%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SWV573_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/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 : Tue Sep 29 01:19:00 PM UTC 2026
% Result : Theorem 3.88s 1.33s
% Output : Refutation 3.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 4
% Syntax : Number of formulae : 15 ( 12 unt; 0 typ; 0 def)
% Number of atoms : 18 ( 12 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 7 ~; 2 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 6 ( 5 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 14 usr; 1 prp; 0-3 aty)
% Number of functors : 26 ( 26 usr; 4 con; 0-4 aty)
% Number of variables : 9 ( 9 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
complex1: $tType ).
tff(type_def_6,type,
bool: $tType ).
tff(type_def_7,type,
int: $tType ).
tff(type_def_8,type,
nat: $tType ).
tff(type_def_9,type,
real: $tType ).
tff(type_def_10,type,
fun: ( $tType * $tType ) > $tType ).
tff(func_def_0,type,
im: complex1 > real ).
tff(func_def_1,type,
re: complex1 > real ).
tff(func_def_2,type,
complex: ( real * real ) > complex1 ).
tff(func_def_3,type,
complex_case:
!>[X0: $tType] : ( ( fun(real,fun(real,X0)) * complex1 ) > X0 ) ).
tff(func_def_4,type,
complex_rec:
!>[X0: $tType] : ( ( fun(real,fun(real,X0)) * complex1 ) > X0 ) ).
tff(func_def_5,type,
complex_size: complex1 > nat ).
tff(func_def_6,type,
ii: complex1 ).
tff(func_def_7,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_8,type,
if:
!>[X0: $tType] : ( ( bool * X0 * X0 ) > X0 ) ).
tff(func_def_9,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_10,type,
semiri532925092at_aux:
!>[X0: $tType] : ( ( fun(X0,X0) * nat * X0 ) > X0 ) ).
tff(func_def_11,type,
size_size:
!>[X0: $tType] : ( X0 > nat ) ).
tff(func_def_12,type,
norm_norm:
!>[X0: $tType] : ( X0 > real ) ).
tff(func_def_13,type,
of_real:
!>[X0: $tType] : ( real > X0 ) ).
tff(func_def_14,type,
aa:
!>[X0: $tType,X1: $tType] : ( ( fun(X0,X1) * X0 ) > X1 ) ).
tff(func_def_15,type,
fFalse: bool ).
tff(func_def_16,type,
fTrue: bool ).
tff(func_def_17,type,
n: nat ).
tff(func_def_18,type,
sK0: complex1 > real ).
tff(func_def_19,type,
sK1: complex1 > real ).
tff(func_def_20,type,
sK2: fun(int,bool) > nat ).
tff(func_def_21,type,
sK3: fun(int,bool) > int ).
tff(func_def_22,type,
sK4: fun(int,bool) > int ).
tff(func_def_23,type,
sK5: fun(int,bool) > nat ).
tff(func_def_24,type,
sK6:
!>[X0: $tType,X1: $tType] : ( ( fun(X1,X0) * fun(X1,X0) ) > X1 ) ).
tff(pred_def_1,type,
zero:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ord:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
order:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
semiring_1:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
preorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
semiring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linordered_semidom:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
real_algebra_1:
!>[X0: $tType] : $o ).
tff(pred_def_10,type,
real_normed_vector:
!>[X0: $tType] : $o ).
tff(pred_def_11,type,
real_n2089651433ebra_1:
!>[X0: $tType] : $o ).
tff(pred_def_12,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_13,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_14,type,
pp: bool > $o ).
tff(f9,axiom,
! [X0: $tType] :
( real_algebra_1(X0)
=> ! [X1: nat] : ( of_real(X0,semiring_1_of_nat(real,X1)) = semiring_1_of_nat(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_of__real__of__nat__eq) ).
tff(f28,axiom,
! [X0: real] : ( of_real(complex1,X0) = complex(X0,zero_zero(real)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_complex__of__real__def) ).
tff(f136,axiom,
real_algebra_1(complex1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Complex_Ocomplex___RealVector_Oreal__algebra__1) ).
tff(f145,conjecture,
semiring_1_of_nat(complex1,n) = complex(semiring_1_of_nat(real,n),zero_zero(real)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
tff(f146,negated_conjecture,
( ( ~ semiring_1_of_nat(complex1,n) ) = complex(semiring_1_of_nat(real,n),zero_zero(real)) ),
inference(negated_conjecture,[status(cth)],[f145]) ).
tff(f149,plain,
semiring_1_of_nat(complex1,n) != complex(semiring_1_of_nat(real,n),zero_zero(real)),
inference(flattening,[],[f146]) ).
tff(f153,plain,
! [X0: $tType] :
( ! [X1: nat] : ( of_real(X0,semiring_1_of_nat(real,X1)) = semiring_1_of_nat(X0,X1) )
| ~ real_algebra_1(X0) ),
inference(ennf_transformation,[],[f9]) ).
tff(f269,plain,
! [X0: $tType,X1: nat] :
( ~ real_algebra_1(X0)
| ( semiring_1_of_nat(X0,X1) = of_real(X0,semiring_1_of_nat(real,X1)) ) ),
inference(cnf_transformation,[],[f153]) ).
tff(f297,plain,
! [X0: real] : ( of_real(complex1,X0) = complex(X0,zero_zero(real)) ),
inference(cnf_transformation,[],[f28]) ).
tff(f444,plain,
real_algebra_1(complex1),
inference(cnf_transformation,[],[f136]) ).
tff(f453,plain,
semiring_1_of_nat(complex1,n) != complex(semiring_1_of_nat(real,n),zero_zero(real)),
inference(cnf_transformation,[],[f149]) ).
