%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO206_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 : n007.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 02:25:42 PM UTC 2026
% Result : Theorem 2.49s 1.11s
% Output : Refutation 2.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 9 unt; 0 typ; 3 def)
% Number of atoms : 261 ( 72 equ)
% Maximal formula atoms : 16 ( 7 avg)
% Number of connectives : 125 ( 49 ~; 57 |; 10 &)
% ( 8 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 235 ( 148 fml; 87 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 25 ( 0 sgn 19 !; 6 ?; 25 :)
% 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) )
= ( (X1) = (X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCT265) ).
tff(f2,negated_conjecture,
~ ? [X0: $o] :
! [X1: $o] :
( ( (X0) = (X1) )
= ( (X1) = (X0) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ? [X0: $o] :
! [X1: $o] :
( ( (X0) = (X1) )
= ( (X1) = (X0) ) ),
inference(rectify,[],[f2]) ).
tff(f4,plain,
~ ? [X0: $o] :
! [X1: $o] :
( ( ( $true = (X0) )
<=> ( $true = (X1) ) )
<=> ( ( $true = (X1) )
<=> ( $true = (X0) ) ) ),
inference(fool_elimination,[],[f3]) ).
tff(f5,plain,
! [X0: $o] :
? [X1: $o] :
( ( ( $true = (X0) )
<=> ( $true = (X1) ) )
<~> ( ( $true = (X1) )
<=> ( $true = (X0) ) ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f6,plain,
! [X0: $o] :
? [X1: $o] :
( ( ( ( ( $true != (X0) )
| ( $true != (X1) ) )
& ( ( $true = (X0) )
| ( $true = (X1) ) ) )
| ( ( ( $true != (X1) )
| ( $true != (X0) ) )
& ( ( $true = (X1) )
| ( $true = (X0) ) ) ) )
& ( ( ( ( $true = (X1) )
| ( $true != (X0) ) )
& ( ( $true = (X0) )
| ( $true != (X1) ) ) )
| ( ( ( $true = (X0) )
| ( $true != (X1) ) )
& ( ( $true = (X1) )
| ( $true != (X0) ) ) ) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f7,plain,
! [X0: $o] :
( ( ( ( ( $true != (X0) )
| ( $true != sK0((X0)) ) )
& ( ( $true = (X0) )
| ( $true = sK0((X0)) ) ) )
| ( ( ( $true != sK0((X0)) )
| ( $true != (X0) ) )
& ( ( $true = sK0((X0)) )
| ( $true = (X0) ) ) ) )
& ( ( ( ( $true = sK0((X0)) )
| ( $true != (X0) ) )
& ( ( $true = (X0) )
| ( $true != sK0((X0)) ) ) )
| ( ( ( $true = (X0) )
| ( $true != sK0((X0)) ) )
& ( ( $true = sK0((X0)) )
| ( $true != (X0) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X1,sK0(X0))],[f6]) ).
tff(f9,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $true != sK0((X0)) )
| ( $true = (X0) )
| ( $true != sK0((X0)) ) ),
inference(cnf_transformation,[],[f7]) ).
tff(f10,plain,
! [X0: $o] :
( ( $true = sK0((X0)) )
| ( $true != (X0) )
| ( $true = sK0((X0)) )
| ( $true != (X0) ) ),
inference(cnf_transformation,[],[f7]) ).
tff(f12,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $true = sK0((X0)) )
| ( $true = sK0((X0)) )
| ( $true = (X0) ) ),
inference(cnf_transformation,[],[f7]) ).
tff(f15,plain,
! [X0: $o] :
( ( $true != (X0) )
| ( $true != sK0((X0)) )
| ( $true != sK0((X0)) )
| ( $true != (X0) ) ),
inference(cnf_transformation,[],[f7]) ).
tff(f18,plain,
( ( $true != sK0($true) )
| ( $true != sK0($true) )
| ( $true != $true ) ),
inference(equality_resolution,[],[f15]) ).
tff(f22,plain,
( ( $true = sK0($true) )
| ( $true = sK0($true) )
| ( $true != $true ) ),
inference(equality_resolution,[],[f10]) ).
tff(f24,definition,
! [X0: $o,X1: $o] :
( sQ1_eqProxy((X0),(X1))
<=> ( (X0) = (X1) ) ),
introduced(definition,[new_symbols(definition,[sQ1_eqProxy])],[equality_proxy_definition]) ).
tff(f27,plain,
( ~ sQ1_eqProxy($true,sK0($true))
| ~ sQ1_eqProxy($true,sK0($true))
| ~ sQ1_eqProxy($true,$true) ),
inference(equality_proxy_replacement,[],[f18,f24,f24,f24]) ).
tff(f30,plain,
! [X0: $o] :
( sQ1_eqProxy($true,(X0))
| sQ1_eqProxy($true,sK0((X0)))
| sQ1_eqProxy($true,sK0((X0)))
| sQ1_eqProxy($true,(X0)) ),
inference(equality_proxy_replacement,[],[f12,f24,f24,f24,f24]) ).
