%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ083_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 : n005.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 12:31:32 PM UTC 2026
% Result : Theorem 3.53s 1.38s
% Output : Refutation 3.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 59 ( 13 unt; 0 typ; 7 def)
% Number of atoms : 280 ( 56 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 136 ( 59 ~; 51 |; 8 &)
% ( 9 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 210 ( 149 fml; 61 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 29 ( 0 sgn 27 !; 2 ?; 29 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_3,type,
bG0: $o > $o ).
tff(func_def_4,type,
bG1: $o ).
tff(func_def_5,type,
bG2: $o > $o ).
tff(func_def_6,type,
sK3: $o ).
tff(pred_def_1,type,
says: ( $i * $o ) > $o ).
tff(f1,axiom,
says(peter,
! [X0: $o] :
( says(peter,(X0))
=> ~ (X0) )),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).
tff(f2,conjecture,
~ ! [X0: $o] :
( says(peter,(X0))
=> (X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
tff(f3,negated_conjecture,
~ ~ ! [X0: $o] :
( says(peter,(X0))
=> (X0) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
tff(f4,plain,
says(peter,
! [X0: $o] :
( says(peter,(X0))
=> ~ (X0) )),
inference(rectify,[],[f1]) ).
tff(f5,definition,
! [X0: $o] :
( ( $true = (X0) )
<=> ( $true = bG0((X0)) ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f6,definition,
( ! [X0: $o] :
( says(peter,bG0((X0)))
=> ( $true != (X0) ) )
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition]) ).
tff(f7,plain,
says(peter,bG1),
inference(fool_elimination,[],[f4,f6,f5]) ).
tff(f8,plain,
~ ~ ! [X0: $o] :
( says(peter,(X0))
=> (X0) ),
inference(rectify,[],[f3]) ).
tff(f9,definition,
! [X0: $o] :
( ( $true = (X0) )
<=> ( $true = bG2((X0)) ) ),
introduced(definition,[new_symbols(definition,[bG2])],[fool_formula_definition]) ).
tff(f10,plain,
~ ~ ! [X0: $o] :
( says(peter,bG2((X0)))
=> ( $true = (X0) ) ),
inference(fool_elimination,[],[f8,f9]) ).
tff(f11,plain,
( ! [X0: $o] :
( says(peter,bG0((X0)))
=> ( $true != (X0) ) )
<=> ( $true = bG1 ) ),
inference(flattening,[],[f6]) ).
tff(f12,plain,
! [X0: $o] :
( says(peter,bG2((X0)))
=> ( $true = (X0) ) ),
inference(flattening,[],[f10]) ).
tff(f13,plain,
( ! [X0: $o] :
( ( $true != (X0) )
| ~ says(peter,bG0((X0))) )
<=> ( $true = bG1 ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f14,plain,
! [X0: $o] :
( ( $true = (X0) )
| ~ says(peter,bG2((X0))) ),
inference(ennf_transformation,[],[f12]) ).
tff(f15,plain,
! [X0: $o] :
( ( ( $true = (X0) )
| ( $true != bG2((X0)) ) )
& ( ( $true = bG2((X0)) )
| ( $true != (X0) ) ) ),
inference(nnf_transformation,[],[f9]) ).
tff(f16,plain,
( ( ! [X0: $o] :
( ( $true != (X0) )
| ~ says(peter,bG0((X0))) )
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ? [X0: $o] :
( ( $true = (X0) )
& says(peter,bG0((X0))) ) ) ),
inference(nnf_transformation,[],[f13]) ).
tff(f17,plain,
( ( ! [X0: $o] :
( ( $true != (X0) )
| ~ says(peter,bG0((X0))) )
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ? [X1: $o] :
( ( $true = (X1) )
& says(peter,bG0((X1))) ) ) ),
inference(rectify,[],[f16]) ).
tff(f18,plain,
( ( ! [X0: $o] :
( ( $true != (X0) )
| ~ says(peter,bG0((X0))) )
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ( ( $true = sK3 )
& says(peter,bG0(sK3)) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X1,sK3)],[f17]) ).
tff(f19,plain,
! [X0: $o] :
( ( ( $true = (X0) )
| ( $true != bG0((X0)) ) )
& ( ( $true = bG0((X0)) )
| ( $true != (X0) ) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f21,plain,
! [X0: $o] :
( ( $true != bG2((X0)) )
| ( $true = (X0) ) ),
inference(cnf_transformation,[],[f15]) ).
tff(f24,plain,
! [X0: $o] :
( ( $true != (X0) )
| ~ says(peter,bG0((X0)))
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f18]) ).
