0.10/0.46 % Clause-clause subsumption calls (NU) : 857
% 0.10/0.46 % Rec. Clause-clause subsumption calls : 798
% 0.10/0.46 % Non-unit clause-clause subsumptions : 26
% 0.10/0.46 % Unit Clause-clause subsumption calls : 263
% 0.10/0.46 % Rewrite failures with RHS unbound : 40
% 0.10/0.46 % BW rewrite match attempts : 33
% 0.10/0.46 % BW rewrite match successes : 20
% 0.10/0.46 % Condensation attempts : 0
% 0.10/0.46 % Condensation successes : 0
% 0.10/0.46 % Termbank termtop insertions : 12153
% 0.10/0.46 % Search garbage collected termcells : 1960
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.015 s
% 0.10/0.46 % System time : 0.002 s
% 0.10/0.46 % Total time : 0.017 s
% 0.10/0.46 % Maximum resident set size: 4100 pages
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.019 s
% 0.10/0.46 % System time : 0.008 s
% 0.10/0.46 % Total time : 0.027 s
% 0.10/0.46 % Maximum resident set size: 5120 pages
% 0.10/0.46 % E exiting
%------------------------------------------------------------------------------