%------------------------------------------------------------------------------
% File : E-SAT---3.5.1
% Problem : NUM925+6 : TPTP v9.3.1. Released v5.3.0.
% 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 01:56:58 PM UTC 2026
% Result : Theorem 0.15s 5.63s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 13
% Syntax : Number of formulae : 42 ( 34 unt; 0 def)
% Number of atoms : 67 ( 39 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 49 ( 24 ~; 15 |; 2 &)
% ( 2 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-4 aty)
% Number of variables : 43 ( 1 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_119_number__of__is__id,axiom,
! [X20] : number_number_of(int,X20) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_119_number__of__is__id) ).
fof(conj_0,conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(fact_421_not__less__iff__gr__or__eq,axiom,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ( ti(X1,X5) = ti(X1,X6)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_421_not__less__iff__gr__or__eq) ).
fof(fact_37_one__is__num__one,axiom,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_one__is__num__one) ).
fof(tsy_c_hAPP_4_res,axiom,
! [X1,X2,X4] : ti(X1,hAPP(X1,X1,X2,X4)) = hAPP(X1,X1,X2,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_4_res) ).
fof(fact_75_add__Pls__right,axiom,
! [X20] : hAPP(int,int,plus_plus(int,X20),pls) = X20,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_add__Pls__right) ).
fof(fact_164_field__power__not__zero,axiom,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X15,X31] :
( ti(X1,X31) != zero_zero(X1)
=> hAPP(nat,X1,power_power(X1,X31),X15) != zero_zero(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_164_field__power__not__zero) ).
fof(fact_316_succ__Bit1,axiom,
! [X20] : hAPP(int,int,succ,hAPP(int,int,bit1,X20)) = hAPP(int,int,bit0,hAPP(int,int,succ,X20)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_316_succ__Bit1) ).
fof(fact_0_n1pos,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
fof(fact_73_Pls__def,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Pls__def) ).
fof(fact_314_succ__Pls,axiom,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_314_succ__Pls) ).
fof(arity_Int_Oint___Orderings_Olinorder,axiom,
linorder(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
fof(arity_Int_Oint___Rings_Oring__1__no__zero__divisors,axiom,
ring_11004092258visors(int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring__1__no__zero__divisors) ).
fof(c_0_13,plain,
! [X324] : number_number_of(int,X324) = X324,
inference(variable_rename,[status(thm)],[fact_119_number__of__is__id]) ).
fof(c_0_14,negated_conjecture,
~ ( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(c_0_15,plain,
! [X1] :
( linorder(X1)
=> ! [X5,X6] :
( ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X5),X6))
<=> ( ti(X1,X5) = ti(X1,X6)
| hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X6),X5)) ) ) ),
inference(fof_simplification,[status(thm)],[fact_421_not__less__iff__gr__or__eq]) ).
cnf(c_0_16,plain,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
inference(split_conjunct,[status(thm)],[fact_37_one__is__num__one]) ).
cnf(c_0_17,plain,
number_number_of(int,X1) = X1,
inference(split_conjunct,[status(thm)],[c_0_13]) ).
fof(c_0_18,plain,
! [X141,X142,X143] : ti(X141,hAPP(X141,X141,X142,X143)) = hAPP(X141,X141,X142,X143),
inference(variable_rename,[status(thm)],[tsy_c_hAPP_4_res]) ).
fof(c_0_19,plain,
! [X248] : hAPP(int,int,plus_plus(int,X248),pls) = X248,
inference(variable_rename,[status(thm)],[fact_75_add__Pls__right]) ).
fof(c_0_20,plain,
! [X1] :
( ring_11004092258visors(X1)
=> ! [X15,X31] :
( ti(X1,X31) != zero_zero(X1)
=> hAPP(nat,X1,power_power(X1,X31),X15) != zero_zero(X1) ) ),
inference(fof_simplification,[status(thm)],[fact_164_field__power__not__zero]) ).
fof(c_0_21,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(fof_simplification,[status(thm)],[c_0_14]) ).
fof(c_0_22,plain,
! [X820] : hAPP(int,int,succ,hAPP(int,int,bit1,X820)) = hAPP(int,int,bit0,hAPP(int,int,succ,X820)),
inference(variable_rename,[status(thm)],[fact_316_succ__Bit1]) ).
fof(c_0_23,plain,
! [X1109,X1110,X1111] :
( ( ~ linorder(X1109)
| ~ hBOOL(hAPP(X1109,bool,hAPP(X1109,fun(X1109,bool),ord_less(X1109),X1110),X1111))
| ti(X1109,X1110) != ti(X1109,X1111) )
& ( ~ linorder(X1109)
| ~ hBOOL(hAPP(X1109,bool,hAPP(X1109,fun(X1109,bool),ord_less(X1109),X1110),X1111))
| ~ hBOOL(hAPP(X1109,bool,hAPP(X1109,fun(X1109,bool),ord_less(X1109),X1111),X1110)) )
& ( ~ linorder(X1109)
| ti(X1109,X1110) = ti(X1109,X1111)
| hBOOL(hAPP(X1109,bool,hAPP(X1109,fun(X1109,bool),ord_less(X1109),X1111),X1110))
| hBOOL(hAPP(X1109,bool,hAPP(X1109,fun(X1109,bool),ord_less(X1109),X1110),X1111)) ) ),
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_15])])])])]) ).
