%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUN015_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n013.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 : Tue Sep 29 12:26:35 PM UTC 2026
% Result : Theorem 3.75s 1.49s
% Output : Refutation 3.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 5
% Syntax : Number of formulae : 21 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 34 ( 14 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 27 ( 14 ~; 9 |; 1 &)
% ( 2 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-4 aty)
% Number of variables : 11 ( 11 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(type_def_8,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
bit0: int > int ).
tff(func_def_3,type,
bit1: int > int ).
tff(func_def_4,type,
pls: int ).
tff(func_def_5,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_6,type,
power_power:
!>[X0: $tType] : ( ( X0 * nat ) > X0 ) ).
tff(func_def_7,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_8,type,
fFalse: bool ).
tff(func_def_9,type,
fTrue: bool ).
tff(func_def_10,type,
n: nat ).
tff(func_def_11,type,
tn: nat ).
tff(func_def_12,type,
v: int ).
tff(func_def_13,type,
w: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
power:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
mult_zero:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
zero_neq_one:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
number_semiring:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
no_zero_divisors:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_13,type,
cancel_semigroup_add:
!>[X0: $tType] : $o ).
tff(pred_def_14,type,
ring_11004092258visors:
!>[X0: $tType] : $o ).
tff(pred_def_15,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_16,type,
ordere236663937imp_le:
!>[X0: $tType] : $o ).
tff(pred_def_17,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_18,type,
pp: bool > $o ).
tff(f1,axiom,
v != zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__096v_A_126_061_A0_096) ).
tff(f2,axiom,
! [X0: $tType] :
( linordered_idom(X0)
=> ! [X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ( X1 != zero_zero(X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_zero__less__power2) ).
tff(f38,axiom,
pls = zero_zero(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Pls__def) ).
tff(f104,axiom,
linordered_idom(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f127,conjecture,
ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f128,negated_conjecture,
~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
inference(negated_conjecture,[status(cth)],[f127]) ).
tff(f129,plain,
~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
inference(flattening,[],[f128]) ).
tff(f132,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
<=> ( X1 != zero_zero(X0) ) )
| ~ linordered_idom(X0) ),
inference(ennf_transformation,[],[f2]) ).
tff(f183,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls)))))
| ( zero_zero(X0) = X1 ) )
& ( ( X1 != zero_zero(X0) )
| ~ ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ) )
| ~ linordered_idom(X0) ),
inference(nnf_transformation,[],[f132]) ).
tff(f240,plain,
v != zero_zero(int),
inference(cnf_transformation,[],[f1]) ).
tff(f242,plain,
! [X0: $tType,X1: X0] :
( ~ linordered_idom(X0)
| ( zero_zero(X0) = X1 )
| ord_less(X0,zero_zero(X0),power_power(X0,X1,number_number_of(nat,bit0(bit1(pls))))) ),
inference(cnf_transformation,[],[f183]) ).
tff(f305,plain,
zero_zero(int) = pls,
inference(cnf_transformation,[],[f38]) ).
tff(f408,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f104]) ).
tff(f429,plain,
~ ord_less(int,zero_zero(int),power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
inference(cnf_transformation,[],[f129]) ).
tff(f464,plain,
v != pls,
inference(superposition,[],[f240,f305]) ).
tff(f465,plain,
~ ord_less(int,pls,power_power(int,v,number_number_of(nat,bit0(bit1(pls))))),
inference(superposition,[],[f429,f305]) ).
tff(f881,plain,
! [X0: int] :
( ( zero_zero(int) = X0 )
| ord_less(int,zero_zero(int),power_power(int,X0,number_number_of(nat,bit0(bit1(pls))))) ),
inference(resolution,[],[f242,f408]) ).
tff(f882,plain,
! [X0: int] :
( ( pls = X0 )
| ord_less(int,zero_zero(int),power_power(int,X0,number_number_of(nat,bit0(bit1(pls))))) ),
inference(forward_demodulation,[],[f881,f305]) ).
tff(f883,plain,
! [X0: int] :
( ord_less(int,pls,power_power(int,X0,number_number_of(nat,bit0(bit1(pls)))))
| ( pls = X0 ) ),
inference(forward_demodulation,[],[f882,f305]) ).
tff(f1228,plain,
v = pls,
inference(resolution,[],[f883,f465]) ).
tff(f1238,plain,
$false,
inference(forward_subsumption_resolution,[],[f1228,f464]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN015_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.38 % Computer : n013.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Sun Sep 27 21:49:52 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.75/1.49 % (585948)Detected formulas, will run a generic FOF schedule.
