%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM237_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 : 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 12:11:47 PM UTC 2026
% Result : Theorem 0.22s 0.57s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 33 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 99 ( 43 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 122 ( 56 ~; 27 |; 29 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-1 aty)
% Number of variables : 34 ( 0 sgn 34 !; 0 ?; 34 :)
% 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_27,type,
vZero: vTerm ).
tff(decl_31,type,
vnoTerm: vOptTerm ).
tff(decl_35,type,
vt1: vTerm ).
tff(decl_36,type,
visValue: vTerm > $o ).
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_73,type,
esk31_0: vTerm ).
tff(decl_74,type,
esk32_0: vTerm ).
tff('Progress-Pred-t1',conjecture,
! [X98: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X98)
& ! [X13: vTerm] : ( vt1 != vSucc(X13) )
& ( vt1 != vZero ) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Progress-Pred-t1') ).
tff('TPred_inv2',axiom,
! [X14: vTerm,X98: vTy] :
( vptchecksimple(vPred(X14),X98)
=> ( X98 = vNat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPred_inv2') ).
tff('Progress-Pred-t1-isSomeTerm-False',axiom,
! [X98: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X98)
& ! [X28: vTerm] : ( vt1 != vSucc(X28) )
& ( vt1 != vZero )
& ~ visSomeTerm(vreduce(vt1)) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Progress-Pred-t1-isSomeTerm-False') ).
tff('TPred_inv1',axiom,
! [X14: vTerm] :
( vptchecksimple(vPred(X14),vNat)
=> vptchecksimple(X14,vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPred_inv1') ).
tff('Progress-Pred-t1-isSomeTerm-True',axiom,
! [X98: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X98)
& ! [X28: vTerm] : ( vt1 != vSucc(X28) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Progress-Pred-t1-isSomeTerm-True') ).
tff('TPred',axiom,
! [X14: vTerm] :
( vptchecksimple(X14,vNat)
=> vptchecksimple(vPred(X14),vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPred') ).
tff(c_0_6,negated_conjecture,
~ ! [X98: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X98)
& ! [X13: vTerm] : ( vt1 != vSucc(X13) )
& ( vt1 != vZero ) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(assume_negation,[status(cth)],['Progress-Pred-t1']) ).
tff(c_0_7,negated_conjecture,
~ ! [X98: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X98)
& ! [X13: vTerm] : ( vt1 != vSucc(X13) )
& ( vt1 != vZero ) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
tff(c_0_8,plain,
! [X166: vTerm,X167: vTy] :
( ( X167 = vNat )
| ~ vptchecksimple(vPred(X166),X167) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TPred_inv2'])])]) ).
tff(c_0_9,negated_conjecture,
! [X100: vTerm] :
( ( vreduce(vPred(vt1)) = vnoTerm )
& ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),esk1_0)
& ( vt1 != vSucc(X100) )
& ( 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_7])])])])]) ).
tff(c_0_10,plain,
! [X98: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X98)
& ! [X28: vTerm] : ( vt1 != vSucc(X28) )
& ( vt1 != vZero )
& ~ visSomeTerm(vreduce(vt1)) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(fof_simplification,[status(thm)],['Progress-Pred-t1-isSomeTerm-False']) ).
tcf(c_0_11,plain,
! [X1: vTerm,X9: vTy] :
( ~ vptchecksimple(vPred(X1),X9)
| ( X9 = vNat ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_12,negated_conjecture,
vptchecksimple(vPred(vt1),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tff(c_0_13,plain,
! [X172: vTy] :
( ( vreduce(vPred(vt1)) != vnoTerm )
| visValue(vPred(vt1))
| ~ vptchecksimple(vPred(vt1),X172)
| ( vt1 = vSucc(esk32_0) )
| ( vt1 = vZero )
| visSomeTerm(vreduce(vt1)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])])])])]) ).
tff(c_0_14,plain,
! [X165: vTerm] :
( vptchecksimple(X165,vNat)
| ~ vptchecksimple(vPred(X165),vNat) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TPred_inv1'])])]) ).
tcf(c_0_15,negated_conjecture,
esk1_0 = vNat,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
tff(c_0_16,plain,
! [X98: vTy] :
( ( ~ visValue(vPred(vt1))
& vptchecksimple(vPred(vt1),X98)
& ! [X28: vTerm] : ( vt1 != vSucc(X28) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> ( vreduce(vPred(vt1)) != vnoTerm ) ),
inference(fof_simplification,[status(thm)],['Progress-Pred-t1-isSomeTerm-True']) ).
