%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM224_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 : n001.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 0.14s 0.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 35 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 71 ( 34 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 56 ( 20 ~; 11 |; 17 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 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 : 11 ( 11 usr; 6 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_25,type,
vPred: vTerm > vTerm ).
tff(decl_26,type,
vsomeTerm: vTerm > vOptTerm ).
tff(decl_27,type,
vZero: vTerm ).
tff(decl_35,type,
vt1: vTerm ).
tff(decl_37,type,
visNV: 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: vTerm ).
tff(decl_44,type,
esk2_0: vTy ).
tff(decl_45,type,
esk3_0: vTerm ).
tff(decl_46,type,
esk4_1: vOptTerm > vTerm ).
tff('Preservation-Pred-Succ-isNV-True',conjecture,
! [X11: vTerm,X98: vTy,X99: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X99) )
& vptchecksimple(vPred(vt1),X98)
& ( vt1 = vSucc(X11) )
& ( vt1 != vZero )
& visNV(X11) )
=> vptchecksimple(X99,X98) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Preservation-Pred-Succ-isNV-True') ).
tff('EQ-someTerm',axiom,
! [X2: vTerm,X3: vTerm] :
( ( vsomeTerm(X2) = vsomeTerm(X3) )
=> ( X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','EQ-someTerm') ).
tff('isSomeTerm-true-INV',axiom,
! [X15: vOptTerm] :
( visSomeTerm(X15)
=> ? [X12: vTerm] : ( X15 = vsomeTerm(X12) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isSomeTerm-true-INV') ).
tff('isSomeTerm-1',axiom,
! [X12: vTerm] : visSomeTerm(vsomeTerm(X12)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','isSomeTerm-1') ).
tff('TPred_inv2',axiom,
! [X14: vTerm,X98: vTy] :
( vptchecksimple(vPred(X14),X98)
=> ( X98 = vNat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','TPred_inv2') ).
tff('reduce-7',axiom,
! [X11: vTerm] :
( visNV(X11)
=> ( vreduce(vPred(vSucc(X11))) = vsomeTerm(X11) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-7') ).
tff(isNVisNat,axiom,
! [X10: vTerm] :
( visNV(X10)
=> vptchecksimple(X10,vNat) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isNVisNat) ).
tff(c_0_7,negated_conjecture,
~ ! [X11: vTerm,X98: vTy,X99: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X99) )
& vptchecksimple(vPred(vt1),X98)
& ( vt1 = vSucc(X11) )
& ( vt1 != vZero )
& visNV(X11) )
=> vptchecksimple(X99,X98) ),
inference(assume_negation,[status(cth)],['Preservation-Pred-Succ-isNV-True']) ).
tff(c_0_8,negated_conjecture,
~ ! [X11: vTerm,X98: vTy,X99: vTerm] :
( ( ( vreduce(vPred(vt1)) = vsomeTerm(X99) )
& vptchecksimple(vPred(vt1),X98)
& ( vt1 = vSucc(X11) )
& ( vt1 != vZero )
& visNV(X11) )
=> vptchecksimple(X99,X98) ),
inference(fof_simplification,[status(thm)],[c_0_7]) ).
tff(c_0_9,plain,
! [X130: vTerm,X131: vTerm] :
( ( X130 = X131 )
| ( vsomeTerm(X130) != vsomeTerm(X131) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['EQ-someTerm'])])]) ).
tff(c_0_10,plain,
! [X133: vOptTerm] :
( ( X133 = vsomeTerm(esk4_1(X133)) )
| ~ visSomeTerm(X133) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['isSomeTerm-true-INV'])])])]) ).
tff(c_0_11,plain,
! [X132: vTerm] : visSomeTerm(vsomeTerm(X132)),
inference(variable_rename,[status(thm)],['isSomeTerm-1']) ).
tff(c_0_12,plain,
! [X118: vTerm,X119: vTy] :
( ( X119 = vNat )
| ~ vptchecksimple(vPred(X118),X119) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['TPred_inv2'])])]) ).
tff(c_0_13,negated_conjecture,
( ~ vptchecksimple(esk3_0,esk2_0)
& ( vreduce(vPred(vt1)) = vsomeTerm(esk3_0) )
& vptchecksimple(vPred(vt1),esk2_0)
& ( vt1 = vSucc(esk1_0) )
& ( vt1 != vZero )
& visNV(esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])])]) ).