tff(f25,plain,
! [X0: $o] :
( ( $true = bG0((X0)) )
| ( $true != (X0) ) ),
inference(cnf_transformation,[],[f19]) ).
tff(f27,plain,
says(peter,bG1),
inference(cnf_transformation,[],[f7]) ).
tff(f28,plain,
! [X0: $o] :
( ~ says(peter,bG2((X0)))
| ( $true = (X0) ) ),
inference(cnf_transformation,[],[f14]) ).
tff(f30,plain,
! [X0: $o] :
( ( $false = (X0) )
| ( $true = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f32,plain,
( ~ says(peter,bG0($true))
| ( $true != bG1 ) ),
inference(equality_resolution,[],[f24]) ).
tff(f33,plain,
$true = bG0($true),
inference(equality_resolution,[],[f25]) ).
tff(f39,definition,
( spl4_2
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[spl4_2])],[avatar_definition]) ).
tff(f40,plain,
( ( $true != bG1 )
| spl4_2 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f41,plain,
( ( $true = bG1 )
| ~ spl4_2 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f49,definition,
( spl4_4
<=> says(peter,bG0($true)) ),
introduced(definition,[new_symbols(definition,[spl4_4])],[avatar_definition]) ).
tff(f51,plain,
( ~ says(peter,bG0($true))
| spl4_4 ),
inference(avatar_component_clause,[],[f49]) ).
tff(f52,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(avatar_split_clause,[],[f32,f49,f39]) ).
tff(f53,plain,
( says(peter,$true)
| ~ spl4_2 ),
inference(superposition,[],[f27,f41]) ).
tff(f54,plain,
( ~ says(peter,$true)
| spl4_4 ),
inference(forward_demodulation,[],[f51,f33]) ).
tff(f55,plain,
( $false
| ~ spl4_2
| spl4_4 ),
inference(forward_subsumption_resolution,[],[f54,f53]) ).
tff(f56,plain,
( ~ spl4_2
| spl4_4 ),
inference(avatar_contradiction_clause,[],[f55]) ).
tff(f65,plain,
( says(peter,$false)
| ( $true = bG1 ) ),
inference(superposition,[],[f27,f30]) ).
tff(f66,plain,
! [X0: $o] :
( ~ says(peter,$false)
| ( $true = (X0) )
| ( $true = bG2((X0)) ) ),
inference(superposition,[],[f28,f30]) ).
tff(f74,definition,
( spl4_5
<=> ! [X0: $o] :
( ( $true = (X0) )
| ( $true = bG2((X0)) ) ) ),
introduced(definition,[new_symbols(definition,[spl4_5])],[avatar_definition]) ).
tff(f75,plain,
( ! [X0: $o] :
( ( $true = (X0) )
| ( $true = bG2((X0)) ) )
| ~ spl4_5 ),
inference(avatar_component_clause,[],[f74]) ).
tff(f77,definition,
( spl4_6
<=> says(peter,$false) ),
introduced(definition,[new_symbols(definition,[spl4_6])],[avatar_definition]) ).
tff(f80,plain,
( spl4_5
| ~ spl4_6 ),
inference(avatar_split_clause,[],[f66,f77,f74]) ).
tff(f81,plain,
( says(peter,$false)
| spl4_2 ),
inference(forward_subsumption_resolution,[],[f65,f40]) ).
tff(f82,plain,
( spl4_6
| spl4_2 ),
inference(avatar_split_clause,[],[f81,f39,f77]) ).
tff(f88,plain,
( ! [X0: $o] : ( $true = (X0) )
| ~ spl4_5 ),
inference(forward_subsumption_resolution,[],[f75,f21]) ).
tff(f95,plain,
( ( $true != $true )
| spl4_2
| ~ spl4_5 ),
inference(superposition,[],[f40,f88]) ).
tff(f100,plain,
( $false
| spl4_2
| ~ spl4_5 ),
inference(trivial_inequality_removal,[],[f95]) ).
tff(f101,plain,
( spl4_2
| ~ spl4_5 ),
inference(avatar_contradiction_clause,[],[f100]) ).
cnf(s3,plain,
( ~ spl4_2
| ~ spl4_4 ),
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
( ~ spl4_2
| spl4_4 ),
inference(sat_conversion,[],[f56]) ).
cnf(s6,plain,
( spl4_5
| ~ spl4_6 ),
inference(sat_conversion,[],[f80]) ).
