%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO012_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 : n016.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 02:24:43 PM UTC 2026
% Result : Theorem 2.74s 1.10s
% Output : Refutation 2.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 57 ( 8 unt; 0 typ; 6 def)
% Number of atoms : 202 ( 26 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 134 ( 55 ~; 55 |; 15 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 68 ( 66 fml; 2 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 9 usr; 10 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 1 ( 0 sgn 1 !; 0 ?; 1 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
bG0: $o ).
tff(func_def_3,type,
bG1: $o ).
tff(pred_def_3,type,
p: $o > $o ).
tff(f1,conjecture,
( p(( a
& b ))
=> p(( b
& a )) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj) ).
tff(f2,negated_conjecture,
~ ( p(( a
& b ))
=> p(( b
& a )) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,definition,
( ( b
& a )
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f4,definition,
( ( a
& b )
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition]) ).
tff(f5,plain,
~ ( p(bG1)
=> p(bG0) ),
inference(fool_elimination,[],[f2,f4,f3]) ).
tff(f6,plain,
( ~ p(bG0)
& p(bG1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f7,plain,
( ( ( a
& b )
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ~ a
| ~ b ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f8,plain,
( ( ( a
& b )
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ~ a
| ~ b ) ),
inference(flattening,[],[f7]) ).
tff(f9,plain,
( ( ( b
& a )
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ~ b
| ~ a ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f10,plain,
( ( ( b
& a )
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ~ b
| ~ a ) ),
inference(flattening,[],[f9]) ).
tff(f11,plain,
( ( $true = bG1 )
| ~ a
| ~ b ),
inference(cnf_transformation,[],[f8]) ).
tff(f12,plain,
( b
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f8]) ).
tff(f13,plain,
( a
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f8]) ).
tff(f14,plain,
( ( bG0 = $true )
| ~ b
| ~ a ),
inference(cnf_transformation,[],[f10]) ).
tff(f15,plain,
( a
| ( bG0 != $true ) ),
inference(cnf_transformation,[],[f10]) ).
tff(f16,plain,
( b
| ( bG0 != $true ) ),
inference(cnf_transformation,[],[f10]) ).
tff(f17,plain,
p(bG1),
inference(cnf_transformation,[],[f6]) ).
tff(f18,plain,
~ p(bG0),
inference(cnf_transformation,[],[f6]) ).
tff(f20,plain,
! [X0: $o] :
( ( $false = (X0) )
| ( $true = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f22,definition,
( spl2_1
<=> a ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f26,definition,
( spl2_2
<=> b ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f30,definition,
( spl2_3
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f31,plain,
( ( bG0 != $true )
| spl2_3 ),
inference(avatar_component_clause,[],[f30]) ).
tff(f32,plain,
( ( bG0 = $true )
| ~ spl2_3 ),
inference(avatar_component_clause,[],[f30]) ).
tff(f33,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_3 ),
inference(avatar_split_clause,[],[f14,f30,f26,f22]) ).
tff(f34,plain,
( ~ spl2_3
| spl2_1 ),
inference(avatar_split_clause,[],[f15,f22,f30]) ).
tff(f35,plain,
( ~ spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f16,f26,f30]) ).
tff(f37,definition,
( spl2_4
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f38,plain,
( ( $true != bG1 )
| spl2_4 ),
inference(avatar_component_clause,[],[f37]) ).
tff(f39,plain,
( ( $true = bG1 )
| ~ spl2_4 ),
inference(avatar_component_clause,[],[f37]) ).
tff(f40,plain,
( ~ spl2_2
| ~ spl2_1
| spl2_4 ),
inference(avatar_split_clause,[],[f11,f37,f22,f26]) ).
tff(f41,plain,
( ~ spl2_4
| spl2_2 ),
inference(avatar_split_clause,[],[f12,f26,f37]) ).
tff(f42,plain,
( ~ spl2_4
| spl2_1 ),
inference(avatar_split_clause,[],[f13,f22,f37]) ).
tff(f45,plain,
( ~ p($false)
| ( bG0 = $true ) ),
inference(superposition,[],[f18,f20]) ).
tff(f47,plain,
( p($false)
| ( $true = bG1 ) ),
inference(superposition,[],[f17,f20]) ).
tff(f49,plain,
( p($false)
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f47,f38]) ).
tff(f50,plain,
( ~ p($false)
| spl2_3 ),
inference(forward_subsumption_resolution,[],[f45,f31]) ).
tff(f52,plain,
( $false
| spl2_3
| spl2_4 ),
inference(forward_subsumption_resolution,[],[f50,f49]) ).
tff(f53,plain,
( spl2_3
| spl2_4 ),
inference(avatar_contradiction_clause,[],[f52]) ).
tff(f61,plain,
( ~ p($true)
| ~ spl2_3 ),
inference(superposition,[],[f18,f32]) ).
