%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 01:51:03 PM UTC 2026
% Result : Theorem 0.10s 0.47s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 36 unt; 0 def)
% Number of atoms : 61 ( 41 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 10 |; 2 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 36 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_92_Bit1__def,axiom,
! [X19] : bit1(X19) = plus_plus(int,plus_plus(int,one_one(int),X19),X19),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_Bit1__def) ).
fof(fact_47_zadd__commute,axiom,
! [X15,X7] : plus_plus(int,X15,X7) = plus_plus(int,X7,X15),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_zadd__commute) ).
fof(conj_0,conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(fact_76_add__Pls,axiom,
! [X19] : plus_plus(int,pls,X19) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_add__Pls) ).
fof(fact_75_add__Pls__right,axiom,
! [X19] : plus_plus(int,X19,pls) = X19,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
fof(fact_43_rel__simps_I48_J,axiom,
! [X11,X12] :
( bit0(X11) = bit0(X12)
<=> X11 = X12 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_rel__simps_I48_J) ).
fof(tsy_c_Int_OBit0_arg1,hypothesis,
! [X2] : bit0(ti(int,X2)) = bit0(X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Int_OBit0_arg1) ).
fof(fact_95_zero__less__power2,axiom,
! [X1] :
( linordered_idom(X1)
=> ! [X6] :
( ord_less(X1,zero_zero(X1),power_power(X1,X6,number_number_of(nat,bit0(bit1(pls)))))
<=> ti(X1,X6) != zero_zero(X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_zero__less__power2) ).
fof(fact_32_rel__simps_I2_J,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rel__simps_I2_J) ).
fof(fact_73_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_Pls__def) ).
fof(fact_0_n1pos,axiom,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(arity_Int_Oint___Rings_Olinordered__idom,axiom,
linordered_idom(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
fof(c_0_12,plain,
! [X79] : bit1(X79) = plus_plus(int,plus_plus(int,one_one(int),X79),X79),
inference(variable_rename,[status(thm)],[fact_92_Bit1__def]) ).
fof(c_0_13,plain,
! [X116,X117] : plus_plus(int,X116,X117) = plus_plus(int,X117,X116),
inference(variable_rename,[status(thm)],[fact_47_zadd__commute]) ).
fof(c_0_14,negated_conjecture,
~ ( power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) != zero_zero(int) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_15,plain,
! [X83] : plus_plus(int,pls,X83) = X83,
inference(variable_rename,[status(thm)],[fact_76_add__Pls]) ).
cnf(c_0_16,plain,
bit1(X1) = plus_plus(int,plus_plus(int,one_one(int),X1),X1),
inference(split_conjunct,[status(thm)],[c_0_12]) ).
cnf(c_0_17,plain,
plus_plus(int,X1,X2) = plus_plus(int,X2,X1),
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X82] : plus_plus(int,X82,pls) = X82,
inference(variable_rename,[status(thm)],[fact_75_add__Pls__right]) ).
fof(c_0_19,plain,
! [X41,X42] :
( ( bit0(X41) = bit0(X42)
| X41 != X42 )
& ( X41 = X42
| bit0(X41) != bit0(X42) ) ),
inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[fact_43_rel__simps_I48_J])])]) ).
fof(c_0_20,hypothesis,
! [X33] : bit0(ti(int,X33)) = bit0(X33),
inference(variable_rename,[status(thm)],[tsy_c_Int_OBit0_arg1]) ).
fof(c_0_21,plain,
! [X1] :
( linordered_idom(X1)
=> ! [X6] :
( ord_less(X1,zero_zero(X1),power_power(X1,X6,number_number_of(nat,bit0(bit1(pls)))))
<=> ti(X1,X6) != zero_zero(X1) ) ),
inference(fof_simplification,[status(thm)],[fact_95_zero__less__power2]) ).
fof(c_0_22,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
cnf(c_0_23,plain,
plus_plus(int,pls,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_15]) ).
cnf(c_0_24,plain,
plus_plus(int,X1,plus_plus(int,one_one(int),X1)) = bit1(X1),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_25,plain,
plus_plus(int,X1,pls) = X1,
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_26,plain,
( bit0(X1) != bit0(X2)
| X1 = X2 ),
inference(split_conjunct,[status(thm)],[c_0_19]) ).
