%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM434+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n006.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 01:49:04 PM UTC 2026
% Result : Theorem 0.14s 10.44s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 43 ( 10 unt; 0 def)
% Number of atoms : 153 ( 41 equ)
% Maximal formula atoms : 18 ( 3 avg)
% Number of connectives : 178 ( 68 ~; 60 |; 37 &)
% ( 4 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 0 sgn 32 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mEquMod,axiom,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEquMod) ).
fof(m__979,hypothesis,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__979) ).
fof(m__,conjecture,
? [X1] :
( sdtasdt0(sdtasdt0(xp,xq),X1) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
fof(mDivisor,axiom,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aInteger0(X3) )
& X2 != sz00
& aInteger0(X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDivisor) ).
fof(m__1003,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__1003) ).
fof(mIntMult,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntMult) ).
fof(mIntPlus,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntPlus) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mIntNeg) ).
fof(mZeroDiv,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> ( sdtasdt0(X1,X2) = sz00
=> ( X2 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mZeroDiv) ).
fof(c_0_9,plain,
! [X1,X2,X3] :
( ( X3 != sz00
& aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> ( sdteqdtlpzmzozddtrp0(X1,X2,X3)
<=> aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ) ),
inference(fof_simplification,[status(thm)],[mEquMod]) ).
fof(c_0_10,hypothesis,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_simplification,[status(thm)],[m__979]) ).
fof(c_0_11,negated_conjecture,
~ ? [X1] :
( sdtasdt0(sdtasdt0(xp,xq),X1) = sdtpldt0(xa,smndt0(xb))
& aInteger0(X1) ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_12,plain,
! [X1] :
( aInteger0(X1)
=> ! [X2] :
( aDivisorOf0(X2,X1)
<=> ( ? [X3] :
( sdtasdt0(X2,X3) = X1
& aInteger0(X3) )
& X2 != sz00
& aInteger0(X2) ) ) ),
inference(fof_simplification,[status(thm)],[mDivisor]) ).
fof(c_0_13,plain,
! [X36,X37,X38] :
( ( X38 = sz00
| ~ aInteger0(X38)
| ~ aInteger0(X37)
| ~ aInteger0(X36)
| sdteqdtlpzmzozddtrp0(X36,X37,X38)
| ~ aDivisorOf0(X38,sdtpldt0(X36,smndt0(X37))) )
& ( X38 = sz00
| ~ aInteger0(X38)
| ~ aInteger0(X37)
| ~ aInteger0(X36)
| aDivisorOf0(X38,sdtpldt0(X36,smndt0(X37)))
| ~ sdteqdtlpzmzozddtrp0(X36,X37,X38) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])])]) ).
fof(c_0_14,hypothesis,
( xq != sz00
& aInteger0(xq)
& xp != sz00
& aInteger0(xp)
& aInteger0(xb)
& aInteger0(xa) ),
inference(fof_nnf,[status(thm)],[c_0_10]) ).
fof(c_0_15,negated_conjecture,
! [X48] :
( sdtasdt0(sdtasdt0(xp,xq),X48) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X48) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])]) ).
fof(c_0_16,plain,
! [X31,X32,X34,X35] :
( ( ~ aInteger0(X31)
| aDivisorOf0(X34,X31)
| sdtasdt0(X34,X35) != X31
| ~ aInteger0(X35)
| X34 = sz00
| ~ aInteger0(X34) )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| sdtasdt0(X32,esk1_2(X31,X32)) = X31 )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| aInteger0(esk1_2(X31,X32)) )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| X32 != sz00 )
& ( ~ aInteger0(X31)
| ~ aDivisorOf0(X32,X31)
| aInteger0(X32) ) ),
inference(distribute,[status(thm)],[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_12])])])])])])]) ).
cnf(c_0_17,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| ~ sdteqdtlpzmzozddtrp0(X1,X2,X3)
| X3 = sz00
| aDivisorOf0(X3,sdtpldt0(X1,smndt0(X2))) ),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_18,hypothesis,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(split_conjunct,[status(thm)],[m__1003]) ).
cnf(c_0_19,hypothesis,
aInteger0(xb),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_20,hypothesis,
aInteger0(xa),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
fof(c_0_21,plain,
! [X9,X10] :
( aInteger0(sdtasdt0(X9,X10))
| ~ aInteger0(X10)
| ~ aInteger0(X9) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntMult])])]) ).
