%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO028_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n010.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 02:24:45 PM UTC 2026
% Result : Theorem 2.51s 1.13s
% Output : Refutation 2.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 7 unt; 0 typ; 1 def)
% Number of atoms : 17 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 10 ( 9 ~; 0 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 19 ( 8 fml; 11 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 9 ( 9 !; 0 ?; 9 :)
% Comments :
%------------------------------------------------------------------------------
tff(pred_def_1,type,
sQ0_eqProxy: ( $o * $o ) > $o ).
tff(f1,conjecture,
~ ! [X0: $o] : (X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ~ ! [X0: $o] : (X0),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ~ ! [X0: $o] : (X0),
inference(rectify,[],[f2]) ).
tff(f4,plain,
~ ~ ! [X0: $o] : ( $true = (X0) ),
inference(fool_elimination,[],[f3]) ).
tff(f5,plain,
! [X0: $o] : ( $true = (X0) ),
inference(flattening,[],[f4]) ).
tff(f6,plain,
! [X0: $o] : ( $true = (X0) ),
inference(cnf_transformation,[],[f5]) ).
tff(f7,plain,
$true != $false,
introduced(definition,[],[fool_distinctness_axiom]) ).
tff(f9,definition,
! [X0: $o,X1: $o] :
( sQ0_eqProxy((X0),(X1))
<=> ( (X0) = (X1) ) ),
introduced(definition,[new_symbols(definition,[sQ0_eqProxy])],[equality_proxy_definition]) ).
tff(f11,plain,
~ sQ0_eqProxy($true,$false),
inference(equality_proxy_replacement,[],[f7,f9]) ).
tff(f12,plain,
! [X0: $o] : sQ0_eqProxy($true,(X0)),
inference(equality_proxy_replacement,[],[f6,f9]) ).
tff(f15,plain,
$false,
inference(resolution,[],[f11,f12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO028_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n010.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Mon Sep 28 17:22:03 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.51/1.13 % (2087532)Detected formulas, will run a generic FOF schedule.
% 2.51/1.13 % (2087543)dis-21_1_sil=8000:lcm=predicate:random_seed=2434768556: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)
% 2.51/1.13 % (2087543)First to succeed.
% 2.51/1.13 % (2087543)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2087532"
% 2.51/1.13 % (2087537)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=1402108832:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.51/1.13 % (2087541)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=906010164:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.51/1.13 % (2087539)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=78580730:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.51/1.13 % (2087538)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=1205218554:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.51/1.13 % (2087540)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1539034531:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.51/1.13 % (2087542)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1805383872:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.51/1.13 % (2087541)Also succeeded, but the first one will report.
% 2.51/1.13 % (2087540)Also succeeded, but the first one will report.
% 2.51/1.13 % (2087542)Also succeeded, but the first one will report.
% 2.51/1.13 % (2087543)Refutation found. Thanks to Tanya!
% 2.51/1.13 % SZS status Theorem for theBenchmark
% 2.51/1.13 % SZS output start Proof for theBenchmark
% See solution above
% 2.51/1.13 % (2087543)------------------------------
% 2.51/1.13 % (2087543)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.51/1.13 % (2087543)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.51/1.13 % (2087543)CaDiCaL version: 2.1.3
% 2.51/1.13 % (2087543)Termination reason: Refutation
% 2.51/1.13 % (2087543)Time elapsed: 0.001 s
% 2.51/1.13 % (2087543)Peak memory usage: 88 MB
% 2.51/1.13 % (2087543)------------------------------
% 2.51/1.13 % (2087543)------------------------------
% 2.51/1.13 % (2087532)Success in time 0.268 s
% 2.51/1.13 % Vampire exiting
%------------------------------------------------------------------------------