cnf(c_0_27,hypothesis,
bit0(ti(int,X1)) = bit0(X1),
inference(split_conjunct,[status(thm)],[c_0_20]) ).
fof(c_0_28,plain,
~ ord_less(int,pls,pls),
inference(fof_simplification,[status(thm)],[fact_32_rel__simps_I2_J]) ).
fof(c_0_29,plain,
! [X96,X97] :
( ( ~ linordered_idom(X96)
| ord_less(X96,zero_zero(X96),power_power(X96,X97,number_number_of(nat,bit0(bit1(pls)))))
| ti(X96,X97) = zero_zero(X96) )
& ( ~ linordered_idom(X96)
| ti(X96,X97) != zero_zero(X96)
| ~ ord_less(X96,zero_zero(X96),power_power(X96,X97,number_number_of(nat,bit0(bit1(pls))))) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_21])])])])]) ).
cnf(c_0_30,negated_conjecture,
power_power(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = zero_zero(int),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_31,plain,
one_one(int) = bit1(pls),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]) ).
cnf(c_0_32,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_73_Pls__def]) ).
cnf(c_0_33,hypothesis,
( bit0(X1) != bit0(X2)
| X1 = ti(int,X2) ),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
fof(c_0_34,plain,
~ ord_less(int,pls,pls),
inference(fof_nnf,[status(thm)],[c_0_28]) ).
cnf(c_0_35,plain,
ord_less(int,zero_zero(int),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_36,plain,
( ~ linordered_idom(X1)
| ord_less(X1,zero_zero(X1),power_power(X1,X2,number_number_of(nat,bit0(bit1(pls)))))
| ti(X1,X2) = zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_29]) ).
cnf(c_0_37,negated_conjecture,
power_power(int,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)),number_number_of(nat,bit0(bit1(pls)))) = pls,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_32]) ).
cnf(c_0_38,hypothesis,
ti(int,X1) = X1,
inference(er,[status(thm)],[c_0_33]) ).
cnf(c_0_39,plain,
linordered_idom(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Olinordered__idom]) ).
cnf(c_0_40,plain,
~ ord_less(int,pls,pls),
inference(split_conjunct,[status(thm)],[c_0_34]) ).
cnf(c_0_41,plain,
ord_less(int,pls,plus_plus(int,bit1(pls),semiring_1_of_nat(int,n))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_32]),c_0_31]) ).
cnf(c_0_42,negated_conjecture,
plus_plus(int,bit1(pls),semiring_1_of_nat(int,n)) = pls,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]),c_0_32]),c_0_32]),c_0_39])]),c_0_40]) ).
cnf(c_0_43,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.36 % Computer : n007.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 03:15:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.47 % Version: 3.5.1
% 0.10/0.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.47 % Starting new_bool_1 with 300s (1) cores
% 0.10/0.47 % Starting sh5l with 300s (1) cores
% 0.10/0.47 % new_bool_3 with pid 51296 completed with status 0
% 0.10/0.47 % Result found by new_bool_3
% 0.10/0.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.47 % Search class: FGHSM-FFLM31-MFFFFFNN
% 0.10/0.47 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.47 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.47 % SubtermCWHack with pid 51304 completed with status 0
% 0.10/0.47 % Result found by SubtermCWHack
% 0.10/0.47 % Preprocessing class: FSLSSMSSSSSNFFN.
% 0.10/0.47 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.10/0.47 % Starting G-E--_207_C18_F1_SE_CS_SP_PI_PS_S5PRR_S2S with 1500s (5) cores
% 0.10/0.47 % Starting new_bool_3 with 300s (1) cores
% 0.10/0.47 % (lift_lambdas = 0, lambda_to_forall = 0,unroll_only_formulas = 0, sine = GSinE(CountFormulas,hypos,1.5,,3,20000,1.0))
% 0.10/0.47 % SinE strategy is GSinE(CountFormulas,hypos,1.5,,3,20000,1.0)
% 0.10/0.47 % Search class: FGHSM-FFLM31-MFFFFFNN
% 0.10/0.47 % Scheduled 9 strats onto 1 cores with 300 seconds (300 total)
% 0.10/0.47 % Starting SubtermCWHack with 28s (1) cores
% 0.10/0.47 % Preprocessing time : 0.003 s
% 0.10/0.47
% 0.10/0.47 % Proof found!