% 3.75/1.49 % (585966)dis-21_1_sil=8000:lcm=predicate:random_seed=1667284465:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 3.75/1.49 % (585960)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=3840516657:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.75/1.49 % (585961)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=25379923:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.75/1.49 % (585963)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1091788927:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.75/1.49 % (585962)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2187169602:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.75/1.49 % (585966)Instruction limit reached!
% 3.75/1.49 % (585966)------------------------------
% 3.75/1.49 % (585966)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.49 % (585966)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.49 % (585966)CaDiCaL version: 2.1.3
% 3.75/1.49 % (585966)Termination reason: Instruction limit
% 3.75/1.49 % (585966)Termination phase: Saturation
% 3.75/1.49 % (585966)Time elapsed: 0.041 s
% 3.75/1.49 % (585966)Peak memory usage: 89 MB
% 3.75/1.49 % (585966)Instructions burned: 130 (million)
% 3.75/1.49 % (585963)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.75/1.49 % (585962)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.75/1.49 % (585963)Refutation not found, incomplete strategy
% 3.75/1.49 % (585963)------------------------------
% 3.75/1.49 % (585963)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.49 % (585963)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.49 % (585963)CaDiCaL version: 2.1.3
% 3.75/1.49 % (585963)Termination reason: Refutation not found, incomplete strategy
% 3.75/1.49 % (585963)Time elapsed: 0.004 s
% 3.75/1.49 % (585963)Peak memory usage: 88 MB
% 3.75/1.49 % (585963)Instructions burned: 5 (million)
% 3.75/1.49 % (585964)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2643897693:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.75/1.49 % (585965)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=167502688:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.75/1.49 % (585965)First to succeed.
% 3.75/1.49 % (585965)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-585948"
% 3.75/1.49 % (585964)Instruction limit reached!
% 3.75/1.49 % (585964)------------------------------
% 3.75/1.49 % (585964)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.49 % (585964)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.49 % (585964)CaDiCaL version: 2.1.3
% 3.75/1.49 % (585964)Termination reason: Instruction limit
% 3.75/1.49 % (585964)Termination phase: Saturation
% 3.75/1.49 % (585964)Time elapsed: 0.067 s
% 3.75/1.49 % (585964)Peak memory usage: 88 MB
% 3.75/1.49 % (585964)Instructions burned: 119 (million)
% 3.75/1.49 % (585972)lrs+10_1_sil=8000:sp=occurrence:random_seed=278133128:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.75/1.49 % (585972)Instruction limit reached!
% 3.75/1.49 % (585972)------------------------------
% 3.75/1.49 % (585972)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.49 % (585972)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.49 % (585972)CaDiCaL version: 2.1.3
% 3.75/1.49 % (585972)Termination reason: Instruction limit
% 3.75/1.49 % (585972)Termination phase: Saturation
% 3.75/1.49 % (585972)Time elapsed: 0.082 s
% 3.75/1.49 % (585972)Peak memory usage: 90 MB
% 3.75/1.49 % (585972)Instructions burned: 289 (million)
% 3.75/1.49 % (585975)lrs+10_1_sil=32000:urr=on:br=off:random_seed=3756112938:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.75/1.49 % (585963)------------------------------
% 3.75/1.49 % (585963)------------------------------
% 3.75/1.49 % (585977)lrs+1011_1_sil=32000:sp=occurrence:random_seed=1069353102:i=325:sd=1:ss=axioms:sgt=32_2996 on theBenchmark for (2996ds/325Mi)
% 3.75/1.49 % (585965)Refutation found. Thanks to Tanya!
% 3.75/1.49 % SZS status Theorem for theBenchmark
% 3.75/1.49 % SZS output start Proof for theBenchmark
% See solution above
% 3.75/1.49 % (585965)------------------------------
% 3.75/1.49 % (585965)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.75/1.49 % (585965)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.75/1.49 % (585965)CaDiCaL version: 2.1.3
% 3.75/1.49 % (585965)Termination reason: Refutation
% 3.75/1.49 % (585965)Time elapsed: 0.031 s
% 3.75/1.49 % (585965)Peak memory usage: 89 MB
% 3.75/1.49 % (585965)Instructions burned: 45 (million)
% 3.75/1.49 % (585965)------------------------------
% 3.75/1.49 % (585965)------------------------------
% 3.75/1.49 % (585948)Success in time 0.444 s
% 3.75/1.49 % Vampire exiting
%------------------------------------------------------------------------------