%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM848+1 : 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 : 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 01:50:50 PM UTC 2026
% Result : Theorem 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 21 ( 17 unt; 0 def)
% Number of atoms : 25 ( 24 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 8 ( 4 ~; 0 |; 4 &)
% ( 0 <=>; 0 =>; 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 : 19 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof('holds(286, 441, 4)',conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) = vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 4)') ).
fof('ass(cond(61, 0), 0)',axiom,
! [X71,X72] : vplus(X72,X71) = vplus(X71,X72),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).
fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
! [X6,X7] :
( vmul(X6,v1) = X6
& vmul(X6,vsucc(X7)) = vplus(vmul(X6,X7),X6) ),
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('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
! [X79,X80] :
( vplus(X79,v1) = vsucc(X79)
& vplus(X79,vsucc(X80)) = vsucc(vplus(X79,X80)) ),
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('holds(286, 441, 3)',axiom,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(286, 441, 3)') ).
fof('holds(285, 440, 0)',axiom,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(285, 440, 0)') ).
fof(c_0_6,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(assume_negation,[status(cth)],['holds(286, 441, 4)']) ).
fof(c_0_7,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(fof_simplification,[status(thm)],[c_0_6]) ).
fof(c_0_8,plain,
! [X113,X114] : vplus(X114,X113) = vplus(X113,X114),
inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).
fof(c_0_9,plain,
! [X123,X124] :
( vmul(X123,v1) = X123
& vmul(X123,vsucc(X124)) = vplus(vmul(X123,X124),X123) ),
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_10,plain,
! [X128,X129] :
( vplus(X128,v1) = vsucc(X128)
& vplus(X128,vsucc(X129)) = vsucc(vplus(X128,X129)) ),
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_11,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(fof_nnf,[status(thm)],[c_0_7]) ).
cnf(c_0_12,plain,
vplus(vplus(vmul(vd436,vd437),vmul(vd436,vd439)),vd436) = vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)),
inference(split_conjunct,[status(thm)],['holds(286, 441, 3)']) ).
cnf(c_0_13,plain,
vmul(vd436,vplus(vd437,vd439)) = vplus(vmul(vd436,vd437),vmul(vd436,vd439)),
inference(split_conjunct,[status(thm)],['holds(285, 440, 0)']) ).
cnf(c_0_14,plain,
vplus(X1,X2) = vplus(X2,X1),
inference(split_conjunct,[status(thm)],[c_0_8]) ).
cnf(c_0_15,plain,
vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1),
inference(split_conjunct,[status(thm)],[c_0_9]) ).
cnf(c_0_16,plain,
vplus(X1,v1) = vsucc(X1),
inference(split_conjunct,[status(thm)],[c_0_10]) ).
cnf(c_0_17,negated_conjecture,
vplus(vmul(vd436,vd437),vplus(vmul(vd436,vd439),vd436)) != vplus(vmul(vd436,vd437),vmul(vd436,vsucc(vd439))),
inference(split_conjunct,[status(thm)],[c_0_11]) ).
cnf(c_0_18,plain,
vplus(vmul(vd436,vd437),vplus(vd436,vmul(vd436,vd439))) = vplus(vd436,vmul(vd436,vplus(vd437,vd439))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_12,c_0_13]),c_0_14]),c_0_14]) ).
cnf(c_0_19,plain,
vmul(X1,vplus(X2,v1)) = vplus(X1,vmul(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_15,c_0_16]),c_0_14]) ).
cnf(c_0_20,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)],[c_0_17,c_0_14]),c_0_18]),c_0_16]),c_0_19]),c_0_18])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM848+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.35 % Computer : n015.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 03:16:20 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.41 % Version: 3.5.1
% 0.13/0.41 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.41 % Starting new_bool_1 with 300s (1) cores
% 0.13/0.41 % Starting sh5l with 300s (1) cores
% 0.13/0.41 % new_bool_3 with pid 433086 completed with status 0
% 0.13/0.41 % Result found by new_bool_3
% 0.13/0.41 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.41 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.41 % Search class: FGHPM-FFMM21-MFFFFFNN
% 0.13/0.41 % partial match(1): FGHSM-FFMM21-MFFFFFNN
% 0.13/0.41 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.41 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.41 % SubtermCWHack with pid 433089 completed with status 0
% 0.13/0.41 % Result found by SubtermCWHack
% 0.13/0.41 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.13/0.41 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.13/0.41 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.13/0.41 % Starting new_bool_3 with 300s (1) cores
% 0.13/0.41 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.13/0.41 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.13/0.41 % Search class: FGHPM-FFMM21-MFFFFFNN
% 0.13/0.41 % partial match(1): FGHSM-FFMM21-MFFFFFNN
% 0.13/0.41 % Scheduled 5 strats onto 1 cores with 300 seconds (300 total)
% 0.13/0.41 % Starting SubtermCWHack with 31s (1) cores
% 0.13/0.41 % Preprocessing time : 0.002 s
% 0.13/0.41
% 0.13/0.41 % Proof found!
