%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.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 01:50:50 PM UTC 2026
% Result : Theorem 0.10s 0.46s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 7
% Syntax : Number of formulae : 30 ( 19 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 18 ( 7 ~; 3 |; 5 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 39 ( 0 sgn 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('qu(ind(296), imp(296))',conjecture,
! [X1] :
( vmul(vmul(vd448,vd449),X1) = vmul(vd448,vmul(vd449,X1))
=> vmul(vmul(vd448,vd449),vsucc(X1)) = vmul(vd448,vmul(vd449,vsucc(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(ind(296), imp(296))') ).
fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [X11,X12] :
( vmul(X11,v1) = X11
& vmul(X11,vsucc(X12)) = vplus(vmul(X11,X12),X11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [X84,X85] :
( vplus(X84,v1) = vsucc(X84)
& vplus(X84,vsucc(X85)) = vsucc(vplus(X84,X85)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X76,X77] : vplus(X77,X76) = vplus(X76,X77),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(261, 0), 0)',axiom,
! [X8,X9] : vmul(vsucc(X8),X9) = vplus(vmul(X8,X9),X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).
fof('ass(cond(270, 0), 0)',axiom,
! [X6,X7] : vmul(X6,X7) = vmul(X7,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).
fof('ass(cond(conseq(292), 1), 1)',axiom,
! [X2] :
( vmul(vmul(vd448,vd449),X2) = vmul(vd448,vmul(vd449,X2))
=> vplus(vmul(vd448,vmul(vd449,X2)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,X2),vd449)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 1)') ).
fof(c_0_7,negated_conjecture,
~ ! [X1] :
( vmul(vmul(vd448,vd449),X1) = vmul(vd448,vmul(vd449,X1))
=> vmul(vmul(vd448,vd449),vsucc(X1)) = vmul(vd448,vmul(vd449,vsucc(X1))) ),
inference(assume_negation,[status(cth)],['qu(ind(296), imp(296))']) ).
fof(c_0_8,plain,
! [X102,X103] :
( vmul(X102,v1) = X102
& vmul(X102,vsucc(X103)) = vplus(vmul(X102,X103),X102) ),
inference(variable_rename,[status(thm)],['qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))']) ).
fof(c_0_9,plain,
! [X107,X108] :
( vplus(X107,v1) = vsucc(X107)
& vplus(X107,vsucc(X108)) = vsucc(vplus(X107,X108)) ),
inference(variable_rename,[status(thm)],['qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))']) ).
fof(c_0_10,plain,
! [X144,X145] : vplus(X145,X144) = vplus(X144,X145),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_11,plain,
! [X99,X100] : vmul(vsucc(X99),X100) = vplus(vmul(X99,X100),X100),
inference(variable_rename,[status(thm)],['ass(cond(261, 0), 0)']) ).
fof(c_0_12,negated_conjecture,
( vmul(vmul(vd448,vd449),vsucc(esk1_0)) != vmul(vd448,vmul(vd449,vsucc(esk1_0)))
& vmul(vmul(vd448,vd449),esk1_0) = vmul(vd448,vmul(vd449,esk1_0)) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])])]) ).
fof(c_0_13,plain,
! [X97,X98] : vmul(X97,X98) = vmul(X98,X97),
inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).
fof(c_0_14,plain,
! [X116] :
( vplus(vmul(vd448,vmul(vd449,X116)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,X116),vd449))
| vmul(vmul(vd448,vd449),X116) != vmul(vd448,vmul(vd449,X116)) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(292), 1), 1)'])])]) ).
cnf(c_0_15,plain,
vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_16,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_17,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_18,plain,
vmul(vsucc(X1),X2) = vplus(vmul(X1,X2),X2),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_19,negated_conjecture,
vmul(vmul(vd448,vd449),esk1_0) = vmul(vd448,vmul(vd449,esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,plain,
vmul(X1,X2) = vmul(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_21,plain,
( vmul(vmul(vd448,vd449),X1) != vmul(vd448,vmul(vd449,X1))
| vplus(vmul(vd448,vmul(vd449,X1)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,X1),vd449)) ),
inference(split_conjunct,[status(thm)],[c_0_14]) ).
cnf(c_0_22,plain,
vplus(X1,vmul(X1,X2)) = vmul(X1,vplus(X2,v1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_17]) ).
cnf(c_0_23,plain,
vplus(X1,vmul(X2,X1)) = vmul(vplus(X2,v1),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_16]),c_0_17]) ).
cnf(c_0_24,negated_conjecture,
vmul(esk1_0,vmul(vd449,vd448)) = vmul(vd448,vmul(vd449,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20]) ).
cnf(c_0_25,negated_conjecture,
vmul(vmul(vd448,vd449),vsucc(esk1_0)) != vmul(vd448,vmul(vd449,vsucc(esk1_0))),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_26,plain,
( vmul(vmul(vd449,vd448),X1) != vmul(vd448,vmul(vd449,X1))
| vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,X1))) = vmul(vd448,vmul(vd449,vplus(X1,v1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_21,c_0_20]),c_0_17]),c_0_17]),c_0_22]),c_0_20]) ).
cnf(c_0_27,negated_conjecture,
vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,esk1_0))) = vmul(vmul(vd449,vd448),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_17]),c_0_20]) ).