tff(f543,plain,
semiring_1_of_nat(complex1,n) != of_real(complex1,semiring_1_of_nat(real,n)),
inference(superposition,[],[f453,f297]) ).
tff(f673,plain,
! [X0: nat] : ( semiring_1_of_nat(complex1,X0) = of_real(complex1,semiring_1_of_nat(real,X0)) ),
inference(resolution,[],[f269,f444]) ).
tff(f783,plain,
semiring_1_of_nat(complex1,n) != semiring_1_of_nat(complex1,n),
inference(superposition,[],[f543,f673]) ).
tff(f791,plain,
$false,
inference(trivial_inequality_removal,[],[f783]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV573_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.20 % Computer : n015.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.20 % CPULimit : 300
% 0.09/0.20 % WCLimit : 300
% 0.09/0.20 % DateTime : Mon Sep 28 11:58:17 UTC 2026
% 0.09/0.20 % CPUTime :
% 0.09/0.20 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.24 Running first-order theorem proving
% 0.09/0.24 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.88/1.33 % (2575911)Detected formulas, will run a generic FOF schedule.
% 3.88/1.33 % (2575921)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=818322683:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.88/1.33 % (2575921)Refutation not found, incomplete strategy
% 3.88/1.33 % (2575921)------------------------------
% 3.88/1.33 % (2575921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.33 % (2575921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.33 % (2575921)CaDiCaL version: 2.1.3
% 3.88/1.33 % (2575921)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.33 % (2575921)Time elapsed: 0.002 s
% 3.88/1.33 % (2575921)Peak memory usage: 88 MB
% 3.88/1.33 % (2575921)Instructions burned: 2 (million)
% 3.88/1.33 % (2575918)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=482288272:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.88/1.33 % (2575919)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=799435650:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.88/1.33 % (2575920)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2506811029:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.88/1.33 % (2575917)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=1117555232:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.88/1.33 % (2575920)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.88/1.33 % (2575920)Refutation not found, incomplete strategy
% 3.88/1.33 % (2575920)------------------------------
% 3.88/1.33 % (2575920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.33 % (2575920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.33 % (2575920)CaDiCaL version: 2.1.3
% 3.88/1.33 % (2575920)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.33 % (2575920)Time elapsed: 0.002 s
% 3.88/1.33 % (2575920)Peak memory usage: 88 MB
% 3.88/1.33 % (2575920)Instructions burned: 1 (million)
% 3.88/1.33 % (2575919)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 3.88/1.33 % (2575922)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=832770578:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.88/1.33 % (2575923)dis-21_1_sil=8000:lcm=predicate:random_seed=4066033607: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)
% 3.88/1.33 % (2575922)First to succeed.
% 3.88/1.33 % (2575922)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2575911"
% 3.88/1.33 % (2575923)Instruction limit reached!
% 3.88/1.33 % (2575923)------------------------------
% 3.88/1.33 % (2575923)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.33 % (2575923)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.33 % (2575923)CaDiCaL version: 2.1.3
% 3.88/1.33 % (2575923)Termination reason: Instruction limit
% 3.88/1.33 % (2575923)Termination phase: Saturation
% 3.88/1.33 % (2575923)Time elapsed: 0.074 s
% 3.88/1.33 % (2575923)Peak memory usage: 90 MB
% 3.88/1.33 % (2575923)Instructions burned: 131 (million)
% 3.88/1.33 % (2575921)------------------------------
% 3.88/1.33 % (2575921)------------------------------
% 3.88/1.33 % (2575931)lrs+10_1_sil=8000:sp=occurrence:random_seed=941840352:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.88/1.33 % (2575931)Refutation not found, incomplete strategy
% 3.88/1.33 % (2575931)------------------------------
% 3.88/1.33 % (2575931)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.33 % (2575931)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.33 % (2575931)CaDiCaL version: 2.1.3
% 3.88/1.33 % (2575931)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.33 % (2575931)Time elapsed: 0.003 s
% 3.88/1.33 % (2575931)Peak memory usage: 88 MB
% 3.88/1.33 % (2575931)Instructions burned: 3 (million)
% 3.88/1.33 % (2575920)------------------------------
% 3.88/1.33 % (2575920)------------------------------
% 3.88/1.33 % (2575932)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2147675966:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.88/1.33 % (2575932)Refutation not found, incomplete strategy
% 3.88/1.33 % (2575932)------------------------------
% 3.88/1.33 % (2575932)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.33 % (2575932)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.33 % (2575932)CaDiCaL version: 2.1.3
% 3.88/1.33 % (2575932)Termination reason: Refutation not found, incomplete strategy
% 3.88/1.33 % (2575932)Time elapsed: 0.003 s
% 3.88/1.33 % (2575932)Peak memory usage: 88 MB
% 3.88/1.33 % (2575932)Instructions burned: 5 (million)
% 3.88/1.33 % (2575922)Refutation found. Thanks to Tanya!
% 3.88/1.33 % SZS status Theorem for theBenchmark
% 3.88/1.33 % SZS output start Proof for theBenchmark
% See solution above
% 3.88/1.33 % (2575922)------------------------------
% 3.88/1.33 % (2575922)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.88/1.33 % (2575922)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.88/1.33 % (2575922)CaDiCaL version: 2.1.3
% 3.88/1.33 % (2575922)Termination reason: Refutation
% 3.88/1.33 % (2575922)Time elapsed: 0.017 s
% 3.88/1.33 % (2575922)Peak memory usage: 89 MB
% 3.88/1.33 % (2575922)Instructions burned: 23 (million)
% 3.88/1.33 % (2575922)------------------------------
% 3.88/1.33 % (2575922)------------------------------
% 3.88/1.33 % (2575911)Success in time 0.458 s
% 3.88/1.33 % Vampire exiting
%------------------------------------------------------------------------------