%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM221_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 : n002.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 0.28s 0.46s
% Output : CNFRefutation 0.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 33 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 78 ( 17 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 74 ( 29 ~; 25 |; 11 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn 48 !; 0 ?; 48 :)
% 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_26,type,
vsomeTerm: vTerm > vOptTerm ).
tff(decl_32,type,
vPlus: ( vTerm * vTerm ) > vTerm ).
tff(decl_33,type,
vt2: vTerm ).
tff(decl_36,type,
vt1: vTerm ).
tff(decl_38,type,
visNV: vTerm > $o ).
tff(decl_39,type,
vreduce: vTerm > vOptTerm ).
tff(decl_42,type,
vptchecksimple: ( vTy * vTerm ) > $o ).
tff(decl_44,type,
esk1_0: vTy ).
tff(decl_45,type,
esk2_0: vTerm ).
tff('Preservation-Plus',conjecture,
! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X99) )
& vptchecksimple(vPlus(vt1,vt2),X98) )
=> vptchecksimple(X99,X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Plus') ).
tff('TPlus_inv0',axiom,
! [X14: vTerm,X16: vTerm,X98: vTy] :
( vptchecksimple(vPlus(X14,X16),X98)
=> ( X98 = vNat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','TPlus_inv0') ).
tff('Preservation-Plus-isNV-False',axiom,
! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X99) )
& vptchecksimple(vPlus(vt1,vt2),X98)
& ~ visNV(vt1) )
=> vptchecksimple(X99,X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Plus-isNV-False') ).
tff('Preservation-Plus-isNV-True',axiom,
! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X99) )
& vptchecksimple(vPlus(vt1,vt2),X98)
& visNV(vt1) )
=> vptchecksimple(X99,X98) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','Preservation-Plus-isNV-True') ).
tff('TPlus_inv2',axiom,
! [X14: vTerm,X16: vTerm] :
( vptchecksimple(vPlus(X14,X16),vNat)
=> vptchecksimple(X16,vNat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','TPlus_inv2') ).
tff('TPlus_inv1',axiom,
! [X14: vTerm,X16: vTerm] :
( vptchecksimple(vPlus(X14,X16),vNat)
=> vptchecksimple(X14,vNat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','TPlus_inv1') ).
tff('TPlus',axiom,
! [X14: vTerm,X16: vTerm] :
( ( vptchecksimple(X16,vNat)
& vptchecksimple(X14,vNat) )
=> vptchecksimple(vPlus(X14,X16),vNat) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','TPlus') ).
tff(c_0_7,negated_conjecture,
~ ! [X98: vTy,X99: vTerm] :
( ( ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X99) )
& vptchecksimple(vPlus(vt1,vt2),X98) )
=> vptchecksimple(X99,X98) ),
inference(assume_negation,[status(cth)],['Preservation-Plus']) ).
tff(c_0_8,plain,
! [X156: vTerm,X157: vTerm,X158: vTy] :
( ( X158 = vNat )
| ~ vptchecksimple(vPlus(X156,X157),X158) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TPlus_inv0'])])]) ).
tff(c_0_9,negated_conjecture,
( ~ vptchecksimple(esk2_0,esk1_0)
& ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(esk2_0) )
& vptchecksimple(vPlus(vt1,vt2),esk1_0) ),
inference(fof_nnf,[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,X99: vTerm] :
( ( ( vreduce(vPlus(vt1,vt2)) = vsomeTerm(X99) )
& vptchecksimple(vPlus(vt1,vt2),X98)
& ~ visNV(vt1) )
=> vptchecksimple(X99,X98) ),
inference(fof_simplification,[status(thm)],['Preservation-Plus-isNV-False']) ).
tcf(c_0_11,plain,
! [X1: vTerm,X2: vTerm,X9: vTy] :
( ~ vptchecksimple(vPlus(X1,X2),X9)
| ( X9 = vNat ) ),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_12,negated_conjecture,
vptchecksimple(vPlus(vt1,vt2),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tff(c_0_13,plain,
! [X165: vTy,X166: vTerm] :
( vptchecksimple(X166,X165)
| ( vreduce(vPlus(vt1,vt2)) != vsomeTerm(X166) )
| ~ vptchecksimple(vPlus(vt1,vt2),X165)
| ~ visNV(vt1) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['Preservation-Plus-isNV-True'])])]) ).
tff(c_0_14,plain,
! [X167: vTy,X168: vTerm] :
( vptchecksimple(X168,X167)
| ( vreduce(vPlus(vt1,vt2)) != vsomeTerm(X168) )
| ~ vptchecksimple(vPlus(vt1,vt2),X167)
| visNV(vt1) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).