cnf(c_0_28,negated_conjecture,
vmul(vmul(vd449,vd448),vplus(v1,esk1_0)) != vmul(vd448,vmul(vd449,vplus(v1,esk1_0))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_20]),c_0_16]),c_0_17]),c_0_16]),c_0_17]) ).
cnf(c_0_29,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_17]),c_0_20]),c_0_24])]),c_0_28]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM849+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Mon Sep 21 03:13:10 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.46 % Version: 3.5.1
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.46 % Starting sh5l with 300s (1) cores
% 0.10/0.46 % new_bool_3 with pid 838134 completed with status 0
% 0.10/0.46 % Result found by new_bool_3
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.46 % Search class: FGHPM-FFMS21-MFFFFFNN
% 0.10/0.46 % partial match(1): FGHSM-FFMS21-MFFFFFNN
% 0.10/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.46 % SubtermCWHack with pid 838137 completed with status 0
% 0.10/0.46 % Result found by SubtermCWHack
% 0.10/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.46 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.46 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.46 % Search class: FGHPM-FFMS21-MFFFFFNN
% 0.10/0.46 % partial match(1): FGHSM-FFMS21-MFFFFFNN
% 0.10/0.46 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.46 % Starting SubtermCWHack with 31s (1) cores
% 0.10/0.46 % Preprocessing time : 0.002 s
% 0.10/0.46
% 0.10/0.46 % Proof found!
% 0.10/0.46 % SZS status Theorem
% 0.10/0.46 % SZS output start CNFRefutation
% See solution above
% 0.10/0.46 % Parsed axioms : 56
% 0.10/0.46 % Removed by relevancy pruning/SinE : 27
% 0.10/0.46 % Initial clauses : 32
% 0.10/0.46 % Removed in clause preprocessing : 2
% 0.10/0.46 % Initial clauses in saturation : 30
% 0.10/0.46 % Processed clauses : 418
% 0.10/0.46 % ...of these trivial : 23
% 0.10/0.46 % ...subsumed : 299
% 0.10/0.46 % ...remaining for further processing : 96
% 0.10/0.46 % Other redundant clauses eliminated : 33
% 0.10/0.46 % Clauses deleted for lack of memory : 0
% 0.10/0.46 % Backward-subsumed : 11
% 0.10/0.46 % Backward-rewritten : 4
% 0.10/0.46 % Generated clauses : 1158
% 0.10/0.46 % ...of the previous two non-redundant : 1091
% 0.10/0.46 % ...aggressively subsumed : 0
% 0.10/0.46 % Contextual simplify-reflections : 0
% 0.10/0.46 % Paramodulations : 1121
% 0.10/0.46 % Factorizations : 0
% 0.10/0.46 % NegExts : 0
% 0.10/0.46 % Equation resolutions : 37
% 0.10/0.46 % Disequality decompositions : 0
% 0.10/0.46 % Total rewrite steps : 270
% 0.10/0.46 % ...of those cached : 181
% 0.10/0.46 % Propositional unsat checks : 0
% 0.10/0.46 % Propositional check models : 0
% 0.10/0.46 % Propositional check unsatisfiable : 0
% 0.10/0.46 % Propositional clauses : 0
% 0.10/0.46 % Propositional clauses after purity: 0
% 0.10/0.46 % Propositional unsat core size : 0
% 0.10/0.46 % Propositional preprocessing time : 0.000
% 0.10/0.46 % Propositional encoding time : 0.000
% 0.10/0.46 % Propositional solver time : 0.000
% 0.10/0.46 % Success case prop preproc time : 0.000
% 0.10/0.46 % Success case prop encoding time : 0.000
% 0.10/0.46 % Success case prop solver time : 0.000
% 0.10/0.46 % Current number of processed clauses : 78
% 0.10/0.46 % Positive orientable unit clauses : 18
% 0.10/0.46 % Positive unorientable unit clauses: 4
% 0.10/0.46 % Negative unit clauses : 47
% 0.10/0.46 % Non-unit-clauses : 9
% 0.10/0.46 % Current number of unprocessed clauses: 616
% 0.10/0.46 % ...number of literals in the above : 945
% 0.10/0.46 % Current number of archived formulas : 0
% 0.10/0.46 % Current number of archived clauses : 15
% 0.10/0.46 % Clause-clause subsumption calls (NU) : 48
% 0.10/0.46 % Rec. Clause-clause subsumption calls : 47
% 0.10/0.46 % Non-unit clause-clause subsumptions : 13
% 0.10/0.46 % Unit Clause-clause subsumption calls : 503
% 0.10/0.46 % Rewrite failures with RHS unbound : 0
% 0.10/0.46 % BW rewrite match attempts : 59
% 0.10/0.46 % BW rewrite match successes : 17
% 0.10/0.46 % Condensation attempts : 0
% 0.10/0.46 % Condensation successes : 0
% 0.10/0.46 % Termbank termtop insertions : 9994
% 0.10/0.46 % Search garbage collected termcells : 465
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.016 s
% 0.10/0.46 % System time : 0.004 s
% 0.10/0.46 % Total time : 0.021 s
% 0.10/0.46 % Maximum resident set size: 3724 pages
% 0.10/0.46
% 0.10/0.46 % -------------------------------------------------
% 0.10/0.46 % User time : 0.019 s
% 0.10/0.46 % System time : 0.009 s
% 0.10/0.46 % Total time : 0.028 s
% 0.10/0.46 % Maximum resident set size: 4608 pages
% 0.10/0.46 % E exiting
%------------------------------------------------------------------------------