tff(f32,plain,
( sQ1_eqProxy($true,sK0($true))
| sQ1_eqProxy($true,sK0($true))
| ~ sQ1_eqProxy($true,$true) ),
inference(equality_proxy_replacement,[],[f22,f24,f24,f24]) ).
tff(f33,plain,
! [X0: $o] :
( sQ1_eqProxy($true,(X0))
| ~ sQ1_eqProxy($true,sK0((X0)))
| sQ1_eqProxy($true,(X0))
| ~ sQ1_eqProxy($true,sK0((X0))) ),
inference(equality_proxy_replacement,[],[f9,f24,f24,f24,f24]) ).
tff(f37,plain,
! [X0: $o] :
( ~ sQ1_eqProxy($true,sK0((X0)))
| sQ1_eqProxy($true,(X0)) ),
inference(duplicate_literal_removal,[],[f33]) ).
tff(f38,plain,
( sQ1_eqProxy($true,sK0($true))
| ~ sQ1_eqProxy($true,$true) ),
inference(duplicate_literal_removal,[],[f32]) ).
tff(f39,plain,
! [X0: $o] :
( sQ1_eqProxy($true,sK0((X0)))
| sQ1_eqProxy($true,(X0)) ),
inference(duplicate_literal_removal,[],[f30]) ).
tff(f40,plain,
( ~ sQ1_eqProxy($true,sK0($true))
| ~ sQ1_eqProxy($true,$true) ),
inference(duplicate_literal_removal,[],[f27]) ).
tff(f42,definition,
( spl2_1
<=> sQ1_eqProxy($true,$true) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f43,plain,
( ~ sQ1_eqProxy($true,$true)
| spl2_1 ),
inference(avatar_component_clause,[],[f42]) ).
tff(f45,definition,
( spl2_2
<=> sQ1_eqProxy($true,sK0($true)) ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f47,plain,
( ~ spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f38,f45,f42]) ).
tff(f49,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(avatar_split_clause,[],[f40,f45,f42]) ).
tff(f50,plain,
! [X0: $o] :
( sQ1_eqProxy($true,(X0))
| sQ1_eqProxy($true,(X0)) ),
inference(resolution,[],[f39,f37]) ).
tff(f51,plain,
! [X0: $o] : sQ1_eqProxy($true,(X0)),
inference(duplicate_literal_removal,[],[f50]) ).
tff(f53,plain,
( $false
| spl2_1 ),
inference(resolution,[],[f51,f43]) ).
tff(f54,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f53]) ).
cnf(s1,plain,
( ~ spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f47]) ).
cnf(s2,plain,
( ~ spl2_1
| ~ spl2_2 ),
inference(sat_conversion,[],[f49]) ).
cnf(s3,plain,
spl2_1,
inference(sat_conversion,[],[f54]) ).
cnf(s4,plain,
~ spl2_2,
inference(rat,[],[s2,s3]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s4,s3]) ).
tff(f55,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO206_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 17:30:11 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 2.49/1.11 % (2594100)Detected formulas, will run a generic FOF schedule.
% 2.49/1.11 % (2594111)dis-21_1_sil=8000:lcm=predicate:random_seed=387950274: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)
% 2.49/1.11 % (2594111)First to succeed.
% 2.49/1.11 % (2594111)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2594100"
% 2.49/1.11 % (2594107)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=787686609:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.49/1.11 % (2594105)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=1689134212:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.49/1.11 % (2594106)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=4041345759:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.49/1.11 % (2594108)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=464022551:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.49/1.11 % (2594109)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=169649287:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.49/1.11 % (2594110)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3858091492:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.49/1.11 % (2594109)Also succeeded, but the first one will report.
% 2.49/1.11 % (2594110)Also succeeded, but the first one will report.
% 2.49/1.11 % (2594108)Also succeeded, but the first one will report.
% 2.49/1.11 % (2594111)Refutation found. Thanks to Tanya!
% 2.49/1.11 % SZS status Theorem for theBenchmark
% 2.49/1.11 % SZS output start Proof for theBenchmark
% See solution above
% 2.49/1.12 % (2594111)------------------------------
% 2.49/1.12 % (2594111)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.49/1.12 % (2594111)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.49/1.12 % (2594111)CaDiCaL version: 2.1.3
% 2.49/1.12 % (2594111)Termination reason: Refutation
% 2.49/1.12 % (2594111)Time elapsed: 0.001 s
% 2.49/1.12 % (2594111)Peak memory usage: 89 MB
% 2.49/1.12 % (2594111)Instructions burned: 1 (million)
% 2.49/1.12 % (2594111)------------------------------
% 2.49/1.12 % (2594111)------------------------------
% 2.49/1.12 % (2594100)Success in time 0.267 s
% 2.49/1.12 % Vampire exiting
%------------------------------------------------------------------------------