TSTP Solution File: NUM925+4 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM925+4 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 14:38:46 EDT 2024
% Result : Theorem 14.13s 2.68s
% Output : Refutation 14.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 47 ( 40 unt; 0 def)
% Number of atoms : 60 ( 41 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 19 ~; 9 |; 0 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 15 con; 0-2 aty)
% Number of variables : 32 ( 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f71772,plain,
$false,
inference(resolution,[],[f70256,f17762]) ).
fof(f17762,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X0)),
inference(cnf_transformation,[],[f5544]) ).
fof(f5544,plain,
! [X0] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X0),X0)),
inference(rectify,[],[f1923]) ).
fof(f1923,axiom,
! [X542] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X542),X542)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1856_order__less__irrefl) ).
fof(f70256,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),zero_zero_int)),
inference(backward_demodulation,[],[f52179,f70251]) ).
fof(f70251,plain,
zero_zero_int = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)),
inference(resolution,[],[f70250,f61637]) ).
fof(f61637,plain,
! [X0] : is_int(hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,X0))),
inference(superposition,[],[f17285,f52165]) ).
fof(f52165,plain,
! [X0] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X0)) = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,X0)),
inference(backward_demodulation,[],[f18268,f51930]) ).
fof(f51930,plain,
! [X0] : hAPP_int_int(succ,X0) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),X0),
inference(superposition,[],[f19666,f18116]) ).
fof(f18116,plain,
! [X0] : hAPP_int_int(succ,X0) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int),
inference(cnf_transformation,[],[f5898]) ).
fof(f5898,plain,
! [X0] : hAPP_int_int(succ,X0) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),one_one_int),
inference(rectify,[],[f924]) ).
fof(f924,axiom,
! [X21] : hAPP_int_int(succ,X21) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X21),one_one_int),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_857_succ__def) ).
fof(f19666,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0),
inference(cnf_transformation,[],[f7016]) ).
fof(f7016,plain,
! [X0,X1] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X0),X1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X1),X0),
inference(rectify,[],[f916]) ).
fof(f916,axiom,
! [X201,X202] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X201),X202) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,X202),X201),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_849_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) ).
fof(f18268,plain,
! [X0] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X0)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X0)),
inference(cnf_transformation,[],[f6050]) ).
fof(f6050,plain,
! [X0] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X0)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X0)),
inference(rectify,[],[f3172]) ).
fof(f3172,axiom,
! [X15] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,X15)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,X15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3105_int__Suc) ).
fof(f17285,plain,
! [X0,X1] : is_int(hAPP_nat_int(X0,X1)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] : is_int(hAPP_nat_int(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gsy_c_hAPP_000tc__Nat__Onat_000tc__Int__Oint) ).
fof(f70250,plain,
( ~ is_int(hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))
| zero_zero_int = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(trivial_inequality_removal,[],[f70248]) ).
fof(f70248,plain,
( zero_zero_int != zero_zero_int
| zero_zero_int = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))
| ~ is_int(hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(superposition,[],[f20204,f52184]) ).
fof(f52184,plain,
zero_zero_int = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_nat(suc,one_one_nat)),
inference(backward_demodulation,[],[f26514,f52165]) ).
fof(f26514,plain,
zero_zero_int = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)),
inference(backward_demodulation,[],[f26151,f18268]) ).
fof(f26151,plain,
zero_zero_int = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_nat(suc,one_one_nat)),
inference(backward_demodulation,[],[f26031,f26150]) ).
fof(f26150,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int))) = hAPP_nat_nat(suc,one_one_nat),
inference(forward_demodulation,[],[f26149,f17330]) ).
fof(f17330,plain,
zero_zero_int = pls,
inference(cnf_transformation,[],[f218]) ).
fof(f218,axiom,
zero_zero_int = pls,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_151_Pls__def) ).
fof(f26149,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_nat_nat(suc,one_one_nat),
inference(forward_demodulation,[],[f17583,f17380]) ).
fof(f17380,plain,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
inference(cnf_transformation,[],[f3114]) ).
fof(f3114,axiom,
one_one_nat = hAPP_nat_nat(suc,zero_zero_nat),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3047_One__nat__def) ).
fof(f17583,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat)),
inference(cnf_transformation,[],[f3201]) ).
fof(f3201,axiom,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_nat_nat(suc,hAPP_nat_nat(suc,zero_zero_nat)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3134_numeral__2__eq__2) ).
fof(f26031,plain,
zero_zero_int = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,zero_zero_int)))),
inference(forward_demodulation,[],[f17281,f17330]) ).
fof(f17281,plain,
zero_zero_int = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(cnf_transformation,[],[f5489]) ).
fof(f5489,plain,
zero_zero_int = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(flattening,[],[f5488]) ).
fof(f5488,negated_conjecture,
~ ( zero_zero_int != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ),
inference(negated_conjecture,[],[f5487]) ).
fof(f5487,conjecture,
zero_zero_int != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
fof(f20204,plain,
! [X0,X1] :
( zero_zero_int != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),X0)
| zero_zero_int = X1
| ~ is_int(X1) ),
inference(cnf_transformation,[],[f11157]) ).
fof(f11157,plain,
! [X0,X1] :
( zero_zero_int != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),X0)
| zero_zero_int = X1
| ~ is_int(X1) ),
inference(flattening,[],[f11156]) ).
fof(f11156,plain,
! [X0,X1] :
( zero_zero_int != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),X0)
| zero_zero_int = X1
| ~ is_int(X1) ),
inference(ennf_transformation,[],[f7498]) ).
fof(f7498,plain,
! [X0,X1] :
( is_int(X1)
=> ( zero_zero_int != X1
=> zero_zero_int != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X1),X0) ) ),
inference(rectify,[],[f414]) ).
fof(f414,axiom,
! [X65,X66] :
( is_int(X66)
=> ( zero_zero_int != X66
=> zero_zero_int != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,X66),X65) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_347_field__power__not__zero) ).
fof(f52179,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(backward_demodulation,[],[f26509,f52165]) ).
fof(f26509,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))),
inference(backward_demodulation,[],[f17559,f18268]) ).
fof(f17559,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(cnf_transformation,[],[f67]) ).
fof(f67,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_n1pos) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM925+4 : TPTP v8.1.2. Released v5.3.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.35 % Computer : n026.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Apr 30 00:17:49 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (8707)Running in auto input_syntax mode. Trying TPTP
% 0.54/0.69 % (8714)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.54/0.69 % (8710)WARNING: value z3 for option sas not known
% 0.54/0.70 % (8709)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.54/0.70 % (8711)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.54/0.70 % (8710)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.54/0.70 % (8712)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.54/0.70 % (8708)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.54/0.70 % (8713)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 14.13/2.67 % (8713)First to succeed.
% 14.13/2.68 % (8713)Refutation found. Thanks to Tanya!
% 14.13/2.68 % SZS status Theorem for theBenchmark
% 14.13/2.68 % SZS output start Proof for theBenchmark
% See solution above
% 14.13/2.68 % (8713)------------------------------
% 14.13/2.68 % (8713)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 14.13/2.68 % (8713)Termination reason: Refutation
% 14.13/2.68
% 14.13/2.68 % (8713)Memory used [KB]: 47898
% 14.13/2.68 % (8713)Time elapsed: 1.970 s
% 14.13/2.68 % (8713)Instructions burned: 5296 (million)
% 14.13/2.68 % (8713)------------------------------
% 14.13/2.68 % (8713)------------------------------
% 14.13/2.68 % (8707)Success in time 2.309 s
%------------------------------------------------------------------------------