%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO345_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 : 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 02:26:00 PM UTC 2026
% Result : Theorem 3.40s 1.15s
% Output : Refutation 3.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 12 unt; 0 typ; 3 def)
% Number of atoms : 90 ( 26 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 34 ( 19 ~; 11 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 55 ( 53 fml; 2 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 5 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 1 ( 0 sgn 1 !; 0 ?; 1 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
cH: $o > $i ).
tff(func_def_3,type,
bG0: $o ).
tff(f1,conjecture,
cH(cH($true) = cH($false)) = cH($false),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM615) ).
tff(f2,negated_conjecture,
( ( ~ cH(cH($true) = cH($false)) ) = cH($false) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
( ( ~ cH(cH($true) = cH($false)) ) = cH($false) ),
inference(rectify,[],[f2]) ).
tff(f4,definition,
( ( cH($true) = cH($false) )
<=> ( $true = bG0 ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f5,plain,
( ( ~ cH($false) ) = cH(bG0) ),
inference(fool_elimination,[],[f3,f4]) ).
tff(f6,plain,
cH($false) != cH(bG0),
inference(flattening,[],[f5]) ).
tff(f7,plain,
( ( ( cH($true) = cH($false) )
| ( $true != bG0 ) )
& ( ( $true = bG0 )
| ( cH($true) != cH($false) ) ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f9,plain,
( ( cH($true) = cH($false) )
| ( $true != bG0 ) ),
inference(cnf_transformation,[],[f7]) ).
tff(f10,plain,
cH($false) != cH(bG0),
inference(cnf_transformation,[],[f6]) ).
tff(f12,plain,
! [X0: $o] :
( ( $false = (X0) )
| ( $true = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f14,definition,
( spl1_1
<=> ( cH($true) = cH($false) ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
tff(f18,definition,
( spl1_2
<=> ( $true = bG0 ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
tff(f20,plain,
( ( $true = bG0 )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f18]) ).
tff(f22,plain,
( ~ spl1_2
| spl1_1 ),
inference(avatar_split_clause,[],[f9,f14,f18]) ).
tff(f25,plain,
( ( cH($false) != cH($false) )
| ( $true = bG0 ) ),
inference(superposition,[],[f10,f12]) ).
tff(f27,plain,
$true = bG0,
inference(trivial_inequality_removal,[],[f25]) ).
tff(f30,plain,
spl1_2,
inference(avatar_split_clause,[],[f27,f18]) ).
tff(f32,plain,
( ( cH($true) != cH($false) )
| ~ spl1_2 ),
inference(superposition,[],[f10,f20]) ).
tff(f34,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[],[f32,f18,f14]) ).
cnf(s2,plain,
( spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s4,plain,
spl1_2,
inference(sat_conversion,[],[f30]) ).
cnf(s5,plain,
( ~ spl1_1
| ~ spl1_2 ),
inference(sat_conversion,[],[f34]) ).
cnf(s6,plain,
~ spl1_1,
inference(rat,[],[s5,s4]) ).
cnf(s7,plain,
$false,
inference(rat,[],[s2,s4,s6]) ).
tff(f35,plain,
$false,
inference(avatar_sat_refutation,[],[s7]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO345_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 : n011.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 17:35:16 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
% 3.40/1.15 % (3571508)Detected formulas, will run a generic FOF schedule.
% 3.40/1.15 % (3571570)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=642780356:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 3.40/1.15 % (3571572)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2822087186:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 3.40/1.15 % (3571573)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2078062623:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 3.40/1.15 % (3571571)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=1037665289:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 3.40/1.15 % (3571575)dis-21_1_sil=8000:lcm=predicate:random_seed=2602332611:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 3.40/1.15 % (3571569)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=3854449256:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 3.40/1.15 % (3571574)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3511295707:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 3.40/1.15 % (3571572)Refutation not found, incomplete strategy
% 3.40/1.15 % (3571572)------------------------------
% 3.40/1.15 % (3571572)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.15 % (3571572)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.15 % (3571572)CaDiCaL version: 2.1.3
% 3.40/1.15 % (3571572)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.15 % (3571572)Time elapsed: 0.001 s
% 3.40/1.15 % (3571572)Peak memory usage: 88 MB
% 3.40/1.15 % (3571575)Refutation not found, incomplete strategy
% 3.40/1.15 % (3571575)------------------------------
% 3.40/1.15 % (3571575)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.15 % (3571575)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.15 % (3571575)CaDiCaL version: 2.1.3
% 3.40/1.15 % (3571575)Termination reason: Refutation not found, incomplete strategy
% 3.40/1.15 % (3571575)Time elapsed: 0.001 s
% 3.40/1.15 % (3571575)Peak memory usage: 88 MB
% 3.40/1.15 % (3571574)First to succeed.
% 3.40/1.15 % (3571574)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-3571508"
% 3.40/1.15 % (3571573)Instruction limit reached!
% 3.40/1.15 % (3571573)------------------------------
% 3.40/1.15 % (3571573)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.15 % (3571573)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.15 % (3571573)CaDiCaL version: 2.1.3
% 3.40/1.15 % (3571573)Termination reason: Instruction limit
% 3.40/1.15 % (3571573)Termination phase: Saturation
% 3.40/1.15 % (3571573)Time elapsed: 0.051 s
% 3.40/1.15 % (3571573)Peak memory usage: 87 MB
% 3.40/1.15 % (3571573)Instructions burned: 120 (million)
% 3.40/1.15 % (3571583)lrs+10_1_sil=8000:sp=occurrence:random_seed=51492888:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.40/1.15 % (3571583)Also succeeded, but the first one will report.
% 3.40/1.15 % (3571572)------------------------------
% 3.40/1.15 % (3571572)------------------------------
% 3.40/1.15 % (3571575)------------------------------
% 3.40/1.15 % (3571575)------------------------------
% 3.40/1.15 % (3571574)Refutation found. Thanks to Tanya!
% 3.40/1.15 % SZS status Theorem for theBenchmark
% 3.40/1.15 % SZS output start Proof for theBenchmark
% See solution above
% 3.40/1.15 % (3571574)------------------------------
% 3.40/1.15 % (3571574)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.40/1.15 % (3571574)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.40/1.15 % (3571574)CaDiCaL version: 2.1.3
% 3.40/1.15 % (3571574)Termination reason: Refutation
% 3.40/1.15 % (3571574)Time elapsed: 0.002 s
% 3.40/1.15 % (3571574)Peak memory usage: 89 MB
% 3.40/1.15 % (3571574)Instructions burned: 1 (million)
% 3.40/1.15 % (3571574)------------------------------
% 3.40/1.15 % (3571574)------------------------------
% 3.40/1.15 % (3571508)Success in time 0.402 s
% 3.40/1.15 % Vampire exiting
%------------------------------------------------------------------------------