cnf(s7,plain,
( spl4_2
| spl4_6 ),
inference(sat_conversion,[],[f82]) ).
cnf(s8,plain,
( spl4_2
| ~ spl4_5 ),
inference(sat_conversion,[],[f101]) ).
cnf(s9,plain,
~ spl4_2,
inference(rat,[],[s3,s4]) ).
cnf(s10,plain,
~ spl4_5,
inference(rat,[],[s8,s9]) ).
cnf(s11,plain,
spl4_6,
inference(rat,[],[s7,s9]) ).
cnf(s14,plain,
$false,
inference(rat,[],[s6,s11,s10]) ).
tff(f105,plain,
$false,
inference(avatar_sat_refutation,[],[s14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ083_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n005.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sun Sep 27 22:40:31 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 3.53/1.38 % (244705)Detected formulas, will run a generic FOF schedule.
% 3.53/1.38 % (244771)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2380822530:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.53/1.38 % (244771)Refutation not found, incomplete strategy
% 3.53/1.38 % (244771)------------------------------
% 3.53/1.38 % (244771)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.38 % (244771)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.38 % (244771)CaDiCaL version: 2.1.3
% 3.53/1.38 % (244771)Termination reason: Refutation not found, incomplete strategy
% 3.53/1.38 % (244771)Time elapsed: 0.001 s
% 3.53/1.38 % (244771)Peak memory usage: 88 MB
% 3.53/1.38 % (244770)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=283085415:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.53/1.38 % (244773)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=976213961:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.53/1.38 % (244774)dis-21_1_sil=8000:lcm=predicate:random_seed=505675760: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)
% 3.53/1.38 % (244769)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=3387474965:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.53/1.38 % (244768)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=613924427:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.53/1.38 % (244772)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=874251610:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.53/1.38 % (244773)First to succeed.
% 3.53/1.38 % (244773)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-244705"
% 3.53/1.38 % (244772)Instruction limit reached!
% 3.53/1.38 % (244772)------------------------------
% 3.53/1.38 % (244772)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.38 % (244772)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.38 % (244772)CaDiCaL version: 2.1.3
% 3.53/1.38 % (244772)Termination reason: Instruction limit
% 3.53/1.38 % (244772)Termination phase: Saturation
% 3.53/1.38 % (244772)Time elapsed: 0.058 s
% 3.53/1.38 % (244772)Peak memory usage: 88 MB
% 3.53/1.38 % (244772)Instructions burned: 120 (million)
% 3.53/1.38 % (244774)Instruction limit reached!
% 3.53/1.38 % (244774)------------------------------
% 3.53/1.38 % (244774)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.38 % (244774)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.38 % (244774)CaDiCaL version: 2.1.3
% 3.53/1.38 % (244774)Termination reason: Instruction limit
% 3.53/1.38 % (244774)Termination phase: Saturation
% 3.53/1.38 % (244774)Time elapsed: 0.069 s
% 3.53/1.38 % (244774)Peak memory usage: 90 MB
% 3.53/1.38 % (244774)Instructions burned: 131 (million)
% 3.53/1.38 % (244771)------------------------------
% 3.53/1.38 % (244771)------------------------------
% 3.53/1.38 % (244782)lrs+10_1_sil=8000:sp=occurrence:random_seed=1346949331:i=285:sd=3:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/285Mi)
% 3.53/1.38 % (244782)Also succeeded, but the first one will report.
% 3.53/1.38 % (244783)lrs+10_1_sil=32000:urr=on:br=off:random_seed=2271741491:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 3.53/1.38 % (244783)Also succeeded, but the first one will report.
% 3.53/1.38 % (244773)Refutation found. Thanks to Tanya!
% 3.53/1.38 % SZS status Theorem for theBenchmark
% 3.53/1.38 % SZS output start Proof for theBenchmark
% See solution above
% 3.53/1.38 % (244773)------------------------------
% 3.53/1.38 % (244773)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.53/1.38 % (244773)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.53/1.38 % (244773)CaDiCaL version: 2.1.3
% 3.53/1.38 % (244773)Termination reason: Refutation
% 3.53/1.38 % (244773)Time elapsed: 0.004 s
% 3.53/1.38 % (244773)Peak memory usage: 90 MB
% 3.53/1.38 % (244773)Instructions burned: 3 (million)
% 3.53/1.38 % (244773)------------------------------
% 3.53/1.38 % (244773)------------------------------
% 3.53/1.38 % (244705)Success in time 0.433 s
% 3.53/1.38 % Vampire exiting
%------------------------------------------------------------------------------