cnf(c_0_22,negated_conjecture,
( sdtasdt0(sdtasdt0(xp,xq),X1) != sdtpldt0(xa,smndt0(xb))
| ~ aInteger0(X1) ),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( ~ aInteger0(X2)
| ~ aDivisorOf0(X1,X2)
| sdtasdt0(X1,esk1_2(X2,X1)) = X2 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_24,plain,
( ~ aInteger0(X1)
| ~ aDivisorOf0(X2,X1)
| aInteger0(esk1_2(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_25,hypothesis,
( ~ aInteger0(sdtasdt0(xp,xq))
| aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| sdtasdt0(xp,xq) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]),c_0_20])]) ).
cnf(c_0_26,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtasdt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_27,hypothesis,
aInteger0(xq),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_28,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_29,negated_conjecture,
( ~ aInteger0(X1)
| ~ aDivisorOf0(sdtasdt0(xp,xq),X1)
| X1 != sdtpldt0(xa,smndt0(xb)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_30,hypothesis,
( aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| sdtasdt0(xp,xq) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_27]),c_0_28])]) ).
fof(c_0_31,plain,
! [X7,X8] :
( aInteger0(sdtpldt0(X7,X8))
| ~ aInteger0(X8)
| ~ aInteger0(X7) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntPlus])])]) ).
cnf(c_0_32,negated_conjecture,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| sdtasdt0(xp,xq) = sz00 ),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_33,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| aInteger0(sdtpldt0(X1,X2)) ),
inference(split_conjunct,[status(thm)],[c_0_31]) ).
fof(c_0_34,plain,
! [X6] :
( aInteger0(smndt0(X6))
| ~ aInteger0(X6) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
fof(c_0_35,plain,
! [X29,X30] :
( X30 = sz00
| X29 = sz00
| sdtasdt0(X29,X30) != sz00
| ~ aInteger0(X30)
| ~ aInteger0(X29) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mZeroDiv])])]) ).
cnf(c_0_36,negated_conjecture,
( ~ aInteger0(smndt0(xb))
| sdtasdt0(xp,xq) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_20])]) ).
cnf(c_0_37,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_38,plain,
( sdtasdt0(X1,X2) != sz00
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| X2 = sz00
| X1 = sz00 ),
inference(split_conjunct,[status(thm)],[c_0_35]) ).
cnf(c_0_39,negated_conjecture,
sdtasdt0(xp,xq) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_19])]) ).
cnf(c_0_40,hypothesis,
xq != sz00,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_41,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_42,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_27]),c_0_28])]),c_0_40]),c_0_41]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM434+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/10.37 % Computer : n006.cluster.edu
% 0.10/10.37 % Model : x86_64 x86_64
% 0.10/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.37 % Memory : 8046.5625MB
% 0.10/10.37 % OS : Linux 6.8.0-71-generic
% 0.10/10.37 % CPULimit : 300
% 0.10/10.37 % WCLimit : 300
% 0.10/10.37 % DateTime : Mon Sep 21 02:29:13 UTC 2026
% 0.10/10.37 % CPUTime :
% 0.10/10.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.14/10.41 Running first-order theorem proving
% 0.14/10.42 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
% 0.14/10.44 % Version: 3.5.1
% 0.14/10.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/10.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/10.44 % Starting new_bool_3 with 300s (1) cores
% 0.14/10.44 % Starting new_bool_1 with 300s (1) cores
% 0.14/10.44 % Starting sh5l with 300s (1) cores
% 0.14/10.44 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 1810273 completed with status 0
% 0.14/10.44 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.14/10.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/10.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/10.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/10.44 % No SInE strategy applied
% 0.14/10.44 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.14/10.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/10.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/10.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/10.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.14/10.44 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.14/10.44 % Starting H----_047_C09_12_F1_AE_ND_CS_SP_S5PRR_RG_S2S with 136s (1) cores
% 0.14/10.44 % G-E--_208_C18_F1_AE_CS_SP_PS_S3S with pid 1810283 completed with status 0
% 0.14/10.44 % Result found by G-E--_208_C18_F1_AE_CS_SP_PS_S3S
% 0.14/10.44 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.14/10.44 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.14/10.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.14/10.44 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.14/10.44 % No SInE strategy applied
% 0.14/10.44 % Search class: FGHSF-FFMM21-SFFFFFNN
% 0.14/10.44 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.14/10.44 % Starting SubtermCWHack with 136s (1) cores
% 0.14/10.44 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.14/10.44 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S2m with 136s (1) cores
% 0.14/10.44 % Starting G-E--_208_C18_F1_AE_CS_SP_PS_S3S with 136s (1) cores
% 0.14/10.44 % Preprocessing time : 0.001 s
% 0.14/10.44 % Presaturation interreduction done
% 0.14/10.44
% 0.14/10.44 % Proof found!