tcf(c_0_14,plain,
! [X1: vTerm,X2: vTerm] :
( ( vsomeTerm(X1) != vsomeTerm(X2) )
| ( X1 = X2 ) ),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_15,plain,
! [X8: vOptTerm] :
( ~ visSomeTerm(X8)
| ( X8 = vsomeTerm(esk4_1(X8)) ) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
tcf(c_0_16,plain,
! [X1: vTerm] : visSomeTerm(vsomeTerm(X1)),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
tff(c_0_17,plain,
! [X139: vTerm] :
( ( vreduce(vPred(vSucc(X139))) = vsomeTerm(X139) )
| ~ visNV(X139) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['reduce-7'])])]) ).
tcf(c_0_18,plain,
! [X1: vTerm,X9: vTy] :
( ~ vptchecksimple(vPred(X1),X9)
| ( X9 = vNat ) ),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
tcf(c_0_19,negated_conjecture,
vptchecksimple(vPred(vt1),esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_20,plain,
! [X1: vTerm] : esk4_1(vsomeTerm(X1)) = X1,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15])]),c_0_16])]) ).
tcf(c_0_21,plain,
! [X1: vTerm] :
( ~ visNV(X1)
| ( vreduce(vPred(vSucc(X1))) = vsomeTerm(X1) ) ),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
tcf(c_0_22,negated_conjecture,
vreduce(vPred(vt1)) = vsomeTerm(esk3_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tff(c_0_23,plain,
! [X129: vTerm] :
( vptchecksimple(X129,vNat)
| ~ visNV(X129) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[isNVisNat])])]) ).
tcf(c_0_24,negated_conjecture,
~ vptchecksimple(esk3_0,esk2_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_25,negated_conjecture,
esk2_0 = vNat,
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
tcf(c_0_26,plain,
! [X1: vTerm] :
( ~ visNV(X1)
| ( esk4_1(vreduce(vPred(vSucc(X1)))) = X1 ) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
tcf(c_0_27,negated_conjecture,
vt1 = vSucc(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_28,negated_conjecture,
esk4_1(vreduce(vPred(vt1))) = esk3_0,
inference(spm,[status(thm)],[c_0_20,c_0_22]) ).
tcf(c_0_29,negated_conjecture,
visNV(esk1_0),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
tcf(c_0_30,plain,
! [X1: vTerm] :
( ~ visNV(X1)
| vptchecksimple(X1,vNat) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
tcf(c_0_31,negated_conjecture,
~ vptchecksimple(esk3_0,vNat),
inference(rw,[status(thm)],[c_0_24,c_0_25]) ).
tcf(c_0_32,negated_conjecture,
esk3_0 = esk1_0,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29])]) ).
tcf(c_0_33,negated_conjecture,
vptchecksimple(esk1_0,vNat),
inference(spm,[status(thm)],[c_0_30,c_0_29]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_31,c_0_32]),c_0_33])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM224_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.35 % Computer : n001.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 14:26:00 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/0.40 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.44 % Version: 3.5.1
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % Starting sh5l with 300s (1) cores
% 0.14/0.44 % new_bool_1 with pid 3359569 completed with status 0
% 0.14/0.44 % Result found by new_bool_1
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FGUSS-FFMM31-MFFFFFNN
% 0.14/0.44 % partial match(2): FGHSM-FFMM31-MFFFFFNN
% 0.14/0.44 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.44 % SubtermCWHack with pid 3359575 completed with status 0
% 0.14/0.44 % Result found by SubtermCWHack
% 0.14/0.44 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.14/0.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/0.44 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.14/0.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/0.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/0.44 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.14/0.44 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.14/0.44 % Search class: FGUSS-FFMM31-MFFFFFNN
% 0.14/0.44 % partial match(2): FGHSM-FFMM31-MFFFFFNN
% 0.14/0.44 % Scheduled 13 strats onto 1 cores with 300 seconds (300 total)
% 0.14/0.44 % Starting SubtermCWHack with 28s (1) cores
% 0.14/0.44 % Preprocessing time : 0.002 s
% 0.14/0.44
% 0.14/0.44 % Proof found!
