%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM453+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n015.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 01:49:08 PM UTC 2026
% Result : Theorem 0.41s 0.50s
% Output : CNFRefutation 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 14 unt; 0 def)
% Number of atoms : 107 ( 51 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 104 ( 45 ~; 38 |; 16 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__,conjecture,
( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(mAddAsso,axiom,
! [X1,X2,X3] :
( ( aInteger0(X3)
& aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(mAddZero,axiom,
! [X1] :
( aInteger0(X1)
=> ( X1 = sdtpldt0(sz00,X1)
& sdtpldt0(X1,sz00) = X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddZero) ).
fof(mIntZero,axiom,
aInteger0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntZero) ).
fof(m__2171,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__2171) ).
fof(mIntOne,axiom,
aInteger0(sz10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntOne) ).
fof(mIntNeg,axiom,
! [X1] :
( aInteger0(X1)
=> aInteger0(smndt0(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(mAddComm,axiom,
! [X1,X2] :
( ( aInteger0(X2)
& aInteger0(X1) )
=> sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(mAddNeg,axiom,
! [X1] :
( aInteger0(X1)
=> ( sz00 = sdtpldt0(smndt0(X1),X1)
& sdtpldt0(X1,smndt0(X1)) = sz00 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddNeg) ).
fof(c_0_9,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
inference(assume_negation,[status(cth)],[m__]) ).
fof(c_0_10,plain,
! [X54,X55,X56] :
( sdtpldt0(X54,sdtpldt0(X55,X56)) = sdtpldt0(sdtpldt0(X54,X55),X56)
| ~ aInteger0(X56)
| ~ aInteger0(X55)
| ~ aInteger0(X54) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddAsso])])]) ).
fof(c_0_11,plain,
! [X59] :
( ( ~ aInteger0(X59)
| X59 = sdtpldt0(sz00,X59) )
& ( ~ aInteger0(X59)
| sdtpldt0(X59,sz00) = X59 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddZero])])])]) ).
fof(c_0_12,negated_conjecture,
~ ( sdtpldt0(sz10,smndt0(xp)) != sz10
& sdtpldt0(sz10,xp) != sz10 ),
inference(fof_simplification,[status(thm)],[c_0_9]) ).
cnf(c_0_13,plain,
( ~ aInteger0(X3)
| ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,sdtpldt0(X2,X3)) = sdtpldt0(sdtpldt0(X1,X2),X3) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_14,plain,
( ~ aInteger0(X1)
| X1 = sdtpldt0(sz00,X1) ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_15,plain,
aInteger0(sz00),
inference(split_conjunct,[status(thm)],[mIntZero]) ).
fof(c_0_16,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| sdtpldt0(sz10,xp) = sz10 ),
inference(fof_nnf,[status(thm)],[c_0_12]) ).
fof(c_0_17,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ),
inference(fof_simplification,[status(thm)],[m__2171]) ).
cnf(c_0_18,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(sz00,sdtpldt0(X1,X2)) = sdtpldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_19,negated_conjecture,
( sdtpldt0(sz10,smndt0(xp)) = sz10
| sdtpldt0(sz10,xp) = sz10 ),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
aInteger0(sz10),
inference(split_conjunct,[status(thm)],[mIntOne]) ).
fof(c_0_21,plain,
! [X64] :
( aInteger0(smndt0(X64))
| ~ aInteger0(X64) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mIntNeg])])]) ).
fof(c_0_22,hypothesis,
( aSubsetOf0(szAzrzSzezqlpdtcmdtrp0(sz10,xp),stldt0(sbsmnsldt0(xS)))
& xp != sz00
& aInteger0(xp) ),
inference(fof_nnf,[status(thm)],[c_0_17]) ).
cnf(c_0_23,negated_conjecture,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz00,sz10) = sz10
| sdtpldt0(sz10,xp) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_24,plain,
( ~ aInteger0(X1)
| aInteger0(smndt0(X1)) ),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_25,hypothesis,
aInteger0(xp),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_26,negated_conjecture,
( sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz00,sz10) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25])]) ).
cnf(c_0_27,plain,
( ~ aInteger0(X1)
| sdtpldt0(X1,sz00) = X1 ),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_28,plain,
! [X57,X58] :
( sdtpldt0(X57,X58) = sdtpldt0(X58,X57)
| ~ aInteger0(X58)
| ~ aInteger0(X57) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddComm])])]) ).
