%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO365_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 02:26:03 PM UTC 2026
% Result : Theorem 5.64s 1.85s
% Output : Refutation 5.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 10 unt; 0 typ; 8 def)
% Number of atoms : 205 ( 21 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 133 ( 52 ~; 62 |; 4 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 62 ( 60 fml; 2 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 12 usr; 13 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_2,type,
cC: $o > $o ).
tff(f1,axiom,
( ( cEXT2 = cC(cA) )
=> cC(cA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT2_def) ).
tff(f3,conjecture,
( cEXT_eq_0
=> cEXT2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT2A) ).
tff(f4,negated_conjecture,
~ ( cEXT_eq_0
=> cEXT2 ),
inference(negated_conjecture,[status(cth)],[f3]) ).
tff(f5,definition,
( cA
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f6,definition,
( cA
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition]) ).
tff(f7,plain,
( cEXT2
<=> ( cC(bG1)
=> cC(bG0) ) ),
inference(fool_elimination,[],[f1,f6,f5]) ).
tff(f11,plain,
( ( cC(bG1)
=> cC(bG0) )
=> cEXT2 ),
inference(unused_predicate_definition_removal,[],[f7]) ).
tff(f12,plain,
( cEXT2
| ( ~ cC(bG0)
& cC(bG1) ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f14,plain,
( ~ cEXT2
& cEXT_eq_0 ),
inference(ennf_transformation,[],[f4]) ).
tff(f15,plain,
( ( cA
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ~ cA ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f16,plain,
( ( cA
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ~ cA ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f18,plain,
( ( $true = bG1 )
| ~ cA ),
inference(cnf_transformation,[],[f15]) ).
tff(f19,plain,
( cA
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f15]) ).
tff(f20,plain,
( ( bG0 = $true )
| ~ cA ),
inference(cnf_transformation,[],[f16]) ).
tff(f21,plain,
( cA
| ( bG0 != $true ) ),
inference(cnf_transformation,[],[f16]) ).
tff(f22,plain,
( cEXT2
| cC(bG1) ),
inference(cnf_transformation,[],[f12]) ).
tff(f23,plain,
( cEXT2
| ~ cC(bG0) ),
inference(cnf_transformation,[],[f12]) ).
tff(f27,plain,
~ cEXT2,
inference(cnf_transformation,[],[f14]) ).
tff(f29,plain,
! [X0: $o] :
( ( $false = (X0) )
| ( $true = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f35,definition,
( spl2_1
<=> cC(bG1) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
tff(f37,plain,
( cC(bG1)
| ~ spl2_1 ),
inference(avatar_component_clause,[],[f35]) ).
tff(f39,definition,
( spl2_2
<=> cEXT2 ),
introduced(definition,[new_symbols(definition,[spl2_2])],[avatar_definition]) ).
tff(f42,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[],[f22,f39,f35]) ).
tff(f44,definition,
( spl2_3
<=> cC(bG0) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
tff(f46,plain,
( ~ cC(bG0)
| spl2_3 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f47,plain,
( ~ spl2_3
| spl2_2 ),
inference(avatar_split_clause,[],[f23,f39,f44]) ).
tff(f49,definition,
( spl2_4
<=> cA ),
introduced(definition,[new_symbols(definition,[spl2_4])],[avatar_definition]) ).
tff(f53,definition,
( spl2_5
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
tff(f54,plain,
( ( bG0 != $true )
| spl2_5 ),
inference(avatar_component_clause,[],[f53]) ).
tff(f55,plain,
( ( bG0 = $true )
| ~ spl2_5 ),
inference(avatar_component_clause,[],[f53]) ).
tff(f56,plain,
( ~ spl2_4
| spl2_5 ),
inference(avatar_split_clause,[],[f20,f53,f49]) ).
tff(f57,plain,
( ~ spl2_5
| spl2_4 ),
inference(avatar_split_clause,[],[f21,f49,f53]) ).
tff(f59,definition,
( spl2_6
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
tff(f60,plain,
( ( $true != bG1 )
| spl2_6 ),
inference(avatar_component_clause,[],[f59]) ).
tff(f61,plain,
( ( $true = bG1 )
| ~ spl2_6 ),
inference(avatar_component_clause,[],[f59]) ).
