%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : COM231_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 : n016.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 0.30s 0.59s
% Output : CNFRefutation 0.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 17 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 49 ( 31 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 61 ( 29 ~; 6 |; 21 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 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 : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-1 aty)
% Number of variables : 18 ( 0 sgn 18 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_sort1,type,
vOptTerm: $tType ).
tff(decl_sort2,type,
vTy: $tType ).
tff(decl_sort3,type,
vTerm: $tType ).
tff(decl_24,type,
vSucc: vTerm > vTerm ).
tff(decl_26,type,
vsomeTerm: vTerm > vOptTerm ).
tff(decl_27,type,
vZero: vTerm ).
tff(decl_28,type,
vIszero: vTerm > 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_42,type,
vgetTerm: vOptTerm > vTerm ).
tff(decl_83,type,
esk33_1: vTerm > vTerm ).
tff(decl_103,type,
esk53_0: vTy ).
tff('Progress-Iszero-t1-isSomeTerm-True',conjecture,
! [X98: vTy] :
( ( ~ visValue(vIszero(vt1))
& vptchecksimple(vIszero(vt1),X98)
& ! [X28: vTerm] : ( vt1 != vSucc(X28) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> ( vreduce(vIszero(vt1)) != vnoTerm ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Progress-Iszero-t1-isSomeTerm-True') ).
tff('reduce-16',axiom,
! [X14: vTerm] :
( ( visSomeTerm(vreduce(X14))
& ! [X28: vTerm] : ( X14 != vSucc(X28) )
& ( X14 != vZero ) )
=> ( vreduce(vIszero(X14)) = vsomeTerm(vIszero(vgetTerm(vreduce(X14)))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','reduce-16') ).
tff('DIFF-noTerm-someTerm',axiom,
! [X2: vTerm] : ( vnoTerm != vsomeTerm(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','DIFF-noTerm-someTerm') ).
tff(c_0_3,negated_conjecture,
~ ! [X98: vTy] :
( ( ~ visValue(vIszero(vt1))
& vptchecksimple(vIszero(vt1),X98)
& ! [X28: vTerm] : ( vt1 != vSucc(X28) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> ( vreduce(vIszero(vt1)) != vnoTerm ) ),
inference(assume_negation,[status(cth)],['Progress-Iszero-t1-isSomeTerm-True']) ).
tff(c_0_4,plain,
! [X14: vTerm] :
( ( visSomeTerm(vreduce(X14))
& ! [X28: vTerm] : ( X14 != vSucc(X28) )
& ( X14 != vZero ) )
=> ( vreduce(vIszero(X14)) = vsomeTerm(vIszero(vgetTerm(vreduce(X14)))) ) ),
inference(fof_simplification,[status(thm)],['reduce-16']) ).
tff(c_0_5,negated_conjecture,
~ ! [X98: vTy] :
( ( ~ visValue(vIszero(vt1))
& vptchecksimple(vIszero(vt1),X98)
& ! [X28: vTerm] : ( vt1 != vSucc(X28) )
& ( vt1 != vZero )
& visSomeTerm(vreduce(vt1)) )
=> ( vreduce(vIszero(vt1)) != vnoTerm ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
tff(c_0_6,plain,
! [X2: vTerm] : ( vnoTerm != vsomeTerm(X2) ),
inference(fof_simplification,[status(thm)],['DIFF-noTerm-someTerm']) ).
tff(c_0_7,plain,
! [X249: vTerm] :
( ( vreduce(vIszero(X249)) = vsomeTerm(vIszero(vgetTerm(vreduce(X249)))) )
| ~ visSomeTerm(vreduce(X249))
| ( X249 = vSucc(esk33_1(X249)) )
| ( X249 = vZero ) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
tff(c_0_8,negated_conjecture,
! [X337: vTerm] :
( ( vreduce(vIszero(vt1)) = vnoTerm )
& ~ visValue(vIszero(vt1))
& vptchecksimple(vIszero(vt1),esk53_0)
& ( vt1 != vSucc(X337) )
& ( 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(fof_nnf,[status(thm)],[c_0_5])])])])]) ).
tff(c_0_9,plain,
! [X184: vTerm] : ( vnoTerm != vsomeTerm(X184) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[c_0_6])]) ).
tcf(c_0_10,plain,
! [X1: vTerm] :
( ~ visSomeTerm(vreduce(X1))
| ( vreduce(vIszero(X1)) = vsomeTerm(vIszero(vgetTerm(vreduce(X1)))) )
| ( X1 = vSucc(esk33_1(X1)) )
| ( X1 = vZero ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
tcf(c_0_11,negated_conjecture,
visSomeTerm(vreduce(vt1)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_12,negated_conjecture,
vreduce(vIszero(vt1)) = vnoTerm,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_13,plain,
! [X1: vTerm] : vnoTerm != vsomeTerm(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
tcf(c_0_14,negated_conjecture,
! [X1: vTerm] : vt1 != vSucc(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
tcf(c_0_15,negated_conjecture,
vt1 != vZero,
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]),c_0_13]),c_0_14]),c_0_15]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COM231_1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n016.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 14:25:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.41 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
% 0.30/0.59 % Version: 3.5.1
% 0.30/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.30/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.30/0.59 % Starting new_bool_3 with 300s (1) cores
% 0.30/0.59 % Starting new_bool_1 with 300s (1) cores
% 0.30/0.59 % Starting sh5l with 300s (1) cores
% 0.30/0.59 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 2655118 completed with status 0
% 0.30/0.59 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.30/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.30/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.30/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.30/0.59 % No SInE strategy applied
% 0.30/0.59 % Search class: FGUSM-FSLM31-MFFFFFNN
% 0.30/0.59 % partial match(1): FGHSM-FSLM31-MFFFFFNN
% 0.30/0.59 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.30/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.30/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.30/0.59 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 0.30/0.59 % Starting G-E--_207_B07_F1_AE_CS_SP_PI_PS_S0Y with 136s (1) cores
% 0.30/0.59 % Starting U----_116Y_C05_02_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.30/0.59 % G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with pid 2655126 completed with status 0
% 0.30/0.59 % Result found by G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN
% 0.30/0.59 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.30/0.59 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.30/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.30/0.59 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.30/0.59 % No SInE strategy applied
% 0.30/0.59 % Search class: FGUSM-FSLM31-MFFFFFNN
% 0.30/0.59 % partial match(1): FGHSM-FSLM31-MFFFFFNN
% 0.30/0.59 % Scheduled 8 strats onto 5 cores with 1500 seconds (1500 total)
% 0.30/0.59 % Starting SubtermCWHack with 136s (1) cores
% 0.30/0.59 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.30/0.59 % Starting G-E--_208_C12_11_nc_F1_SE_CS_SP_PS_S5PRR_S04BN with 136s (1) cores
% 0.30/0.59 % Preprocessing time : 0.006 s
% 0.30/0.59 % Presaturation interreduction done
% 0.30/0.59
% 0.30/0.59 % Proof found!