fof(c_0_29,plain,
! [X60] :
( ( ~ aInteger0(X60)
| sz00 = sdtpldt0(smndt0(X60),X60) )
& ( ~ aInteger0(X60)
| sdtpldt0(X60,smndt0(X60)) = sz00 ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[mAddNeg])])])]) ).
cnf(c_0_30,negated_conjecture,
sdtpldt0(sz00,sz10) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_26]),c_0_25]),c_0_20])]) ).
cnf(c_0_31,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(X1,sdtpldt0(sz00,X2)) = sdtpldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_27]),c_0_15])]) ).
cnf(c_0_32,plain,
( ~ aInteger0(X2)
| ~ aInteger0(X1)
| sdtpldt0(X1,X2) = sdtpldt0(X2,X1) ),
inference(split_conjunct,[status(thm)],[c_0_28]) ).
cnf(c_0_33,plain,
( ~ aInteger0(X1)
| sz00 = sdtpldt0(smndt0(X1),X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_34,negated_conjecture,
( ~ aInteger0(X1)
| sdtpldt0(sz00,sdtpldt0(sz10,X1)) = sdtpldt0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_30]),c_0_20]),c_0_15])]) ).
cnf(c_0_35,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(X1,sdtpldt0(X2,sz00)) = sdtpldt0(X1,X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_15])]) ).
cnf(c_0_36,plain,
( ~ aInteger0(smndt0(sz00))
| smndt0(sz00) = sz00 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_33]),c_0_15])]) ).
cnf(c_0_37,negated_conjecture,
( ~ aInteger0(X1)
| ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10
| sdtpldt0(sz10,sdtpldt0(smndt0(xp),X1)) = sdtpldt0(sz10,X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_19]),c_0_20])]) ).
cnf(c_0_38,negated_conjecture,
sdtpldt0(sz10,sz00) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_30]),c_0_15]),c_0_20])]) ).
cnf(c_0_39,plain,
smndt0(sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_24]),c_0_15])]) ).
cnf(c_0_40,negated_conjecture,
( ~ aInteger0(smndt0(xp))
| sdtpldt0(sz10,xp) = sz10 ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_33]),c_0_38]),c_0_25])]) ).
cnf(c_0_41,plain,
( ~ aInteger0(X1)
| ~ aInteger0(X2)
| sdtpldt0(smndt0(X1),sdtpldt0(X1,X2)) = sdtpldt0(sz00,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_33]),c_0_24]) ).
cnf(c_0_42,plain,
sdtpldt0(sz00,sz00) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_39]),c_0_15])]) ).
cnf(c_0_43,negated_conjecture,
sdtpldt0(sz10,xp) = sz10,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_24]),c_0_25])]) ).
cnf(c_0_44,negated_conjecture,
sdtpldt0(smndt0(sz10),sz10) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_38]),c_0_42]),c_0_15]),c_0_20])]) ).
cnf(c_0_45,negated_conjecture,
sdtpldt0(sz00,xp) = sz00,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_43]),c_0_44]),c_0_25]),c_0_20])]) ).
cnf(c_0_46,hypothesis,
xp != sz00,
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_45]),c_0_25])]),c_0_46]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM453+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n015.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
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 02:34:36 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.41/0.50 % Version: 3.5.1
% 0.41/0.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.41/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.41/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.41/0.50 % Starting new_bool_1 with 300s (1) cores
% 0.41/0.50 % Starting sh5l with 300s (1) cores
% 0.41/0.50 % new_bool_3 with pid 366922 completed with status 0
% 0.41/0.50 % Result found by new_bool_3
% 0.41/0.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.41/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.41/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.41/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.41/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.41/0.50 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.41/0.50 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.41/0.50 % Starting SubtermCWHack with 31s (1) cores
% 0.41/0.50 % SubtermCWHack with pid 366929 completed with status 0
% 0.41/0.50 % Result found by SubtermCWHack
% 0.41/0.50 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.41/0.50 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.41/0.50 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.41/0.50 % Starting new_bool_3 with 300s (1) cores
% 0.41/0.50 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.41/0.50 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.41/0.50 % Search class: FGHSF-FFMM31-SFFFFFNN
% 0.41/0.50 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.41/0.50 % Starting SubtermCWHack with 31s (1) cores
% 0.41/0.50 % Preprocessing time : 0.002 s
% 0.41/0.50
% 0.41/0.50 % Proof found!