tff(f62,plain,
( ~ spl2_4
| spl2_6 ),
inference(avatar_split_clause,[],[f18,f59,f49]) ).
tff(f63,plain,
( ~ spl2_6
| spl2_4 ),
inference(avatar_split_clause,[],[f19,f49,f59]) ).
tff(f64,plain,
~ spl2_2,
inference(avatar_split_clause,[],[f27,f39]) ).
tff(f67,plain,
( ~ cC($false)
| ( bG0 = $true )
| spl2_3 ),
inference(superposition,[],[f46,f29]) ).
tff(f69,plain,
( cC($false)
| ( $true = bG1 )
| ~ spl2_1 ),
inference(superposition,[],[f37,f29]) ).
tff(f71,plain,
( cC($false)
| ~ spl2_1
| spl2_6 ),
inference(forward_subsumption_resolution,[],[f69,f60]) ).
tff(f72,plain,
( ~ cC($false)
| spl2_3
| spl2_5 ),
inference(forward_subsumption_resolution,[],[f67,f54]) ).
tff(f74,plain,
( $false
| ~ spl2_1
| spl2_3
| spl2_5
| spl2_6 ),
inference(forward_subsumption_resolution,[],[f72,f71]) ).
tff(f75,plain,
( ~ spl2_1
| spl2_3
| spl2_5
| spl2_6 ),
inference(avatar_contradiction_clause,[],[f74]) ).
tff(f83,plain,
( ~ cC($true)
| spl2_3
| ~ spl2_5 ),
inference(superposition,[],[f46,f55]) ).
tff(f86,plain,
( cC($true)
| ~ spl2_1
| ~ spl2_6 ),
inference(superposition,[],[f37,f61]) ).
tff(f88,plain,
( $false
| ~ spl2_1
| spl2_3
| ~ spl2_5
| ~ spl2_6 ),
inference(forward_subsumption_resolution,[],[f86,f83]) ).
tff(f89,plain,
( ~ spl2_1
| spl2_3
| ~ spl2_5
| ~ spl2_6 ),
inference(avatar_contradiction_clause,[],[f88]) ).
cnf(s1,plain,
( spl2_1
| spl2_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( spl2_2
| ~ spl2_3 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
( ~ spl2_4
| spl2_5 ),
inference(sat_conversion,[],[f56]) ).
cnf(s4,plain,
( spl2_4
| ~ spl2_5 ),
inference(sat_conversion,[],[f57]) ).
cnf(s5,plain,
( ~ spl2_4
| spl2_6 ),
inference(sat_conversion,[],[f62]) ).
cnf(s6,plain,
( spl2_4
| ~ spl2_6 ),
inference(sat_conversion,[],[f63]) ).
cnf(s7,plain,
~ spl2_2,
inference(sat_conversion,[],[f64]) ).
cnf(s8,plain,
( ~ spl2_1
| spl2_3
| spl2_5
| spl2_6 ),
inference(sat_conversion,[],[f75]) ).
cnf(s11,plain,
( ~ spl2_1
| spl2_3
| ~ spl2_5
| ~ spl2_6 ),
inference(sat_conversion,[],[f89]) ).
cnf(s12,plain,
~ spl2_3,
inference(rat,[],[s2,s7]) ).
cnf(s13,plain,
spl2_1,
inference(rat,[],[s1,s7]) ).
cnf(s14,plain,
spl2_4,
inference(rat,[],[s8,s4,s6,s12,s13]) ).
cnf(s15,plain,
spl2_6,
inference(rat,[],[s5,s14]) ).
cnf(s16,plain,
spl2_5,
inference(rat,[],[s3,s14]) ).
cnf(s17,plain,
$false,
inference(rat,[],[s11,s13,s12,s15,s16]) ).
tff(f90,plain,
$false,
inference(avatar_sat_refutation,[],[s17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO365_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.27 % Computer : n007.cluster.edu
% 0.12/0.27 % Model : x86_64 x86_64
% 0.12/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.27 % Memory : 8046.5625MB
% 0.12/0.27 % OS : Linux 6.8.0-71-generic
% 0.12/0.27 % CPULimit : 300
% 0.12/0.27 % WCLimit : 300
% 0.12/0.27 % DateTime : Mon Sep 28 17:34:25 UTC 2026
% 0.12/0.28 % CPUTime :
% 0.12/0.28 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.33 Running first-order theorem proving
% 0.27/0.33 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
% 5.64/1.85 % (2606015)Detected formulas, will run a generic FOF schedule.