cnf(c_0_24,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(split_conjunct,[status(thm)],[fact_0_n1pos]) ).
cnf(c_0_25,plain,
pls = zero_zero(int),
inference(split_conjunct,[status(thm)],[fact_73_Pls__def]) ).
cnf(c_0_26,plain,
one_one(int) = hAPP(int,int,bit1,pls),
inference(rw,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_27,plain,
hAPP(int,int,succ,pls) = hAPP(int,int,bit1,pls),
inference(split_conjunct,[status(thm)],[fact_314_succ__Pls]) ).
cnf(c_0_28,plain,
ti(X1,hAPP(X1,X1,X2,X3)) = hAPP(X1,X1,X2,X3),
inference(split_conjunct,[status(thm)],[c_0_18]) ).
cnf(c_0_29,plain,
hAPP(int,int,plus_plus(int,X1),pls) = X1,
inference(split_conjunct,[status(thm)],[c_0_19]) ).
fof(c_0_30,plain,
! [X420,X421,X422] :
( hAPP(nat,X420,power_power(X420,X422),X421) != zero_zero(X420)
| ti(X420,X422) = zero_zero(X420)
| ~ ring_11004092258visors(X420) ),
inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_20])])])]) ).
cnf(c_0_31,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(split_conjunct,[status(thm)],[c_0_21]) ).
cnf(c_0_32,plain,
hAPP(int,int,succ,hAPP(int,int,bit1,X1)) = hAPP(int,int,bit0,hAPP(int,int,succ,X1)),
inference(split_conjunct,[status(thm)],[c_0_22]) ).
cnf(c_0_33,plain,
( ~ linorder(X1)
| ~ hBOOL(hAPP(X1,bool,hAPP(X1,fun(X1,bool),ord_less(X1),X2),X3))
| ti(X1,X2) != ti(X1,X3) ),
inference(split_conjunct,[status(thm)],[c_0_23]) ).
cnf(c_0_34,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,hAPP(int,int,succ,pls)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_24,c_0_25]),c_0_26]),c_0_27]) ).
cnf(c_0_35,plain,
ti(int,X1) = X1,
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_36,plain,
linorder(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Orderings_Olinorder]) ).
cnf(c_0_37,plain,
( hAPP(nat,X1,power_power(X1,X2),X3) != zero_zero(X1)
| ~ ring_11004092258visors(X1)
| ti(X1,X2) = zero_zero(X1) ),
inference(split_conjunct,[status(thm)],[c_0_30]) ).
cnf(c_0_38,negated_conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,hAPP(int,int,succ,pls)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,succ,hAPP(int,int,succ,pls)))) = pls,
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_31,c_0_26]),c_0_27]),c_0_27]),c_0_32]),c_0_27]),c_0_25]) ).
cnf(c_0_39,plain,
ring_11004092258visors(int),
inference(split_conjunct,[status(thm)],[arity_Int_Oint___Rings_Oring__1__no__zero__divisors]) ).
cnf(c_0_40,plain,
hAPP(int,int,plus_plus(int,hAPP(int,int,succ,pls)),hAPP(nat,int,semiring_1_of_nat(int),n)) != pls,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_35]),c_0_28]),c_0_36])]) ).
cnf(c_0_41,negated_conjecture,
$false,
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_37,c_0_38]),c_0_28]),c_0_25]),c_0_25]),c_0_39])]),c_0_40]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM925+6 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/5.38 % Computer : n011.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Mon Sep 21 03:18:16 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/5.43 Running first-order theorem proving
% 0.15/5.43 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
% 0.15/5.63 % Version: 3.5.1
% 0.15/5.63 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.63 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.63 % Starting new_bool_3 with 300s (1) cores
% 0.15/5.63 % Starting new_bool_1 with 300s (1) cores
% 0.15/5.63 % Starting sh5l with 300s (1) cores
% 0.15/5.63 % C07_19_nc_SOS_SAT001_MinMin_p005000_rr with pid 850030 completed with status 0
% 0.15/5.63 % Result found by C07_19_nc_SOS_SAT001_MinMin_p005000_rr
% 0.15/5.63 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.63 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.63 % No SInE strategy applied
% 0.15/5.63 % Search class: FGHSM-FSLM33-DFFFFFNN
% 0.15/5.63 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.63 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.63 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.15/5.63 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/5.63 % Starting G-E--_302_C18_F1_URBAN_S5PRR_RG_S04BN with 136s (1) cores
% 0.15/5.63 % Starting G-E--_208_C09_12_F1_SE_CS_SP_PS_S070I with 136s (1) cores
% 0.15/5.63 % U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with pid 850039 completed with status 0
% 0.15/5.63 % Result found by U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN
% 0.15/5.63 % Preprocessing class: FSLSSMSMSSSNFFN.