tcf(c_0_17,plain,
! [X9: vTy] :
( ( vreduce(vPred(vt1)) != vnoTerm )
| ~ vptchecksimple(vPred(vt1),X9)
| visValue(vPred(vt1))
| ( vt1 = vSucc(esk32_0) )
| ( vt1 = vZero )
| visSomeTerm(vreduce(vt1)) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_18,negated_conjecture,
vreduce(vPred(vt1)) = vnoTerm,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_19,negated_conjecture,
vt1 != vZero,
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_20,negated_conjecture,
! [X1: vTerm] : vt1 != vSucc(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_21,negated_conjecture,
~ visValue(vPred(vt1)),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tff(c_0_22,plain,
! [X164: vTerm] :
( vptchecksimple(vPred(X164),vNat)
| ~ vptchecksimple(X164,vNat) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TPred'])])]) ).
tcf(c_0_23,plain,
! [X1: vTerm] :
( ~ vptchecksimple(vPred(X1),vNat)
| vptchecksimple(X1,vNat) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
tcf(c_0_24,negated_conjecture,
vptchecksimple(vPred(vt1),vNat),
inference(rw,[status(thm)],[c_0_12,c_0_15]) ).
tff(c_0_25,plain,
! [X170: vTy] :
( ( vreduce(vPred(vt1)) != vnoTerm )
| visValue(vPred(vt1))
| ~ vptchecksimple(vPred(vt1),X170)
| ( vt1 = vSucc(esk31_0) )
| ( vt1 = vZero )
| ~ visSomeTerm(vreduce(vt1)) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])])]) ).
tcf(c_0_26,plain,
! [X9: vTy] :
( ~ vptchecksimple(vPred(vt1),X9)
| visSomeTerm(vreduce(vt1)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18])]),c_0_19]),c_0_20]),c_0_21]) ).
tcf(c_0_27,plain,
! [X1: vTerm] :
( ~ vptchecksimple(X1,vNat)
| vptchecksimple(vPred(X1),vNat) ),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
tcf(c_0_28,negated_conjecture,
vptchecksimple(vt1,vNat),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
tcf(c_0_29,plain,
! [X9: vTy] :
( ( vreduce(vPred(vt1)) != vnoTerm )
| ~ vptchecksimple(vPred(vt1),X9)
| ~ visSomeTerm(vreduce(vt1))
| visValue(vPred(vt1))
| ( vt1 = vSucc(esk31_0) )
| ( vt1 = vZero ) ),
inference(split_conjunct,[status(thm)],[c_0_25]) ).
tcf(c_0_30,plain,
visSomeTerm(vreduce(vt1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
tcf(c_0_31,plain,
! [X9: vTy] : ~ vptchecksimple(vPred(vt1),X9),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_18]),c_0_30])]),c_0_19]),c_0_20]),c_0_21]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[c_0_24,c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : COM237_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.07 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.18/0.45 % Computer : n020.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 14:21:32 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.45 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.22/0.51 Running first-order theorem proving
% 0.22/0.51 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
% 0.22/0.57 % Version: 3.5.1
% 0.22/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % Starting new_bool_1 with 300s (1) cores
% 0.22/0.57 % Starting sh5l with 300s (1) cores
% 0.22/0.57 % new_bool_3 with pid 3162526 completed with status 0
% 0.22/0.57 % Result found by new_bool_3
% 0.22/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.57 % Search class: FGUSS-FFMM31-MFFFFFNN
% 0.22/0.57 % partial match(2): FGHSM-FFMM31-MFFFFFNN
% 0.22/0.57 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.57 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.57 % SubtermCWHack with pid 3162529 completed with status 0
% 0.22/0.57 % Result found by SubtermCWHack
% 0.22/0.57 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.22/0.57 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.22/0.57 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.22/0.57 % Starting new_bool_3 with 300s (1) cores
% 0.22/0.57 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.22/0.57 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.22/0.57 % Search class: FGUSS-FFMM31-MFFFFFNN
% 0.22/0.57 % partial match(2): FGHSM-FFMM31-MFFFFFNN
% 0.22/0.57 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.22/0.57 % Starting SubtermCWHack with 28s (1) cores
% 0.22/0.57 % Preprocessing time : 0.004 s
% 0.22/0.57
% 0.22/0.57 % Proof found!