% 5.64/1.85 % (2606023)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2316904180:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.64/1.85 % (2606023)Refutation not found, incomplete strategy
% 5.64/1.85 % (2606023)------------------------------
% 5.64/1.85 % (2606023)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.85 % (2606023)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.85 % (2606023)CaDiCaL version: 2.1.3
% 5.64/1.85 % (2606023)Termination reason: Refutation not found, incomplete strategy
% 5.64/1.85 % (2606023)Time elapsed: 0.001 s
% 5.64/1.85 % (2606023)Peak memory usage: 88 MB
% 5.64/1.85 % (2606026)dis-21_1_sil=8000:lcm=predicate:random_seed=113848652: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)
% 5.64/1.85 % (2606026)Refutation not found, incomplete strategy
% 5.64/1.85 % (2606026)------------------------------
% 5.64/1.85 % (2606026)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.85 % (2606026)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.85 % (2606026)CaDiCaL version: 2.1.3
% 5.64/1.85 % (2606026)Termination reason: Refutation not found, incomplete strategy
% 5.64/1.85 % (2606026)Time elapsed: 0.002 s
% 5.64/1.85 % (2606026)Peak memory usage: 88 MB
% 5.64/1.85 % (2606024)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1641217779:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.64/1.85 % (2606020)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=1934283129:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.64/1.85 % (2606025)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3106942622:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.64/1.85 % (2606022)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=260333504:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.64/1.85 % (2606021)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=2532402990:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.64/1.85 % (2606025)First to succeed.
% 5.64/1.85 % (2606025)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2606015"
% 5.64/1.85 % (2606024)Instruction limit reached!
% 5.64/1.85 % (2606024)------------------------------
% 5.64/1.85 % (2606024)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.85 % (2606024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.85 % (2606024)CaDiCaL version: 2.1.3
% 5.64/1.85 % (2606024)Termination reason: Instruction limit
% 5.64/1.85 % (2606024)Termination phase: Saturation
% 5.64/1.85 % (2606024)Time elapsed: 0.084 s
% 5.64/1.85 % (2606024)Peak memory usage: 87 MB
% 5.64/1.85 % (2606024)Instructions burned: 119 (million)
% 5.64/1.85 % (2606023)------------------------------
% 5.64/1.85 % (2606023)------------------------------
% 5.64/1.85 % (2606026)------------------------------
% 5.64/1.85 % (2606026)------------------------------
% 5.64/1.85 % (2606034)lrs+10_1_sil=8000:sp=occurrence:random_seed=3709963354:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.64/1.85 % (2606035)lrs+10_1_sil=32000:urr=on:br=off:random_seed=1628848305:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2995 on theBenchmark for (2995ds/157Mi)
% 5.64/1.85 % (2606034)Also succeeded, but the first one will report.
% 5.64/1.85 % (2606025)Refutation found. Thanks to Tanya!
% 5.64/1.85 % SZS status Theorem for theBenchmark
% 5.64/1.85 % SZS output start Proof for theBenchmark
% See solution above
% 5.64/1.85 % (2606025)------------------------------
% 5.64/1.85 % (2606025)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.64/1.85 % (2606025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.64/1.85 % (2606025)CaDiCaL version: 2.1.3
% 5.64/1.85 % (2606025)Termination reason: Refutation
% 5.64/1.85 % (2606025)Time elapsed: 0.005 s
% 5.64/1.85 % (2606025)Peak memory usage: 90 MB
% 5.64/1.85 % (2606025)Instructions burned: 2 (million)
% 5.64/1.85 % (2606025)------------------------------
% 5.64/1.85 % (2606025)------------------------------
% 5.64/1.85 % (2606015)Success in time 0.657 s
% 5.64/1.85 % Vampire exiting
%------------------------------------------------------------------------------