% 0.14/0.44 % SZS status Theorem
% 0.14/0.44 % SZS output start CNFRefutation
% See solution above
% 0.14/0.44 % Parsed axioms : 130
% 0.14/0.44 % Removed by relevancy pruning/SinE : 52
% 0.14/0.44 % Initial clauses : 101
% 0.14/0.44 % Removed in clause preprocessing : 0
% 0.14/0.44 % Initial clauses in saturation : 101
% 0.14/0.44 % Processed clauses : 255
% 0.14/0.44 % ...of these trivial : 8
% 0.14/0.44 % ...subsumed : 70
% 0.14/0.44 % ...remaining for further processing : 177
% 0.14/0.44 % Other redundant clauses eliminated : 85
% 0.14/0.44 % Clauses deleted for lack of memory : 0
% 0.14/0.44 % Backward-subsumed : 0
% 0.14/0.44 % Backward-rewritten : 9
% 0.14/0.44 % Generated clauses : 582
% 0.14/0.44 % ...of the previous two non-redundant : 332
% 0.14/0.44 % ...aggressively subsumed : 0
% 0.14/0.44 % Contextual simplify-reflections : 0
% 0.14/0.44 % Paramodulations : 491
% 0.14/0.44 % Factorizations : 0
% 0.14/0.44 % NegExts : 0
% 0.14/0.44 % Equation resolutions : 91
% 0.14/0.44 % Disequality decompositions : 0
% 0.14/0.44 % Total rewrite steps : 220
% 0.14/0.44 % ...of those cached : 153
% 0.14/0.44 % Propositional unsat checks : 0
% 0.14/0.44 % Propositional check models : 0
% 0.14/0.44 % Propositional check unsatisfiable : 0
% 0.14/0.44 % Propositional clauses : 0
% 0.14/0.44 % Propositional clauses after purity: 0
% 0.14/0.44 % Propositional unsat core size : 0
% 0.14/0.44 % Propositional preprocessing time : 0.000
% 0.14/0.44 % Propositional encoding time : 0.000
% 0.14/0.44 % Propositional solver time : 0.000
% 0.14/0.44 % Success case prop preproc time : 0.000
% 0.14/0.44 % Success case prop encoding time : 0.000
% 0.14/0.44 % Success case prop solver time : 0.000
% 0.14/0.44 % Current number of processed clauses : 168
% 0.14/0.44 % Positive orientable unit clauses : 40
% 0.14/0.44 % Positive unorientable unit clauses: 10
% 0.14/0.44 % Negative unit clauses : 52
% 0.14/0.44 % Non-unit-clauses : 66
% 0.14/0.44 % Current number of unprocessed clauses: 175
% 0.14/0.44 % ...number of literals in the above : 542
% 0.14/0.44 % Current number of archived formulas : 0
% 0.14/0.44 % Current number of archived clauses : 9
% 0.14/0.44 % Clause-clause subsumption calls (NU) : 692
% 0.14/0.44 % Rec. Clause-clause subsumption calls : 612
% 0.14/0.44 % Non-unit clause-clause subsumptions : 18
% 0.14/0.44 % Unit Clause-clause subsumption calls : 533
% 0.14/0.44 % Rewrite failures with RHS unbound : 50
% 0.14/0.44 % BW rewrite match attempts : 46
% 0.14/0.44 % BW rewrite match successes : 26
% 0.14/0.44 % Condensation attempts : 0
% 0.14/0.44 % Condensation successes : 0
% 0.14/0.44 % Termbank termtop insertions : 11256
% 0.14/0.44 % Search garbage collected termcells : 1882
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.010 s
% 0.14/0.44 % System time : 0.006 s
% 0.14/0.44 % Total time : 0.017 s
% 0.14/0.44 % Maximum resident set size: 4096 pages
% 0.14/0.44
% 0.14/0.44 % -------------------------------------------------
% 0.14/0.44 % User time : 0.017 s
% 0.14/0.44 % System time : 0.010 s
% 0.14/0.44 % Total time : 0.027 s
% 0.14/0.44 % Maximum resident set size: 4864 pages
% 0.14/0.44 % E exiting
%------------------------------------------------------------------------------