% 0.41/0.50 % SZS status Theorem
% 0.41/0.50 % SZS output start CNFRefutation
% See solution above
% 0.41/0.50 % Parsed axioms : 48
% 0.41/0.50 % Removed by relevancy pruning/SinE : 8
% 0.41/0.50 % Initial clauses : 91
% 0.41/0.50 % Removed in clause preprocessing : 4
% 0.41/0.50 % Initial clauses in saturation : 87
% 0.41/0.50 % Processed clauses : 806
% 0.41/0.50 % ...of these trivial : 10
% 0.41/0.50 % ...subsumed : 546
% 0.41/0.50 % ...remaining for further processing : 250
% 0.41/0.50 % Other redundant clauses eliminated : 18
% 0.41/0.50 % Clauses deleted for lack of memory : 0
% 0.41/0.50 % Backward-subsumed : 5
% 0.41/0.50 % Backward-rewritten : 12
% 0.41/0.50 % Generated clauses : 2896
% 0.41/0.50 % ...of the previous two non-redundant : 2182
% 0.41/0.50 % ...aggressively subsumed : 0
% 0.41/0.50 % Contextual simplify-reflections : 29
% 0.41/0.50 % Paramodulations : 2878
% 0.41/0.50 % Factorizations : 0
% 0.41/0.50 % NegExts : 0
% 0.41/0.50 % Equation resolutions : 18
% 0.41/0.50 % Disequality decompositions : 0
% 0.41/0.50 % Total rewrite steps : 3169
% 0.41/0.50 % ...of those cached : 3145
% 0.41/0.50 % Propositional unsat checks : 0
% 0.41/0.50 % Propositional check models : 0
% 0.41/0.50 % Propositional check unsatisfiable : 0
% 0.41/0.50 % Propositional clauses : 0
% 0.41/0.50 % Propositional clauses after purity: 0
% 0.41/0.50 % Propositional unsat core size : 0
% 0.41/0.50 % Propositional preprocessing time : 0.000
% 0.41/0.50 % Propositional encoding time : 0.000
% 0.41/0.50 % Propositional solver time : 0.000
% 0.41/0.50 % Success case prop preproc time : 0.000
% 0.41/0.50 % Success case prop encoding time : 0.000
% 0.41/0.50 % Success case prop solver time : 0.000
% 0.41/0.50 % Current number of processed clauses : 215
% 0.41/0.50 % Positive orientable unit clauses : 28
% 0.41/0.50 % Positive unorientable unit clauses: 0
% 0.41/0.50 % Negative unit clauses : 1
% 0.41/0.50 % Non-unit-clauses : 186
% 0.41/0.50 % Current number of unprocessed clauses: 1438
% 0.41/0.50 % ...number of literals in the above : 5950
% 0.41/0.50 % Current number of archived formulas : 0
% 0.41/0.50 % Current number of archived clauses : 17
% 0.41/0.50 % Clause-clause subsumption calls (NU) : 6127
% 0.41/0.50 % Rec. Clause-clause subsumption calls : 4360
% 0.41/0.50 % Non-unit clause-clause subsumptions : 580
% 0.41/0.50 % Unit Clause-clause subsumption calls : 50
% 0.41/0.50 % Rewrite failures with RHS unbound : 0
% 0.41/0.50 % BW rewrite match attempts : 8
% 0.41/0.50 % BW rewrite match successes : 6
% 0.41/0.50 % Condensation attempts : 0
% 0.41/0.50 % Condensation successes : 0
% 0.41/0.50 % Termbank termtop insertions : 49937
% 0.41/0.50 % Search garbage collected termcells : 1626
% 0.41/0.50
% 0.41/0.50 % -------------------------------------------------
% 0.41/0.50 % User time : 0.056 s
% 0.41/0.50 % System time : 0.010 s
% 0.41/0.50 % Total time : 0.066 s
% 0.41/0.50 % Maximum resident set size: 3896 pages
% 0.41/0.50
% 0.41/0.50 % -------------------------------------------------
% 0.41/0.50 % User time : 0.060 s
% 0.41/0.50 % System time : 0.013 s
% 0.41/0.50 % Total time : 0.073 s
% 0.41/0.50 % Maximum resident set size: 4608 pages
% 0.41/0.50 % E exiting
%------------------------------------------------------------------------------