tff(c_0_15,plain,
! [X161: vTerm,X162: vTerm] :
( vptchecksimple(X162,vNat)
| ~ vptchecksimple(vPlus(X161,X162),vNat) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TPlus_inv2'])])]) ).
tcf(c_0_16,negated_conjecture,
esk1_0 = vNat,
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
tff(c_0_17,plain,
! [X159: vTerm,X160: vTerm] :
( vptchecksimple(X159,vNat)
| ~ vptchecksimple(vPlus(X159,X160),vNat) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TPlus_inv1'])])]) ).
tcf(c_0_18,plain,
! [X9: vTy,X1: vTerm] :
( ( vreduce(vPlus(vt1,vt2)) != vsomeTerm(X1) )
| ~ vptchecksimple(vPlus(vt1,vt2),X9)
| ~ visNV(vt1)
| vptchecksimple(X1,X9) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_19,plain,
! [X9: vTy,X1: vTerm] :
( ( vreduce(vPlus(vt1,vt2)) != vsomeTerm(X1) )
| ~ vptchecksimple(vPlus(vt1,vt2),X9)
| vptchecksimple(X1,X9)
| visNV(vt1) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
tff(c_0_20,plain,
! [X154: vTerm,X155: vTerm] :
( vptchecksimple(vPlus(X154,X155),vNat)
| ~ vptchecksimple(X155,vNat)
| ~ vptchecksimple(X154,vNat) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TPlus'])])]) ).
tcf(c_0_21,plain,
! [X1: vTerm,X2: vTerm] :
( ~ vptchecksimple(vPlus(X1,X2),vNat)
| vptchecksimple(X2,vNat) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
tcf(c_0_22,negated_conjecture,
vptchecksimple(vPlus(vt1,vt2),vNat),
inference(rw,[status(thm)],[c_0_12,c_0_16]) ).
tcf(c_0_23,plain,
! [X1: vTerm,X2: vTerm] :
( ~ vptchecksimple(vPlus(X1,X2),vNat)
| vptchecksimple(X1,vNat) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_24,plain,
! [X1: vTerm,X9: vTy] :
( ~ vptchecksimple(vPlus(vt1,vt2),X9)
| ( vsomeTerm(X1) != vreduce(vPlus(vt1,vt2)) )
| vptchecksimple(X1,X9) ),
inference(csr,[status(thm)],[c_0_18,c_0_19]) ).
tcf(c_0_25,plain,
! [X1: vTerm,X2: vTerm] :
( ~ vptchecksimple(X2,vNat)
| ~ vptchecksimple(X1,vNat)
| vptchecksimple(vPlus(X1,X2),vNat) ),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
tcf(c_0_26,negated_conjecture,
vptchecksimple(vt2,vNat),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
tcf(c_0_27,negated_conjecture,
vptchecksimple(vt1,vNat),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
tcf(c_0_28,negated_conjecture,
~ vptchecksimple(esk2_0,esk1_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_29,plain,
! [X1: vTerm] :
( ( vsomeTerm(X1) != vreduce(vPlus(vt1,vt2)) )
| vptchecksimple(X1,vNat) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27])]) ).
tcf(c_0_30,negated_conjecture,
vreduce(vPlus(vt1,vt2)) = vsomeTerm(esk2_0),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_31,negated_conjecture,
~ vptchecksimple(esk2_0,vNat),
inference(rw,[status(thm)],[c_0_28,c_0_16]) ).
cnf(c_0_32,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM221_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 14:22:33 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.42 Running first-order theorem proving
% 0.11/0.42 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
% 0.28/0.46 % Version: 3.5.1
% 0.28/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.28/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.28/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.28/0.46 % Starting sh5l with 300s (1) cores
% 0.28/0.46 % new_bool_3 with pid 3502878 completed with status 0
% 0.28/0.46 % Result found by new_bool_3
% 0.28/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.28/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.28/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.46 % Search class: FGUSS-FFMM31-MFFFFFNN
% 0.28/0.46 % partial match(2): FGHSM-FFMM31-MFFFFFNN
% 0.28/0.46 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.46 % SubtermCWHack with pid 3502881 completed with status 0
% 0.28/0.46 % Result found by SubtermCWHack
% 0.28/0.46 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.28/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.28/0.46 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.28/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.28/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.28/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.28/0.46 % Search class: FGUSS-FFMM31-MFFFFFNN
% 0.28/0.46 % partial match(2): FGHSM-FFMM31-MFFFFFNN
% 0.28/0.46 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.28/0.46 % Starting SubtermCWHack with 28s (1) cores
% 0.28/0.46 % Preprocessing time : 0.002 s
% 0.28/0.46
% 0.28/0.46 % Proof found!
