%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ137_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 : n009.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 12:31:42 PM UTC 2026
% Result : Theorem 3.12s 1.18s
% Output : Refutation 3.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 12
% Syntax : Number of formulae : 75 ( 20 unt; 0 typ; 9 def)
% Number of atoms : 319 ( 46 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 148 ( 66 ~; 60 |; 7 &)
% ( 11 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 203 ( 164 fml; 39 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 13 usr; 12 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 21 ( 0 sgn 18 !; 3 ?; 21 :)
% 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(func_def_7,type,
sK4: $o ).
tff(pred_def_1,type,
says: ( $i * $o ) > $o ).
tff(f1,axiom,
says(peter,
! [X0: $o] :
( says(peter,(X0))
=> ~ (X0) )),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax1) ).
tff(f2,conjecture,
! [X0: $o] : says(peter,(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
tff(f3,negated_conjecture,
~ ! [X0: $o] : says(peter,(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)),
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))),
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] :
( ( $true != (X0) )
| ~ says(peter,bG0((X0))) )
<=> ( $true = bG1 ) ),
inference(ennf_transformation,[],[f11]) ).
tff(f13,plain,
? [X0: $o] : ~ says(peter,bG2((X0))),
inference(ennf_transformation,[],[f10]) ).
tff(f15,plain,
( ( ! [X0: $o] :
( ( $true != (X0) )
| ~ says(peter,bG0((X0))) )
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ? [X0: $o] :
( ( $true = (X0) )
& says(peter,bG0((X0))) ) ) ),
inference(nnf_transformation,[],[f12]) ).
tff(f16,plain,
( ( ! [X0: $o] :
( ( $true != (X0) )
| ~ says(peter,bG0((X0))) )
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ? [X1: $o] :
( ( $true = (X1) )
& says(peter,bG0((X1))) ) ) ),
inference(rectify,[],[f15]) ).
tff(f17,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)],[f16]) ).
tff(f18,plain,
! [X0: $o] :
( ( ( $true = (X0) )
| ( $true != bG0((X0)) ) )
& ( ( $true = bG0((X0)) )
| ( $true != (X0) ) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f19,plain,
~ says(peter,bG2(sK4)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X0,sK4)],[f13]) ).
tff(f22,plain,
( ( $true = bG1 )
| says(peter,bG0(sK3)) ),
inference(cnf_transformation,[],[f17]) ).
tff(f23,plain,
( ( $true = bG1 )
| ( $true = sK3 ) ),
inference(cnf_transformation,[],[f17]) ).
tff(f24,plain,
! [X0: $o] :
( ( $true != (X0) )
| ~ says(peter,bG0((X0)))
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f17]) ).
tff(f25,plain,
! [X0: $o] :
( ( $true = bG0((X0)) )
| ( $true != (X0) ) ),
inference(cnf_transformation,[],[f18]) ).
tff(f27,plain,
says(peter,bG1),
inference(cnf_transformation,[],[f7]) ).
tff(f28,plain,
~ says(peter,bG2(sK4)),
inference(cnf_transformation,[],[f19]) ).
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(f35,definition,
( spl5_1
<=> says(peter,bG0(sK3)) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
tff(f37,plain,
( says(peter,bG0(sK3))
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f35]) ).
tff(f39,definition,
( spl5_2
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
tff(f40,plain,
( ( $true != bG1 )
| spl5_2 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f41,plain,
( ( $true = bG1 )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f39]) ).
tff(f42,plain,
( spl5_1
| spl5_2 ),
inference(avatar_split_clause,[],[f22,f39,f35]) ).
tff(f44,definition,
( spl5_3
<=> ( $true = sK3 ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
tff(f46,plain,
( ( $true = sK3 )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f44]) ).
tff(f47,plain,
( spl5_3
| spl5_2 ),
inference(avatar_split_clause,[],[f23,f39,f44]) ).
tff(f49,definition,
( spl5_4
<=> says(peter,bG0($true)) ),
introduced(definition,[new_symbols(definition,[spl5_4])],[avatar_definition]) ).
tff(f50,plain,
( says(peter,bG0($true))
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f49]) ).
tff(f51,plain,
( ~ says(peter,bG0($true))
| spl5_4 ),
inference(avatar_component_clause,[],[f49]) ).
tff(f52,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(avatar_split_clause,[],[f32,f49,f39]) ).
tff(f53,plain,
( says(peter,$true)
| ~ spl5_2 ),
inference(superposition,[],[f27,f41]) ).
tff(f54,plain,
( ~ says(peter,$true)
| spl5_4 ),
inference(superposition,[],[f51,f33]) ).
tff(f55,plain,
( $false
| ~ spl5_2
| spl5_4 ),
inference(forward_subsumption_resolution,[],[f54,f53]) ).
tff(f56,plain,
( ~ spl5_2
| spl5_4 ),
inference(avatar_contradiction_clause,[],[f55]) ).
