%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM845+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/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 0.08s 0.43s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 38 ( 26 unt; 0 def)
% Number of atoms : 50 ( 49 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 23 ( 11 ~; 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/sandbox2/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,
! [X11,X12] :
( vplus(X11,v1) = vsucc(X11)
& vplus(X11,vsucc(X12)) = vsucc(vplus(X11,X12)) ),
file('/export/starexec/sandbox2/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,
! [X7] : vplus(v1,X7) = vsucc(X7),
file('/export/starexec/sandbox2/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,
! [X3,X4] :
( vmul(X3,v1) = X3
& vmul(X3,vsucc(X4)) = vplus(vmul(X3,X4),X3) ),
file('/export/starexec/sandbox2/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,
! [X5,X6] : vplus(X6,X5) = vplus(X5,X6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 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/sandbox2/benchmark/theBenchmark.p','ass(cond(conseq(263), 1), 7)') ).
fof('ass(cond(33, 0), 0)',axiom,
! [X8,X9,X10] : vplus(vplus(X8,X9),X10) = vplus(X8,vplus(X9,X10)),
file('/export/starexec/sandbox2/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,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])])])]) ).
fof(c_0_9,plain,
! [X30,X31] :
( vplus(X30,v1) = vsucc(X30)
& vplus(X30,vsucc(X31)) = vsucc(vplus(X30,X31)) ),
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,
! [X26] : vplus(v1,X26) = vsucc(X26),
inference(variable_rename,[status(thm)],['ass(cond(43, 0), 0)']) ).
fof(c_0_11,plain,
! [X22,X23] :
( vmul(X22,v1) = X22
& vmul(X22,vsucc(X23)) = vplus(vmul(X22,X23),X22) ),
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_12,negated_conjecture,
vmul(vsucc(vd411),vsucc(esk1_0)) != vplus(vmul(vd411,vsucc(esk1_0)),vsucc(esk1_0)),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_13,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_14,plain,
vplus(v1,X1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_15,plain,
vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
fof(c_0_16,plain,
! [X24,X25] : vplus(X25,X24) = vplus(X24,X25),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_17,plain,
! [X21] :
( vmul(vsucc(vd411),vsucc(X21)) = vplus(vmul(vsucc(vd411),X21),vsucc(vd411))
| vmul(vsucc(vd411),X21) != vplus(vmul(vd411,X21),X21) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(263), 1), 7)'])])]) ).
cnf(c_0_18,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_12,c_0_13]),c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_19,plain,
vplus(v1,X1) = vplus(X1,v1),
inference(rw,[status(thm)],[c_0_14,c_0_13]) ).
fof(c_0_20,plain,
! [X27,X28,X29] : vplus(vplus(X27,X28),X29) = vplus(X27,vplus(X28,X29)),
inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).
cnf(c_0_21,plain,
vmul(X1,vplus(X2,v1)) = vplus(vmul(X1,X2),X1),
inference(rw,[status(thm)],[c_0_15,c_0_13]) ).
cnf(c_0_22,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_16]) ).
cnf(c_0_23,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_17]) ).
cnf(c_0_24,negated_conjecture,
vmul(vsucc(vd411),esk1_0) = vplus(vmul(vd411,esk1_0),esk1_0),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_25,negated_conjecture,
vplus(vmul(vd411,vplus(v1,esk1_0)),vplus(v1,esk1_0)) != vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_19]),c_0_19]),c_0_19]) ).
cnf(c_0_26,plain,
vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
cnf(c_0_27,plain,
vmul(X1,vplus(X2,v1)) = vplus(X1,vmul(X1,X2)),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_28,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_23,c_0_13]),c_0_13]),c_0_13]),c_0_13]),c_0_13]) ).
cnf(c_0_29,negated_conjecture,
vplus(vmul(vd411,esk1_0),esk1_0) = vmul(vplus(vd411,v1),esk1_0),
inference(rw,[status(thm)],[c_0_24,c_0_13]) ).
cnf(c_0_30,negated_conjecture,
vplus(v1,vplus(esk1_0,vmul(vd411,vplus(v1,esk1_0)))) != vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_25,c_0_22]),c_0_26]) ).
cnf(c_0_31,plain,
vmul(X1,vplus(v1,X2)) = vplus(X1,vmul(X1,X2)),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_32,plain,
( vmul(vplus(vd411,v1),X1) != vplus(X1,vmul(vd411,X1))
| vplus(vd411,vplus(v1,vmul(vplus(vd411,v1),X1))) = vmul(vplus(vd411,v1),vplus(X1,v1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_22]),c_0_26]),c_0_22]) ).
cnf(c_0_33,negated_conjecture,
vmul(vplus(vd411,v1),esk1_0) = vplus(esk1_0,vmul(vd411,esk1_0)),
inference(rw,[status(thm)],[c_0_29,c_0_22]) ).
cnf(c_0_34,negated_conjecture,
vplus(v1,vplus(esk1_0,vplus(vd411,vmul(vd411,esk1_0)))) != vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_35,plain,
vplus(X1,vplus(X2,X3)) = vplus(X2,vplus(X3,X1)),
inference(spm,[status(thm)],[c_0_22,c_0_26]) ).
cnf(c_0_36,negated_conjecture,
vplus(vd411,vplus(v1,vplus(esk1_0,vmul(vd411,esk1_0)))) = vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_19]) ).