% 0.28/0.46 % SZS status Theorem
% 0.28/0.46 % SZS output start CNFRefutation
% See solution above
% 0.28/0.46 % Parsed axioms : 133
% 0.28/0.46 % Removed by relevancy pruning/SinE : 53
% 0.28/0.46 % Initial clauses : 100
% 0.28/0.46 % Removed in clause preprocessing : 0
% 0.28/0.46 % Initial clauses in saturation : 100
% 0.28/0.46 % Processed clauses : 269
% 0.28/0.46 % ...of these trivial : 2
% 0.28/0.46 % ...subsumed : 90
% 0.28/0.46 % ...remaining for further processing : 177
% 0.28/0.46 % Other redundant clauses eliminated : 83
% 0.28/0.46 % Clauses deleted for lack of memory : 0
% 0.28/0.46 % Backward-subsumed : 1
% 0.28/0.46 % Backward-rewritten : 4
% 0.28/0.46 % Generated clauses : 556
% 0.28/0.46 % ...of the previous two non-redundant : 338
% 0.28/0.46 % ...aggressively subsumed : 0
% 0.28/0.46 % Contextual simplify-reflections : 1
% 0.28/0.46 % Paramodulations : 467
% 0.28/0.46 % Factorizations : 0
% 0.28/0.46 % NegExts : 0
% 0.28/0.46 % Equation resolutions : 89
% 0.28/0.46 % Disequality decompositions : 0
% 0.28/0.46 % Total rewrite steps : 152
% 0.28/0.46 % ...of those cached : 103
% 0.28/0.46 % Propositional unsat checks : 0
% 0.28/0.46 % Propositional check models : 0
% 0.28/0.46 % Propositional check unsatisfiable : 0
% 0.28/0.46 % Propositional clauses : 0
% 0.28/0.46 % Propositional clauses after purity: 0
% 0.28/0.46 % Propositional unsat core size : 0
% 0.28/0.46 % Propositional preprocessing time : 0.000
% 0.28/0.46 % Propositional encoding time : 0.000
% 0.28/0.46 % Propositional solver time : 0.000
% 0.28/0.46 % Success case prop preproc time : 0.000
% 0.28/0.46 % Success case prop encoding time : 0.000
% 0.28/0.46 % Success case prop solver time : 0.000
% 0.28/0.46 % Current number of processed clauses : 172
% 0.28/0.46 % Positive orientable unit clauses : 30
% 0.28/0.46 % Positive unorientable unit clauses: 6
% 0.28/0.46 % Negative unit clauses : 47
% 0.28/0.46 % Non-unit-clauses : 89
% 0.28/0.46 % Current number of unprocessed clauses: 169
% 0.28/0.46 % ...number of literals in the above : 533
% 0.28/0.46 % Current number of archived formulas : 0
% 0.28/0.46 % Current number of archived clauses : 5
% 0.28/0.46 % Clause-clause subsumption calls (NU) : 690
% 0.28/0.46 % Rec. Clause-clause subsumption calls : 583
% 0.28/0.46 % Non-unit clause-clause subsumptions : 30
% 0.28/0.46 % Unit Clause-clause subsumption calls : 272
% 0.28/0.46 % Rewrite failures with RHS unbound : 46
% 0.28/0.46 % BW rewrite match attempts : 29
% 0.28/0.46 % BW rewrite match successes : 21
% 0.28/0.46 % Condensation attempts : 0
% 0.28/0.46 % Condensation successes : 0
% 0.28/0.46 % Termbank termtop insertions : 12131
% 0.28/0.46 % Search garbage collected termcells : 1869
% 0.28/0.46
% 0.28/0.46 % -------------------------------------------------
% 0.28/0.46 % User time : 0.015 s
% 0.28/0.46 % System time : 0.005 s
% 0.28/0.46 % Total time : 0.020 s
% 0.28/0.46 % Maximum resident set size: 4100 pages
% 0.28/0.46
% 0.28/0.46 % -------------------------------------------------
% 0.28/0.46 % User time : 0.021 s
% 0.28/0.46 % System time : 0.008 s
% 0.28/0.46 % Total time : 0.029 s
% 0.28/0.46 % Maximum resident set size: 5120 pages
% 0.28/0.46 % E exiting
%------------------------------------------------------------------------------