%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO189_8 : TPTP v9.3.1. Released v8.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /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 : Tue Sep 29 02:25:39 PM UTC 2026
% Result : Theorem 2.23s 0.87s
% Output : Refutation 2.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 2
% Syntax : Number of formulae : 12 ( 5 unt; 0 typ; 1 def)
% Number of atoms : 26 ( 9 equ)
% Maximal formula atoms : 2 ( 2 avg)
% Number of connectives : 14 ( 7 ~; 0 |; 2 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 33 ( 13 fml; 20 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 2 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 17 ( 12 !; 5 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_2,type,
sK0: $o > $o ).
tff(pred_def_1,type,
sQ1_eqProxy: ( $o * $o ) > $o ).
tff(f1,conjecture,
? [X0: $o] :
! [X1: $o] :
( (X0)
=> (X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCT5) ).
tff(f2,negated_conjecture,
~ ? [X0: $o] :
! [X1: $o] :
( (X0)
=> (X1) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ? [X0: $o] :
! [X1: $o] :
( (X0)
=> (X1) ),
inference(rectify,[],[f2]) ).
tff(f4,plain,
~ ? [X0: $o] :
! [X1: $o] :
( ( $true = (X0) )
=> ( $true = (X1) ) ),
inference(fool_elimination,[],[f3]) ).
tff(f5,plain,
! [X0: $o] :
? [X1: $o] :
( ( $true != (X1) )
& ( $true = (X0) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
! [X0: $o] :
( ( $true != sK0((X0)) )
& ( $true = (X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f5]) ).
tff(f7,plain,
! [X0: $o] : ( $true = (X0) ),
inference(cnf_transformation,[],[f6]) ).
tff(f8,plain,
! [X0: $o] : ( $true != sK0((X0)) ),
inference(cnf_transformation,[],[f6]) ).
tff(f11,definition,
! [X0: $o,X1: $o] :
( sQ1_eqProxy((X0),(X1))
<=> ( (X0) = (X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1_eqProxy])],[equality_proxy_definition]) ).
tff(f14,plain,
! [X0: $o] : ~ sQ1_eqProxy($true,sK0((X0))),
inference(equality_proxy_replacement,[],[f8,f11]) ).
tff(f15,plain,
! [X0: $o] : sQ1_eqProxy($true,(X0)),
inference(equality_proxy_replacement,[],[f7,f11]) ).
tff(f18,plain,
$false,
inference(resolution,[],[f14,f15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO189_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.19 % Computer : n011.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 17:31:46 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 Running first-order theorem proving
% 0.09/0.23 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
% 2.23/0.87 % (3563433)Detected formulas, will run a generic FOF schedule.
% 2.23/0.87 % (3563444)dis-21_1_sil=8000:lcm=predicate:random_seed=3614580322: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)
% 2.23/0.87 % (3563444)First to succeed.
% 2.23/0.87 % (3563444)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3563433"
% 2.23/0.87 % (3563442)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2668866317:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.23/0.87 % (3563438)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=922918531:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.23/0.87 % (3563443)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=854386823:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.23/0.87 % (3563440)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=893171643:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.23/0.87 % (3563441)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2917014025:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.23/0.87 % (3563439)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=3713021806:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.23/0.87 % (3563442)Also succeeded, but the first one will report.
% 2.23/0.87 % (3563441)Also succeeded, but the first one will report.
% 2.23/0.87 % (3563443)Also succeeded, but the first one will report.
% 2.23/0.87 % (3563444)Refutation found. Thanks to Tanya!
% 2.23/0.87 % SZS status Theorem for theBenchmark
% 2.23/0.87 % SZS output start Proof for theBenchmark
% See solution above
% 2.23/0.87 % (3563444)------------------------------
% 2.23/0.87 % (3563444)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.23/0.87 % (3563444)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.23/0.87 % (3563444)CaDiCaL version: 2.1.3
% 2.23/0.87 % (3563444)Termination reason: Refutation
% 2.23/0.87 % (3563444)Time elapsed: 0.001 s
% 2.23/0.87 % (3563444)Peak memory usage: 89 MB
% 2.23/0.87 % (3563444)------------------------------
% 2.23/0.87 % (3563444)------------------------------
% 2.23/0.87 % (3563433)Success in time 0.259 s
% 2.23/0.87 % Vampire exiting
%------------------------------------------------------------------------------