% 0.22/0.57 % SZS status Theorem
% 0.22/0.57 % SZS output start CNFRefutation
% See solution above
% 0.22/0.58 % Parsed axioms : 131
% 0.22/0.58 % Removed by relevancy pruning/SinE : 47
% 0.22/0.58 % Initial clauses : 113
% 0.22/0.58 % Removed in clause preprocessing : 0
% 0.22/0.58 % Initial clauses in saturation : 113
% 0.22/0.58 % Processed clauses : 275
% 0.22/0.58 % ...of these trivial : 6
% 0.22/0.58 % ...subsumed : 87
% 0.22/0.58 % ...remaining for further processing : 182
% 0.22/0.58 % Other redundant clauses eliminated : 82
% 0.22/0.58 % Clauses deleted for lack of memory : 0
% 0.22/0.58 % Backward-subsumed : 2
% 0.22/0.58 % Backward-rewritten : 5
% 0.22/0.58 % Generated clauses : 526
% 0.22/0.58 % ...of the previous two non-redundant : 336
% 0.22/0.58 % ...aggressively subsumed : 0
% 0.22/0.58 % Contextual simplify-reflections : 0
% 0.22/0.58 % Paramodulations : 437
% 0.22/0.58 % Factorizations : 0
% 0.22/0.58 % NegExts : 0
% 0.22/0.58 % Equation resolutions : 88
% 0.22/0.58 % Disequality decompositions : 0
% 0.22/0.58 % Total rewrite steps : 140
% 0.22/0.58 % ...of those cached : 97
% 0.22/0.58 % Propositional unsat checks : 0
% 0.22/0.58 % Propositional check models : 0
% 0.22/0.58 % Propositional check unsatisfiable : 0
% 0.22/0.58 % Propositional clauses : 0
% 0.22/0.58 % Propositional clauses after purity: 0
% 0.22/0.58 % Propositional unsat core size : 0
% 0.22/0.58 % Propositional preprocessing time : 0.000
% 0.22/0.58 % Propositional encoding time : 0.000
% 0.22/0.58 % Propositional solver time : 0.000
% 0.22/0.58 % Success case prop preproc time : 0.000
% 0.22/0.58 % Success case prop encoding time : 0.000
% 0.22/0.58 % Success case prop solver time : 0.000
% 0.22/0.58 % Current number of processed clauses : 174
% 0.22/0.58 % Positive orientable unit clauses : 45
% 0.22/0.58 % Positive unorientable unit clauses: 4
% 0.22/0.58 % Negative unit clauses : 48
% 0.22/0.58 % Non-unit-clauses : 77
% 0.22/0.58 % Current number of unprocessed clauses: 173
% 0.22/0.58 % ...number of literals in the above : 571
% 0.22/0.58 % Current number of archived formulas : 0
% 0.22/0.58 % Current number of archived clauses : 8
% 0.22/0.58 % Clause-clause subsumption calls (NU) : 913
% 0.22/0.58 % Rec. Clause-clause subsumption calls : 785
% 0.22/0.58 % Non-unit clause-clause subsumptions : 26
% 0.22/0.58 % Unit Clause-clause subsumption calls : 440
% 0.22/0.58 % Rewrite failures with RHS unbound : 38
% 0.22/0.58 % BW rewrite match attempts : 39
% 0.22/0.58 % BW rewrite match successes : 17
% 0.22/0.58 % Condensation attempts : 0
% 0.22/0.58 % Condensation successes : 0
% 0.22/0.58 % Termbank termtop insertions : 12114
% 0.22/0.58 % Search garbage collected termcells : 2034
% 0.22/0.58
% 0.22/0.58 % -------------------------------------------------
% 0.22/0.58 % User time : 0.033 s
% 0.22/0.58 % System time : 0.003 s
% 0.22/0.58 % Total time : 0.036 s
% 0.22/0.58 % Maximum resident set size: 4100 pages
% 0.22/0.58
% 0.22/0.58 % -------------------------------------------------
% 0.22/0.58 % User time : 0.037 s
% 0.22/0.58 % System time : 0.008 s
% 0.22/0.58 % Total time : 0.045 s
% 0.22/0.58 % Maximum resident set size: 4864 pages
% 0.22/0.58 % E exiting
%------------------------------------------------------------------------------