% 0.13/0.41 % SZS status Theorem
% 0.13/0.41 % SZS output start CNFRefutation
% See solution above
% 0.13/0.41 % Parsed axioms : 57
% 0.13/0.41 % Removed by relevancy pruning/SinE : 27
% 0.13/0.41 % Initial clauses : 32
% 0.13/0.41 % Removed in clause preprocessing : 1
% 0.13/0.41 % Initial clauses in saturation : 31
% 0.13/0.41 % Processed clauses : 154
% 0.13/0.41 % ...of these trivial : 10
% 0.13/0.41 % ...subsumed : 88
% 0.13/0.41 % ...remaining for further processing : 55
% 0.13/0.41 % Other redundant clauses eliminated : 13
% 0.13/0.41 % Clauses deleted for lack of memory : 0
% 0.13/0.41 % Backward-subsumed : 4
% 0.13/0.41 % Backward-rewritten : 5
% 0.13/0.41 % Generated clauses : 483
% 0.13/0.41 % ...of the previous two non-redundant : 461
% 0.13/0.41 % ...aggressively subsumed : 0
% 0.13/0.41 % Contextual simplify-reflections : 0
% 0.13/0.41 % Paramodulations : 467
% 0.13/0.41 % Factorizations : 0
% 0.13/0.41 % NegExts : 0
% 0.13/0.41 % Equation resolutions : 16
% 0.13/0.41 % Disequality decompositions : 0
% 0.13/0.41 % Total rewrite steps : 136
% 0.13/0.41 % ...of those cached : 76
% 0.13/0.41 % Propositional unsat checks : 0
% 0.13/0.41 % Propositional check models : 0
% 0.13/0.41 % Propositional check unsatisfiable : 0
% 0.13/0.41 % Propositional clauses : 0
% 0.13/0.41 % Propositional clauses after purity: 0
% 0.13/0.41 % Propositional unsat core size : 0
% 0.13/0.41 % Propositional preprocessing time : 0.000
% 0.13/0.41 % Propositional encoding time : 0.000
% 0.13/0.41 % Propositional solver time : 0.000
% 0.13/0.41 % Success case prop preproc time : 0.000
% 0.13/0.41 % Success case prop encoding time : 0.000
% 0.13/0.41 % Success case prop solver time : 0.000
% 0.13/0.41 % Current number of processed clauses : 43
% 0.13/0.41 % Positive orientable unit clauses : 11
% 0.13/0.41 % Positive unorientable unit clauses: 6
% 0.13/0.41 % Negative unit clauses : 23
% 0.13/0.41 % Non-unit-clauses : 3
% 0.13/0.41 % Current number of unprocessed clauses: 330
% 0.13/0.41 % ...number of literals in the above : 438
% 0.13/0.41 % Current number of archived formulas : 0
% 0.13/0.41 % Current number of archived clauses : 9
% 0.13/0.41 % Clause-clause subsumption calls (NU) : 5
% 0.13/0.41 % Rec. Clause-clause subsumption calls : 4
% 0.13/0.41 % Non-unit clause-clause subsumptions : 2
% 0.13/0.41 % Unit Clause-clause subsumption calls : 63
% 0.13/0.41 % Rewrite failures with RHS unbound : 0
% 0.13/0.41 % BW rewrite match attempts : 61
% 0.13/0.41 % BW rewrite match successes : 19
% 0.13/0.41 % Condensation attempts : 0
% 0.13/0.41 % Condensation successes : 0
% 0.13/0.41 % Termbank termtop insertions : 4733
% 0.13/0.41 % Search garbage collected termcells : 403
% 0.13/0.41
% 0.13/0.41 % -------------------------------------------------
% 0.13/0.41 % User time : 0.012 s
% 0.13/0.41 % System time : 0.001 s
% 0.13/0.41 % Total time : 0.013 s
% 0.13/0.41 % Maximum resident set size: 3720 pages
% 0.13/0.41
% 0.13/0.41 % -------------------------------------------------
% 0.13/0.41 % User time : 0.015 s
% 0.13/0.41 % System time : 0.005 s
% 0.13/0.41 % Total time : 0.019 s
% 0.13/0.41 % Maximum resident set size: 4864 pages
% 0.13/0.41 % E exiting
%------------------------------------------------------------------------------