%------------------------------------------------------------------------------
% File : E---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 : 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 01:50:49 PM UTC 2026
% Result : Theorem 0.11s 0.46s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 24 unt; 0 def)
% Number of atoms : 48 ( 47 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 21 ( 9 ~; 4 |; 5 &)
% ( 0 <=>; 3 =>; 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 : 46 ( 0 sgn 24 !; 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)), 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('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(conseq(263), 1), 7)',axiom,
! [X2] :
( vmul(vsucc(vd411),X2) = vplus(vmul(vd411,X2),X2)
=> vmul(vsucc(vd411),vsucc(X2)) = vplus(vmul(vsucc(vd411),X2),vsucc(vd411)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 7)') ).
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('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_7,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_8,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)))']) ).
fof(c_0_9,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_10,plain,
! [X94] :
( vmul(vsucc(vd411),vsucc(X94)) = vplus(vmul(vsucc(vd411),X94),vsucc(vd411))
| vmul(vsucc(vd411),X94) != vplus(vmul(vd411,X94),X94) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(263), 1), 7)'])])]) ).
fof(c_0_11,plain,
! [X199] : vplus(v1,X199) = vsucc(X199),
inference(variable_rename,[status(thm)],['ass(cond(43, 0), 0)']) ).
fof(c_0_12,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_7])])])]) ).
cnf(c_0_13,plain,
vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_14,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
fof(c_0_15,plain,
! [X195,X196] : vplus(X196,X195) = vplus(X195,X196),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
cnf(c_0_16,plain,
( vmul(vsucc(vd411),X1) != vplus(vmul(vd411,X1),X1)
| vmul(vsucc(vd411),vsucc(X1)) = vplus(vmul(vsucc(vd411),X1),vsucc(vd411)) ),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,plain,
vplus(v1,X1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_18,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_19,negated_conjecture,
vmul(vsucc(vd411),esk1_0) = vplus(vmul(vd411,esk1_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_20,negated_conjecture,
vmul(vsucc(vd411),vsucc(esk1_0)) != vplus(vmul(vd411,vsucc(esk1_0)),vsucc(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_21,plain,
vmul(X1,vplus(X2,v1)) = vplus(vmul(X1,X2),X1),
inference(rw,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_22,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_23,plain,
( vmul(vplus(vd411,v1),X1) != vplus(vmul(vd411,X1),X1)
| vmul(vplus(vd411,v1),vplus(X1,v1)) = vplus(vmul(vplus(vd411,v1),X1),vplus(vd411,v1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_14]),c_0_14]),c_0_14]),c_0_14]),c_0_14]) ).
cnf(c_0_24,plain,
vplus(v1,X1) = vplus(X1,v1),
inference(rw,[status(thm)],[c_0_17,c_0_14]) ).
cnf(c_0_25,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,negated_conjecture,
vplus(vmul(vd411,esk1_0),esk1_0) = vmul(vplus(vd411,v1),esk1_0),
inference(rw,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_27,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_20,c_0_14]),c_0_14]),c_0_14]),c_0_14]) ).
cnf(c_0_28,plain,
vmul(X1,vplus(X2,v1)) = vplus(X1,vmul(X1,X2)),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_29,plain,
( vmul(vplus(v1,vd411),X1) != vplus(X1,vmul(vd411,X1))
| vplus(v1,vplus(vd411,vmul(vplus(v1,vd411),X1))) = vmul(vplus(v1,vd411),vplus(X1,v1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_24]),c_0_24]),c_0_22]),c_0_25]),c_0_24]),c_0_24]),c_0_22]) ).
cnf(c_0_30,negated_conjecture,
vmul(vplus(v1,vd411),esk1_0) = vplus(esk1_0,vmul(vd411,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_24]),c_0_22]) ).
cnf(c_0_31,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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_27,c_0_24]),c_0_24]),c_0_24]),c_0_24]),c_0_22]),c_0_25]) ).
cnf(c_0_32,plain,
vmul(X1,vplus(v1,X2)) = vplus(X1,vmul(X1,X2)),
inference(spm,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_33,plain,
vplus(X1,vplus(X2,X3)) = vplus(X3,vplus(X1,X2)),
inference(spm,[status(thm)],[c_0_22,c_0_25]) ).
cnf(c_0_34,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(spm,[status(thm)],[c_0_29,c_0_30]),c_0_24]) ).