cnf(c_0_37,negated_conjecture,
$false,
inference(cn,[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)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35]),c_0_22]),c_0_35]),c_0_26]),c_0_22]),c_0_35]),c_0_22]),c_0_36])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM845+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.04 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.36 % Computer : n011.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 03:12:55 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.41 Running first-order theorem proving
% 0.08/0.41 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
% 0.08/0.43 % Version: 3.5.1
% 0.08/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.08/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.08/0.43 % Starting new_bool_3 with 300s (1) cores
% 0.08/0.43 % Starting new_bool_1 with 300s (1) cores
% 0.08/0.43 % Starting sh5l with 300s (1) cores
% 0.08/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 837357 completed with status 0
% 0.08/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.08/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.08/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.08/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.43 % No SInE strategy applied
% 0.08/0.43 % Search class: FHUPM-FFMF22-MFFFFFNN
% 0.08/0.43 % partial match(1): FHUPM-FFSF22-MFFFFFNN
% 0.08/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.08/0.43 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 0.08/0.43 % Starting U----_210g_05_C07_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.08/0.43 % Starting new_bool_3 with 136s (1) cores
% 0.08/0.43 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 837363 completed with status 0
% 0.08/0.43 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 0.08/0.43 % Preprocessing class: FSMSSMSSSSSNFFN.
% 0.08/0.43 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.08/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 0.08/0.43 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.08/0.43 % No SInE strategy applied
% 0.08/0.43 % Search class: FHUPM-FFMF22-MFFFFFNN
% 0.08/0.43 % partial match(1): FHUPM-FFSF22-MFFFFFNN
% 0.08/0.43 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.08/0.43 % Starting SubtermCWHack with 136s (1) cores
% 0.08/0.43 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 0.08/0.43 % Preprocessing time : 0.001 s
% 0.08/0.43 % Presaturation interreduction done
% 0.08/0.43
% 0.08/0.43 % Proof found!
% 0.08/0.43 % SZS status Theorem
% 0.08/0.43 % SZS output start CNFRefutation
% See solution above
% 0.08/0.43 % Parsed axioms : 15
% 0.08/0.43 % Removed by relevancy pruning/SinE : 0
% 0.08/0.43 % Initial clauses : 18
% 0.08/0.43 % Removed in clause preprocessing : 3
% 0.08/0.43 % Initial clauses in saturation : 15
% 0.08/0.43 % Processed clauses : 39
% 0.08/0.43 % ...of these trivial : 8
% 0.08/0.43 % ...subsumed : 4
% 0.08/0.43 % ...remaining for further processing : 27
% 0.08/0.43 % Other redundant clauses eliminated : 0
% 0.08/0.43 % Clauses deleted for lack of memory : 0
% 0.08/0.43 % Backward-subsumed : 1
% 0.08/0.43 % Backward-rewritten : 7
% 0.08/0.43 % Generated clauses : 91
% 0.08/0.43 % ...of the previous two non-redundant : 49
% 0.08/0.43 % ...aggressively subsumed : 0
% 0.08/0.43 % Contextual simplify-reflections : 0
% 0.08/0.43 % Paramodulations : 91
% 0.08/0.43 % Factorizations : 0
% 0.08/0.43 % NegExts : 0
% 0.08/0.43 % Equation resolutions : 0
% 0.08/0.43 % Disequality decompositions : 0
% 0.08/0.43 % Total rewrite steps : 136
% 0.08/0.43 % ...of those cached : 61
% 0.08/0.43 % Propositional unsat checks : 0
% 0.08/0.43 % Propositional check models : 0
% 0.08/0.43 % Propositional check unsatisfiable : 0
% 0.08/0.43 % Propositional clauses : 0
% 0.08/0.43 % Propositional clauses after purity: 0
% 0.08/0.43 % Propositional unsat core size : 0
% 0.08/0.43 % Propositional preprocessing time : 0.000
% 0.08/0.43 % Propositional encoding time : 0.000
% 0.08/0.43 % Propositional solver time : 0.000
% 0.08/0.43 % Success case prop preproc time : 0.000
% 0.08/0.43 % Success case prop encoding time : 0.000
% 0.08/0.43 % Success case prop solver time : 0.000
% 0.08/0.43 % Current number of processed clauses : 12
% 0.08/0.43 % Positive orientable unit clauses : 5
% 0.08/0.43 % Positive unorientable unit clauses: 5
% 0.08/0.43 % Negative unit clauses : 1
% 0.08/0.43 % Non-unit-clauses : 1
% 0.08/0.43 % Current number of unprocessed clauses: 29
% 0.08/0.43 % ...number of literals in the above : 32
% 0.08/0.43 % Current number of archived formulas : 0
% 0.08/0.43 % Current number of archived clauses : 16
% 0.08/0.43 % Clause-clause subsumption calls (NU) : 0
% 0.08/0.43 % Rec. Clause-clause subsumption calls : 0
% 0.08/0.43 % Non-unit clause-clause subsumptions : 0
% 0.08/0.43 % Unit Clause-clause subsumption calls : 18
% 0.08/0.43 % Rewrite failures with RHS unbound : 0
% 0.08/0.43 % BW rewrite match attempts : 89
% 0.08/0.43 % BW rewrite match successes : 51
% 0.08/0.43 % Condensation attempts : 0
% 0.08/0.43 % Condensation successes : 0
% 0.08/0.43 % Termbank termtop insertions : 2893
% 0.08/0.43 % Search garbage collected termcells : 89
% 0.08/0.43
% 0.08/0.43 % -------------------------------------------------
% 0.08/0.43 % User time : 0.006 s
% 0.08/0.43 % System time : 0.002 s
% 0.08/0.43 % Total time : 0.008 s
% 0.08/0.43 % Maximum resident set size: 3644 pages
% 0.08/0.43
% 0.08/0.43 % -------------------------------------------------
% 0.08/0.43 % User time : 0.015 s
% 0.08/0.43 % System time : 0.011 s
% 0.08/0.43 % Total time : 0.026 s
% 0.08/0.43 % Maximum resident set size: 4864 pages
% 0.08/0.43 % E exiting
%------------------------------------------------------------------------------