%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM845+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 : n018.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 01:56:44 PM UTC 2026
% Result : Theorem 0.15s 0.47s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 34 ( 27 unt; 0 def)
% Number of atoms : 41 ( 40 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 0 |; 5 &)
% ( 0 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('qu(ind(267), imp(267))',conjecture,
! [X1] :
( vmul(vsucc(vd411),X1) = vplus(vmul(vd411,X1),X1)
=> vmul(vsucc(vd411),vsucc(X1)) = vplus(vmul(vd411,vsucc(X1)),vsucc(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(ind(267), imp(267))') ).
fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [X77,X78] :
( vplus(X77,v1) = vsucc(X77)
& vplus(X77,vsucc(X78)) = vsucc(vplus(X77,X78)) ),
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(43, 0), 0)',axiom,
! [X73] : vplus(v1,X73) = vsucc(X73),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).
fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [X4,X5] :
( vmul(X4,v1) = X4
& vmul(X4,vsucc(X5)) = vplus(vmul(X4,X5),X4) ),
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('ass(cond(61, 0), 0)',axiom,
! [X69,X70] : vplus(X70,X69) = vplus(X69,X70),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X74,X75,X76] : vplus(vplus(X74,X75),X76) = vplus(X74,vplus(X75,X76)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).
fof(c_0_6,negated_conjecture,
~ ! [X1] :
( vmul(vsucc(vd411),X1) = vplus(vmul(vd411,X1),X1)
=> vmul(vsucc(vd411),vsucc(X1)) = vplus(vmul(vd411,vsucc(X1)),vsucc(X1)) ),
inference(assume_negation,[status(cth)],['qu(ind(267), imp(267))']) ).
fof(c_0_7,negated_conjecture,
( vmul(vsucc(vd411),vsucc(esk1_0)) != vplus(vmul(vd411,vsucc(esk1_0)),vsucc(esk1_0))
& vmul(vsucc(vd411),esk1_0) = vplus(vmul(vd411,esk1_0),esk1_0) ),
inference(fof_nnf,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])])]) ).
fof(c_0_8,plain,
! [X203,X204] :
( vplus(X203,v1) = vsucc(X203)
& vplus(X203,vsucc(X204)) = vsucc(vplus(X203,X204)) ),
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_9,plain,
! [X199] : vplus(v1,X199) = vsucc(X199),
inference(variable_rename,[status(thm)],['ass(cond(43, 0), 0)']) ).
cnf(c_0_10,negated_conjecture,
vmul(vsucc(vd411),vsucc(esk1_0)) != vplus(vmul(vd411,vsucc(esk1_0)),vsucc(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_11,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_12,plain,
vplus(v1,X1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_13,plain,
! [X96,X97] :
( vmul(X96,v1) = X96
& vmul(X96,vsucc(X97)) = vplus(vmul(X96,X97),X96) ),
inference(variable_rename,[status(thm)],['qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))']) ).
cnf(c_0_14,negated_conjecture,
vmul(vsucc(vd411),esk1_0) = vplus(vmul(vd411,esk1_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
cnf(c_0_15,negated_conjecture,
vmul(vplus(vd411,v1),vplus(esk1_0,v1)) != vplus(vmul(vd411,vplus(esk1_0,v1)),vplus(esk1_0,v1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_10,c_0_11]),c_0_11]),c_0_11]),c_0_11]) ).
cnf(c_0_16,plain,
vplus(v1,X1) = vplus(X1,v1),
inference(rw,[status(thm)],[c_0_12,c_0_11]) ).
fof(c_0_17,plain,
! [X195,X196] : vplus(X196,X195) = vplus(X195,X196),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_18,plain,
vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
cnf(c_0_19,negated_conjecture,
vplus(vmul(vd411,esk1_0),esk1_0) = vmul(vplus(vd411,v1),esk1_0),
inference(rw,[status(thm)],[c_0_14,c_0_11]) ).
cnf(c_0_20,negated_conjecture,
vplus(vmul(vd411,vplus(v1,esk1_0)),vplus(v1,esk1_0)) != vmul(vplus(v1,vd411),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_16]),c_0_16]),c_0_16]) ).
cnf(c_0_21,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_17]) ).
fof(c_0_22,plain,
! [X200,X201,X202] : vplus(vplus(X200,X201),X202) = vplus(X200,vplus(X201,X202)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_23,plain,
vmul(X1,vplus(X2,v1)) = vplus(vmul(X1,X2),X1),
inference(rw,[status(thm)],[c_0_18,c_0_11]) ).
cnf(c_0_24,negated_conjecture,
vmul(vplus(v1,vd411),esk1_0) = vplus(vmul(vd411,esk1_0),esk1_0),
inference(rw,[status(thm)],[c_0_19,c_0_16]) ).
cnf(c_0_25,negated_conjecture,
vplus(vplus(v1,esk1_0),vmul(vd411,vplus(v1,esk1_0))) != vmul(vplus(v1,vd411),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_26,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_27,plain,
vmul(X1,vplus(X2,v1)) = vplus(X1,vmul(X1,X2)),
inference(rw,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_28,negated_conjecture,
vmul(vplus(v1,vd411),esk1_0) = vplus(esk1_0,vmul(vd411,esk1_0)),
inference(rw,[status(thm)],[c_0_24,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
vplus(v1,vplus(esk1_0,vmul(vd411,vplus(v1,esk1_0)))) != vmul(vplus(v1,vd411),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_30,plain,
vmul(X1,vplus(v1,X2)) = vplus(X1,vmul(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_21]) ).
cnf(c_0_31,plain,
vplus(X1,vplus(X2,X3)) = vplus(X3,vplus(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_32,negated_conjecture,
vplus(v1,vplus(vd411,vplus(esk1_0,vmul(vd411,esk1_0)))) = vmul(vplus(v1,vd411),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_16]),c_0_26]) ).