cnf(c_0_35,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_31,c_0_32]),c_0_33]),c_0_22]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM845+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.36 % Computer : n011.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 03:12:55 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.46 % Version: 3.5.1
% 0.11/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.46 % Starting new_bool_3 with 300s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 300s (1) cores
% 0.11/0.46 % Starting sh5l with 300s (1) cores
% 0.11/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 837329 completed with status 0
% 0.11/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.11/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.46 % No SInE strategy applied
% 0.11/0.46 % Search class: FGHSM-FFMS21-MFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.11/0.46 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 0.11/0.46 % Starting new_bool_3 with 136s (1) cores
% 0.11/0.46 % Starting new_bool_1 with 136s (1) cores
% 0.11/0.46 % G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with pid 837337 completed with status 0
% 0.11/0.46 % Result found by G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S
% 0.11/0.46 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.11/0.46 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.11/0.46 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.11/0.46 % No SInE strategy applied
% 0.11/0.46 % Search class: FGHSM-FFMS21-MFFFFFNN
% 0.11/0.46 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.11/0.46 % Starting SubtermCWHack with 136s (1) cores
% 0.11/0.46 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 151s (1) cores
% 0.11/0.46 % Preprocessing time : 0.001 s
% 0.11/0.46 % Presaturation interreduction done
% 0.11/0.46
% 0.11/0.46 % Proof found!
% 0.11/0.46 % SZS status Theorem
% 0.11/0.46 % SZS output start CNFRefutation
% See solution above
% 0.11/0.46 % Parsed axioms : 58
% 0.11/0.46 % Removed by relevancy pruning/SinE : 0
% 0.11/0.46 % Initial clauses : 69
% 0.11/0.46 % Removed in clause preprocessing : 4
% 0.11/0.46 % Initial clauses in saturation : 65
% 0.11/0.46 % Processed clauses : 578
% 0.11/0.46 % ...of these trivial : 19
% 0.11/0.46 % ...subsumed : 319
% 0.11/0.46 % ...remaining for further processing : 240
% 0.11/0.46 % Other redundant clauses eliminated : 47
% 0.11/0.46 % Clauses deleted for lack of memory : 0
% 0.11/0.46 % Backward-subsumed : 6
% 0.11/0.46 % Backward-rewritten : 11
% 0.11/0.46 % Generated clauses : 2515
% 0.11/0.46 % ...of the previous two non-redundant : 2321
% 0.11/0.46 % ...aggressively subsumed : 0
% 0.11/0.46 % Contextual simplify-reflections : 0
% 0.11/0.46 % Paramodulations : 2464
% 0.11/0.46 % Factorizations : 0
% 0.11/0.46 % NegExts : 0
% 0.11/0.46 % Equation resolutions : 51
% 0.11/0.46 % Disequality decompositions : 0
% 0.11/0.46 % Total rewrite steps : 758
% 0.11/0.46 % ...of those cached : 502
% 0.11/0.46 % Propositional unsat checks : 0
% 0.11/0.46 % Propositional check models : 0
% 0.11/0.46 % Propositional check unsatisfiable : 0
% 0.11/0.46 % Propositional clauses : 0
% 0.11/0.46 % Propositional clauses after purity: 0
% 0.11/0.46 % Propositional unsat core size : 0
% 0.11/0.46 % Propositional preprocessing time : 0.000
% 0.11/0.46 % Propositional encoding time : 0.000
% 0.11/0.46 % Propositional solver time : 0.000
% 0.11/0.46 % Success case prop preproc time : 0.000
% 0.11/0.46 % Success case prop encoding time : 0.000
% 0.11/0.46 % Success case prop solver time : 0.000
% 0.11/0.46 % Current number of processed clauses : 167
% 0.11/0.46 % Positive orientable unit clauses : 28
% 0.11/0.46 % Positive unorientable unit clauses: 9
% 0.11/0.46 % Negative unit clauses : 73
% 0.11/0.46 % Non-unit-clauses : 57
% 0.11/0.46 % Current number of unprocessed clauses: 1777
% 0.11/0.46 % ...number of literals in the above : 2749
% 0.11/0.46 % Current number of archived formulas : 0
% 0.11/0.46 % Current number of archived clauses : 65
% 0.11/0.46 % Clause-clause subsumption calls (NU) : 645
% 0.11/0.46 % Rec. Clause-clause subsumption calls : 621
% 0.11/0.46 % Non-unit clause-clause subsumptions : 53
% 0.11/0.46 % Unit Clause-clause subsumption calls : 825
% 0.11/0.46 % Rewrite failures with RHS unbound : 0
% 0.11/0.46 % BW rewrite match attempts : 263
% 0.11/0.46 % BW rewrite match successes : 125
% 0.11/0.46 % Condensation attempts : 0
% 0.11/0.46 % Condensation successes : 0
% 0.11/0.46 % Termbank termtop insertions : 26204
% 0.11/0.46 % Search garbage collected termcells : 752
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.026 s
% 0.11/0.46 % System time : 0.007 s
% 0.11/0.46 % Total time : 0.033 s
% 0.11/0.46 % Maximum resident set size: 3416 pages
% 0.11/0.46
% 0.11/0.46 % -------------------------------------------------
% 0.11/0.46 % User time : 0.110 s
% 0.11/0.46 % System time : 0.023 s
% 0.11/0.46 % Total time : 0.133 s
% 0.11/0.46 % Maximum resident set size: 4608 pages
% 0.11/0.46 % E exiting
%------------------------------------------------------------------------------