% 0.30/0.59 % SZS status Theorem
% 0.30/0.59 % SZS output start CNFRefutation
% See solution above
% 0.30/0.59 % Parsed axioms : 129
% 0.30/0.59 % Removed by relevancy pruning/SinE : 0
% 0.30/0.59 % Initial clauses : 796
% 0.30/0.59 % Removed in clause preprocessing : 23
% 0.30/0.59 % Initial clauses in saturation : 773
% 0.30/0.59 % Processed clauses : 2393
% 0.30/0.59 % ...of these trivial : 68
% 0.30/0.59 % ...subsumed : 960
% 0.30/0.59 % ...remaining for further processing : 1365
% 0.30/0.59 % Other redundant clauses eliminated : 276
% 0.30/0.59 % Clauses deleted for lack of memory : 0
% 0.30/0.59 % Backward-subsumed : 8
% 0.30/0.59 % Backward-rewritten : 14
% 0.30/0.59 % Generated clauses : 5551
% 0.30/0.59 % ...of the previous two non-redundant : 4770
% 0.30/0.59 % ...aggressively subsumed : 0
% 0.30/0.59 % Contextual simplify-reflections : 8
% 0.30/0.59 % Paramodulations : 5343
% 0.30/0.59 % Factorizations : 33
% 0.30/0.59 % NegExts : 0
% 0.30/0.59 % Equation resolutions : 287
% 0.30/0.59 % Disequality decompositions : 0
% 0.30/0.59 % Total rewrite steps : 1361
% 0.30/0.59 % ...of those cached : 1193
% 0.30/0.59 % Propositional unsat checks : 0
% 0.30/0.59 % Propositional check models : 0
% 0.30/0.59 % Propositional check unsatisfiable : 0
% 0.30/0.59 % Propositional clauses : 0
% 0.30/0.59 % Propositional clauses after purity: 0
% 0.30/0.59 % Propositional unsat core size : 0
% 0.30/0.59 % Propositional preprocessing time : 0.000
% 0.30/0.59 % Propositional encoding time : 0.000
% 0.30/0.59 % Propositional solver time : 0.000
% 0.30/0.59 % Success case prop preproc time : 0.000
% 0.30/0.59 % Success case prop encoding time : 0.000
% 0.30/0.59 % Success case prop solver time : 0.000
% 0.30/0.59 % Current number of processed clauses : 530
% 0.30/0.59 % Positive orientable unit clauses : 136
% 0.30/0.59 % Positive unorientable unit clauses: 0
% 0.30/0.59 % Negative unit clauses : 41
% 0.30/0.59 % Non-unit-clauses : 353
% 0.30/0.59 % Current number of unprocessed clauses: 3769
% 0.30/0.59 % ...number of literals in the above : 12946
% 0.30/0.59 % Current number of archived formulas : 0
% 0.30/0.59 % Current number of archived clauses : 755
% 0.30/0.59 % Clause-clause subsumption calls (NU) : 124837
% 0.30/0.59 % Rec. Clause-clause subsumption calls : 26969
% 0.30/0.59 % Non-unit clause-clause subsumptions : 286
% 0.30/0.59 % Unit Clause-clause subsumption calls : 1129
% 0.30/0.59 % Rewrite failures with RHS unbound : 0
% 0.30/0.59 % BW rewrite match attempts : 2286
% 0.30/0.59 % BW rewrite match successes : 13
% 0.30/0.59 % Condensation attempts : 0
% 0.30/0.59 % Condensation successes : 0
% 0.30/0.59 % Termbank termtop insertions : 181676
% 0.30/0.59 % Search garbage collected termcells : 5981
% 0.30/0.59
% 0.30/0.59 % -------------------------------------------------
% 0.30/0.59 % User time : 0.151 s
% 0.30/0.59 % System time : 0.006 s
% 0.30/0.59 % Total time : 0.157 s
% 0.30/0.59 % Maximum resident set size: 4864 pages
% 0.30/0.59
% 0.30/0.59 % -------------------------------------------------
% 0.30/0.59 % User time : 0.666 s
% 0.30/0.59 % System time : 0.034 s
% 0.30/0.59 % Total time : 0.700 s
% 0.30/0.59 % Maximum resident set size: 4864 pages
% 0.30/0.59 % E exiting
%------------------------------------------------------------------------------