% 0.14/10.44 % SZS status Theorem
% 0.14/10.44 % SZS output start CNFRefutation
% See solution above
% 0.14/10.44 % Parsed axioms : 25
% 0.14/10.44 % Removed by relevancy pruning/SinE : 0
% 0.14/10.44 % Initial clauses : 41
% 0.14/10.44 % Removed in clause preprocessing : 1
% 0.14/10.44 % Initial clauses in saturation : 40
% 0.14/10.44 % Processed clauses : 159
% 0.14/10.44 % ...of these trivial : 4
% 0.14/10.44 % ...subsumed : 40
% 0.14/10.44 % ...remaining for further processing : 115
% 0.14/10.44 % Other redundant clauses eliminated : 3
% 0.14/10.44 % Clauses deleted for lack of memory : 0
% 0.14/10.44 % Backward-subsumed : 6
% 0.14/10.44 % Backward-rewritten : 14
% 0.14/10.44 % Generated clauses : 252
% 0.14/10.44 % ...of the previous two non-redundant : 227
% 0.14/10.44 % ...aggressively subsumed : 0
% 0.14/10.44 % Contextual simplify-reflections : 5
% 0.14/10.44 % Paramodulations : 248
% 0.14/10.44 % Factorizations : 0
% 0.14/10.44 % NegExts : 0
% 0.14/10.44 % Equation resolutions : 4
% 0.14/10.44 % Disequality decompositions : 0
% 0.14/10.44 % Total rewrite steps : 183
% 0.14/10.44 % ...of those cached : 173
% 0.14/10.44 % Propositional unsat checks : 0
% 0.14/10.44 % Propositional check models : 0
% 0.14/10.44 % Propositional check unsatisfiable : 0
% 0.14/10.44 % Propositional clauses : 0
% 0.14/10.44 % Propositional clauses after purity: 0
% 0.14/10.44 % Propositional unsat core size : 0
% 0.14/10.44 % Propositional preprocessing time : 0.000
% 0.14/10.44 % Propositional encoding time : 0.000
% 0.14/10.44 % Propositional solver time : 0.000
% 0.14/10.44 % Success case prop preproc time : 0.000
% 0.14/10.44 % Success case prop encoding time : 0.000
% 0.14/10.44 % Success case prop solver time : 0.000
% 0.14/10.44 % Current number of processed clauses : 55
% 0.14/10.44 % Positive orientable unit clauses : 9
% 0.14/10.44 % Positive unorientable unit clauses: 0
% 0.14/10.44 % Negative unit clauses : 2
% 0.14/10.44 % Non-unit-clauses : 44
% 0.14/10.44 % Current number of unprocessed clauses: 140
% 0.14/10.44 % ...number of literals in the above : 612
% 0.14/10.44 % Current number of archived formulas : 0
% 0.14/10.44 % Current number of archived clauses : 60
% 0.14/10.44 % Clause-clause subsumption calls (NU) : 752
% 0.14/10.44 % Rec. Clause-clause subsumption calls : 357
% 0.14/10.44 % Non-unit clause-clause subsumptions : 51
% 0.14/10.44 % Unit Clause-clause subsumption calls : 2
% 0.14/10.44 % Rewrite failures with RHS unbound : 0
% 0.14/10.44 % BW rewrite match attempts : 2
% 0.14/10.44 % BW rewrite match successes : 2
% 0.14/10.44 % Condensation attempts : 0
% 0.14/10.44 % Condensation successes : 0
% 0.14/10.44 % Termbank termtop insertions : 7367
% 0.14/10.44 % Search garbage collected termcells : 532
% 0.14/10.44
% 0.14/10.44 % -------------------------------------------------
% 0.14/10.44 % User time : 0.011 s
% 0.14/10.44 % System time : 0.002 s
% 0.14/10.44 % Total time : 0.014 s
% 0.14/10.44 % Maximum resident set size: 3656 pages
% 0.14/10.44
% 0.14/10.44 % -------------------------------------------------
% 0.14/10.44 % User time : 0.041 s
% 0.14/10.44 % System time : 0.013 s
% 0.14/10.44 % Total time : 0.054 s
% 0.14/10.44 % Maximum resident set size: 4608 pages
% 0.14/10.44 % E exiting
%------------------------------------------------------------------------------