tff(f64,plain,
( p($true)
| ~ spl2_4 ),
inference(superposition,[],[f17,f39]) ).
tff(f66,plain,
( $false
| ~ spl2_3
| ~ spl2_4 ),
inference(forward_subsumption_resolution,[],[f64,f61]) ).
tff(f67,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[],[f66]) ).
cnf(s1,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_3 ),
inference(sat_conversion,[],[f33]) ).
cnf(s2,plain,
( spl2_1
| ~ spl2_3 ),
inference(sat_conversion,[],[f34]) ).
cnf(s3,plain,
( spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f35]) ).
cnf(s4,plain,
( ~ spl2_1
| ~ spl2_2
| spl2_4 ),
inference(sat_conversion,[],[f40]) ).
cnf(s5,plain,
( spl2_2
| ~ spl2_4 ),
inference(sat_conversion,[],[f41]) ).
cnf(s6,plain,
( spl2_1
| ~ spl2_4 ),
inference(sat_conversion,[],[f42]) ).
cnf(s7,plain,
( spl2_3
| spl2_4 ),
inference(sat_conversion,[],[f53]) ).
cnf(s10,plain,
( ~ spl2_3
| ~ spl2_4 ),
inference(sat_conversion,[],[f67]) ).
cnf(s11,plain,
spl2_1,
inference(rat,[],[s7,s2,s6]) ).
cnf(s12,plain,
spl2_2,
inference(rat,[],[s7,s3,s5]) ).
cnf(s13,plain,
spl2_4,
inference(rat,[],[s4,s11,s12]) ).
cnf(s14,plain,
spl2_3,
inference(rat,[],[s1,s11,s12]) ).
cnf(s15,plain,
$false,
inference(rat,[],[s10,s13,s14]) ).
tff(f68,plain,
$false,
inference(avatar_sat_refutation,[],[s15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO012_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 % Computer : n016.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Mon Sep 28 17:26:03 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.25 Running first-order theorem proving
% 0.09/0.25 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
% 2.74/1.10 % (3776533)Detected formulas, will run a generic FOF schedule.
% 2.74/1.10 % (3776626)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2357047832:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.74/1.10 % (3776626)First to succeed.
% 2.74/1.10 % (3776626)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-3776533"
% 2.74/1.10 % (3776624)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1860257139:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.74/1.10 % (3776621)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=2234498144:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.74/1.10 % (3776622)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=1498464682:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.74/1.10 % (3776625)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=4251385341:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.74/1.10 % (3776624)Refutation not found, incomplete strategy
% 2.74/1.10 % (3776624)------------------------------
% 2.74/1.10 % (3776624)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.10 % (3776624)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.10 % (3776624)CaDiCaL version: 2.1.3
% 2.74/1.10 % (3776624)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.10 % (3776624)Time elapsed: 0.002 s
% 2.74/1.10 % (3776624)Peak memory usage: 88 MB
% 2.74/1.10 % (3776624)Instructions burned: 1 (million)
% 2.74/1.10 % (3776625)Also succeeded, but the first one will report.
% 2.74/1.10 % (3776628)dis-21_1_sil=8000:lcm=predicate:random_seed=249331637: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)
% 2.74/1.10 % (3776628)Refutation not found, incomplete strategy
% 2.74/1.10 % (3776628)------------------------------
% 2.74/1.10 % (3776628)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.10 % (3776628)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.10 % (3776628)CaDiCaL version: 2.1.3
% 2.74/1.10 % (3776628)Termination reason: Refutation not found, incomplete strategy
% 2.74/1.10 % (3776628)Time elapsed: 0.002 s
% 2.74/1.10 % (3776628)Peak memory usage: 88 MB
% 2.74/1.10 % (3776623)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=1290441723:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.74/1.10 % (3776626)Refutation found. Thanks to Tanya!
% 2.74/1.10 % SZS status Theorem for theBenchmark
% 2.74/1.10 % SZS output start Proof for theBenchmark
% See solution above
% 2.74/1.11 % (3776626)------------------------------
% 2.74/1.11 % (3776626)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.74/1.11 % (3776626)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.74/1.11 % (3776626)CaDiCaL version: 2.1.3
% 2.74/1.11 % (3776626)Termination reason: Refutation
% 2.74/1.11 % (3776626)Time elapsed: 0.002 s
% 2.74/1.11 % (3776626)Peak memory usage: 90 MB
% 2.74/1.11 % (3776626)Instructions burned: 2 (million)
% 2.74/1.11 % (3776626)------------------------------
% 2.74/1.11 % (3776626)------------------------------
% 2.74/1.11 % (3776533)Success in time 0.313 s
% 2.74/1.11 % Vampire exiting
%------------------------------------------------------------------------------