% 0.10/0.47 % SZS status Theorem
% 0.10/0.47 % SZS output start CNFRefutation
% See solution above
% 0.10/0.47 % Parsed axioms : 153
% 0.10/0.47 % Removed by relevancy pruning/SinE : 43
% 0.10/0.47 % Initial clauses : 148
% 0.10/0.47 % Removed in clause preprocessing : 3
% 0.10/0.47 % Initial clauses in saturation : 145
% 0.10/0.47 % Processed clauses : 556
% 0.10/0.47 % ...of these trivial : 31
% 0.10/0.47 % ...subsumed : 299
% 0.10/0.47 % ...remaining for further processing : 226
% 0.10/0.47 % Other redundant clauses eliminated : 4
% 0.10/0.47 % Clauses deleted for lack of memory : 0
% 0.10/0.47 % Backward-subsumed : 0
% 0.10/0.47 % Backward-rewritten : 36
% 0.10/0.47 % Generated clauses : 1399
% 0.10/0.47 % ...of the previous two non-redundant : 1088
% 0.10/0.47 % ...aggressively subsumed : 0
% 0.10/0.47 % Contextual simplify-reflections : 0
% 0.10/0.47 % Paramodulations : 1385
% 0.10/0.47 % Factorizations : 4
% 0.10/0.47 % NegExts : 0
% 0.10/0.47 % Equation resolutions : 10
% 0.10/0.47 % Disequality decompositions : 0
% 0.10/0.47 % Total rewrite steps : 1492
% 0.10/0.47 % ...of those cached : 1377
% 0.10/0.47 % Propositional unsat checks : 0
% 0.10/0.47 % Propositional check models : 0
% 0.10/0.47 % Propositional check unsatisfiable : 0
% 0.10/0.47 % Propositional clauses : 0
% 0.10/0.47 % Propositional clauses after purity: 0
% 0.10/0.47 % Propositional unsat core size : 0
% 0.10/0.47 % Propositional preprocessing time : 0.000
% 0.10/0.47 % Propositional encoding time : 0.000
% 0.10/0.47 % Propositional solver time : 0.000
% 0.10/0.47 % Success case prop preproc time : 0.000
% 0.10/0.47 % Success case prop encoding time : 0.000
% 0.10/0.47 % Success case prop solver time : 0.000
% 0.10/0.47 % Current number of processed clauses : 186
% 0.10/0.47 % Positive orientable unit clauses : 48
% 0.10/0.47 % Positive unorientable unit clauses: 3
% 0.10/0.47 % Negative unit clauses : 29
% 0.10/0.47 % Non-unit-clauses : 106
% 0.10/0.47 % Current number of unprocessed clauses: 641
% 0.10/0.47 % ...number of literals in the above : 1270
% 0.10/0.47 % Current number of archived formulas : 0
% 0.10/0.47 % Current number of archived clauses : 36
% 0.10/0.47 % Clause-clause subsumption calls (NU) : 2666
% 0.10/0.47 % Rec. Clause-clause subsumption calls : 2508
% 0.10/0.47 % Non-unit clause-clause subsumptions : 147
% 0.10/0.47 % Unit Clause-clause subsumption calls : 1406
% 0.10/0.47 % Rewrite failures with RHS unbound : 0
% 0.10/0.47 % BW rewrite match attempts : 223
% 0.10/0.47 % BW rewrite match successes : 36
% 0.10/0.47 % Condensation attempts : 0
% 0.10/0.47 % Condensation successes : 0
% 0.10/0.47 % Termbank termtop insertions : 27361
% 0.10/0.47 % Search garbage collected termcells : 1366
% 0.10/0.47
% 0.10/0.47 % -------------------------------------------------
% 0.10/0.47 % User time : 0.030 s
% 0.10/0.47 % System time : 0.009 s
% 0.10/0.47 % Total time : 0.039 s
% 0.10/0.47 % Maximum resident set size: 4040 pages
% 0.10/0.47
% 0.10/0.47 % -------------------------------------------------
% 0.10/0.47 % User time : 0.034 s
% 0.10/0.47 % System time : 0.014 s
% 0.10/0.47 % Total time : 0.048 s
% 0.10/0.47 % Maximum resident set size: 4864 pages
% 0.10/0.47 % E exiting
%------------------------------------------------------------------------------