% 0.15/5.63 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.15/5.63 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 1500s (5) cores
% 0.15/5.63 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.15/5.63 % No SInE strategy applied
% 0.15/5.63 % Search class: FGHSM-FSLM33-DFFFFFNN
% 0.15/5.63 % Scheduled 11 strats onto 5 cores with 1500 seconds (1500 total)
% 0.15/5.63 % Starting SubtermCWHack with 136s (1) cores
% 0.15/5.63 % Starting C07_19_nc_SOS_SAT001_MinMin_p005000_rr with 151s (1) cores
% 0.15/5.63 % Starting U----_206b_01_C11_23_F1_SE_PI_CS_SP_PS_S5PRR_RG_S04AN with 136s (1) cores
% 0.15/5.63 % Preprocessing time : 0.010 s
% 0.15/5.63 % Presaturation interreduction done
% 0.15/5.63
% 0.15/5.63 % Proof found!
% 0.15/5.63 % SZS status Theorem
% 0.15/5.63 % SZS output start CNFRefutation
% See solution above
% 0.15/5.63 % Parsed axioms : 660
% 0.15/5.63 % Removed by relevancy pruning/SinE : 0
% 0.15/5.63 % Initial clauses : 904
% 0.15/5.63 % Removed in clause preprocessing : 51
% 0.15/5.63 % Initial clauses in saturation : 853
% 0.15/5.63 % Processed clauses : 1529
% 0.15/5.63 % ...of these trivial : 23
% 0.15/5.63 % ...subsumed : 369
% 0.15/5.63 % ...remaining for further processing : 1137
% 0.15/5.63 % Other redundant clauses eliminated : 82
% 0.15/5.63 % Clauses deleted for lack of memory : 0
% 0.15/5.63 % Backward-subsumed : 14
% 0.15/5.63 % Backward-rewritten : 23
% 0.15/5.63 % Generated clauses : 1416
% 0.15/5.63 % ...of the previous two non-redundant : 1041
% 0.15/5.63 % ...aggressively subsumed : 0
% 0.15/5.63 % Contextual simplify-reflections : 2
% 0.15/5.63 % Paramodulations : 1330
% 0.15/5.63 % Factorizations : 1
% 0.15/5.63 % NegExts : 0
% 0.15/5.63 % Equation resolutions : 87
% 0.15/5.63 % Disequality decompositions : 0
% 0.15/5.63 % Total rewrite steps : 1981
% 0.15/5.63 % ...of those cached : 1707
% 0.15/5.63 % Propositional unsat checks : 0
% 0.15/5.63 % Propositional check models : 0
% 0.15/5.63 % Propositional check unsatisfiable : 0
% 0.15/5.63 % Propositional clauses : 0
% 0.15/5.63 % Propositional clauses after purity: 0
% 0.15/5.63 % Propositional unsat core size : 0
% 0.15/5.63 % Propositional preprocessing time : 0.000
% 0.15/5.63 % Propositional encoding time : 0.000
% 0.15/5.63 % Propositional solver time : 0.000
% 0.15/5.63 % Success case prop preproc time : 0.000
% 0.15/5.63 % Success case prop encoding time : 0.000
% 0.15/5.63 % Success case prop solver time : 0.000
% 0.15/5.63 % Current number of processed clauses : 390
% 0.15/5.63 % Positive orientable unit clauses : 193
% 0.15/5.63 % Positive unorientable unit clauses: 4
% 0.15/5.63 % Negative unit clauses : 55
% 0.15/5.63 % Non-unit-clauses : 138
% 0.15/5.63 % Current number of unprocessed clauses: 1033
% 0.15/5.63 % ...number of literals in the above : 2373
% 0.15/5.63 % Current number of archived formulas : 0
% 0.15/5.63 % Current number of archived clauses : 714
% 0.15/5.63 % Clause-clause subsumption calls (NU) : 49482
% 0.15/5.63 % Rec. Clause-clause subsumption calls : 25032
% 0.15/5.63 % Non-unit clause-clause subsumptions : 188
% 0.15/5.63 % Unit Clause-clause subsumption calls : 472
% 0.15/5.63 % Rewrite failures with RHS unbound : 0
% 0.15/5.63 % BW rewrite match attempts : 2624
% 0.15/5.63 % BW rewrite match successes : 64
% 0.15/5.63 % Condensation attempts : 0
% 0.15/5.63 % Condensation successes : 0
% 0.15/5.63 % Termbank termtop insertions : 167854
% 0.15/5.63 % Search garbage collected termcells : 11703
% 0.15/5.63
% 0.15/5.63 % -------------------------------------------------
% 0.15/5.63 % User time : 0.139 s
% 0.15/5.63 % System time : 0.014 s
% 0.15/5.63 % Total time : 0.153 s
% 0.15/5.63 % Maximum resident set size: 7268 pages
% 0.15/5.63
% 0.15/5.63 % -------------------------------------------------
% 0.15/5.63 % User time : 0.522 s
% 0.15/5.63 % System time : 0.070 s
% 0.15/5.63 % Total time : 0.592 s
% 0.15/5.63 % Maximum resident set size: 5376 pages
% 0.15/5.63 % E exiting
%------------------------------------------------------------------------------