cnf(c_0_33,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]),c_0_21]),c_0_32])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM845+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.36 % Computer : n018.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 03:14:58 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.40 Running first-order theorem proving
% 0.15/0.40 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
% 0.15/0.47 % Version: 3.5.1
% 0.15/0.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.15/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.15/0.47 % Starting sh5l with 300s (1) cores
% 0.15/0.47 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 837776 completed with status 0
% 0.15/0.47 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.15/0.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.47 % No SInE strategy applied
% 0.15/0.47 % Search class: FGHSM-FFMS21-MFFFFFNN
% 0.15/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.47 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.47 % new_bool_1 with pid 837787 completed with status 0
% 0.15/0.47 % Result found by new_bool_1
% 0.15/0.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.15/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.15/0.47 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/0.47 % No SInE strategy applied
% 0.15/0.47 % Search class: FGHSM-FFMS21-MFFFFFNN
% 0.15/0.47 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/0.47 % Starting SubtermCWHack with 136s (1) cores
% 0.15/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.15/0.47 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.15/0.47 % Starting new_bool_3 with 136s (1) cores
% 0.15/0.47 % Starting new_bool_1 with 136s (1) cores
% 0.15/0.47 % Preprocessing time : 0.002 s
% 0.15/0.47 % Presaturation interreduction done
% 0.15/0.47
% 0.15/0.47 % Proof found!
% 0.15/0.47 % SZS status Theorem
% 0.15/0.47 % SZS output start CNFRefutation
% See solution above
% 0.15/0.47 % Parsed axioms : 58
% 0.15/0.47 % Removed by relevancy pruning/SinE : 0
% 0.15/0.47 % Initial clauses : 69
% 0.15/0.47 % Removed in clause preprocessing : 4
% 0.15/0.47 % Initial clauses in saturation : 65
% 0.15/0.47 % Processed clauses : 655
% 0.15/0.47 % ...of these trivial : 21
% 0.15/0.47 % ...subsumed : 384
% 0.15/0.47 % ...remaining for further processing : 250
% 0.15/0.47 % Other redundant clauses eliminated : 41
% 0.15/0.47 % Clauses deleted for lack of memory : 0
% 0.15/0.47 % Backward-subsumed : 6
% 0.15/0.47 % Backward-rewritten : 14
% 0.15/0.47 % Generated clauses : 2604
% 0.15/0.47 % ...of the previous two non-redundant : 2418
% 0.15/0.47 % ...aggressively subsumed : 0
% 0.15/0.47 % Contextual simplify-reflections : 0
% 0.15/0.47 % Paramodulations : 2561
% 0.15/0.47 % Factorizations : 0
% 0.15/0.47 % NegExts : 0
% 0.15/0.47 % Equation resolutions : 43
% 0.15/0.47 % Disequality decompositions : 0
% 0.15/0.47 % Total rewrite steps : 791
% 0.15/0.47 % ...of those cached : 551
% 0.15/0.47 % Propositional unsat checks : 0
% 0.15/0.47 % Propositional check models : 0
% 0.15/0.47 % Propositional check unsatisfiable : 0
% 0.15/0.47 % Propositional clauses : 0
% 0.15/0.47 % Propositional clauses after purity: 0
% 0.15/0.47 % Propositional unsat core size : 0
% 0.15/0.47 % Propositional preprocessing time : 0.000
% 0.15/0.47 % Propositional encoding time : 0.000
% 0.15/0.47 % Propositional solver time : 0.000
% 0.15/0.47 % Success case prop preproc time : 0.000
% 0.15/0.47 % Success case prop encoding time : 0.000
% 0.15/0.47 % Success case prop solver time : 0.000
% 0.15/0.47 % Current number of processed clauses : 174
% 0.15/0.47 % Positive orientable unit clauses : 30
% 0.15/0.47 % Positive unorientable unit clauses: 9
% 0.15/0.47 % Negative unit clauses : 79
% 0.15/0.47 % Non-unit-clauses : 56
% 0.15/0.47 % Current number of unprocessed clauses: 1800
% 0.15/0.47 % ...number of literals in the above : 2699
% 0.15/0.47 % Current number of archived formulas : 0
% 0.15/0.47 % Current number of archived clauses : 68
% 0.15/0.47 % Clause-clause subsumption calls (NU) : 676
% 0.15/0.47 % Rec. Clause-clause subsumption calls : 642
% 0.15/0.47 % Non-unit clause-clause subsumptions : 46
% 0.15/0.47 % Unit Clause-clause subsumption calls : 850
% 0.15/0.47 % Rewrite failures with RHS unbound : 0
% 0.15/0.47 % BW rewrite match attempts : 253
% 0.15/0.47 % BW rewrite match successes : 147
% 0.15/0.47 % Condensation attempts : 0
% 0.15/0.47 % Condensation successes : 0
% 0.15/0.47 % Termbank termtop insertions : 26415
% 0.15/0.47 % Search garbage collected termcells : 752
% 0.15/0.47
% 0.15/0.47 % -------------------------------------------------
% 0.15/0.47 % User time : 0.047 s
% 0.15/0.47 % System time : 0.006 s
% 0.15/0.47 % Total time : 0.054 s
% 0.15/0.47 % Maximum resident set size: 3724 pages
% 0.15/0.47
% 0.15/0.47 % -------------------------------------------------
% 0.15/0.47 % User time : 0.215 s
% 0.15/0.47 % System time : 0.024 s
% 0.15/0.47 % Total time : 0.239 s
% 0.15/0.47 % Maximum resident set size: 4608 pages
% 0.15/0.47 % E exiting
%------------------------------------------------------------------------------