tff(f57,plain,
( says(peter,bG0($true))
| ~ spl5_1
| ~ spl5_3 ),
inference(forward_demodulation,[],[f37,f46]) ).
tff(f58,plain,
( $false
| ~ spl5_1
| ~ spl5_3
| spl5_4 ),
inference(forward_subsumption_resolution,[],[f57,f51]) ).
tff(f59,plain,
( ~ spl5_1
| ~ spl5_3
| spl5_4 ),
inference(avatar_contradiction_clause,[],[f58]) ).
tff(f60,plain,
( says(peter,$true)
| ~ spl5_4 ),
inference(forward_demodulation,[],[f50,f33]) ).
tff(f65,plain,
( says(peter,$false)
| ( $true = bG1 ) ),
inference(superposition,[],[f27,f30]) ).
tff(f66,plain,
( ~ says(peter,$false)
| ( $true = bG2(sK4) ) ),
inference(superposition,[],[f28,f30]) ).
tff(f85,definition,
( spl5_7
<=> ( $true = bG2(sK4) ) ),
introduced(definition,[new_symbols(definition,[spl5_7])],[avatar_definition]) ).
tff(f87,plain,
( ( $true = bG2(sK4) )
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f85]) ).
tff(f89,definition,
( spl5_8
<=> says(peter,$false) ),
introduced(definition,[new_symbols(definition,[spl5_8])],[avatar_definition]) ).
tff(f92,plain,
( spl5_7
| ~ spl5_8 ),
inference(avatar_split_clause,[],[f66,f89,f85]) ).
tff(f93,plain,
( says(peter,$false)
| spl5_2 ),
inference(forward_subsumption_resolution,[],[f65,f40]) ).
tff(f94,plain,
( spl5_8
| spl5_2 ),
inference(avatar_split_clause,[],[f93,f39,f89]) ).
tff(f102,plain,
( ~ says(peter,$true)
| ~ spl5_7 ),
inference(superposition,[],[f28,f87]) ).
tff(f107,plain,
( $false
| ~ spl5_4
| ~ spl5_7 ),
inference(forward_subsumption_resolution,[],[f102,f60]) ).
tff(f108,plain,
( ~ spl5_4
| ~ spl5_7 ),
inference(avatar_contradiction_clause,[],[f107]) ).
cnf(s1,plain,
( spl5_1
| spl5_2 ),
inference(sat_conversion,[],[f42]) ).
cnf(s2,plain,
( spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f47]) ).
cnf(s3,plain,
( ~ spl5_2
| ~ spl5_4 ),
inference(sat_conversion,[],[f52]) ).
cnf(s4,plain,
( ~ spl5_2
| spl5_4 ),
inference(sat_conversion,[],[f56]) ).
cnf(s5,plain,
( ~ spl5_1
| ~ spl5_3
| spl5_4 ),
inference(sat_conversion,[],[f59]) ).
cnf(s7,plain,
( spl5_7
| ~ spl5_8 ),
inference(sat_conversion,[],[f92]) ).
cnf(s8,plain,
( spl5_2
| spl5_8 ),
inference(sat_conversion,[],[f94]) ).
cnf(s10,plain,
( ~ spl5_4
| ~ spl5_7 ),
inference(sat_conversion,[],[f108]) ).
cnf(s12,plain,
~ spl5_2,
inference(rat,[],[s3,s4]) ).
cnf(s13,plain,
spl5_8,
inference(rat,[],[s8,s12]) ).
cnf(s14,plain,
spl5_3,
inference(rat,[],[s2,s12]) ).
cnf(s15,plain,
spl5_1,
inference(rat,[],[s1,s12]) ).
cnf(s16,plain,
spl5_7,
inference(rat,[],[s7,s13]) ).
cnf(s17,plain,
spl5_4,
inference(rat,[],[s5,s14,s15]) ).
cnf(s19,plain,
$false,
inference(rat,[],[s10,s16,s17]) ).
tff(f114,plain,
$false,
inference(avatar_sat_refutation,[],[s19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ137_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 27 22:45:30 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 3.12/1.18 % (2482861)Detected formulas, will run a generic FOF schedule.
% 3.12/1.18 % (2482871)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2166876699:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.12/1.18 % (2482867)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=2369269129:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.12/1.18 % (2482869)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1938507709:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.12/1.18 % (2482872)dis-21_1_sil=8000:lcm=predicate:random_seed=906920965: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)
% 3.12/1.18 % (2482870)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3197434849:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.12/1.18 % (2482866)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=203662517:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.12/1.18 % (2482868)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=362251432:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.12/1.18 % (2482869)Refutation not found, incomplete strategy
% 3.12/1.18 % (2482869)------------------------------
% 3.12/1.18 % (2482869)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.18 % (2482869)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.18 % (2482869)CaDiCaL version: 2.1.3
% 3.12/1.18 % (2482869)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.18 % (2482869)Time elapsed: 0.001 s
% 3.12/1.18 % (2482869)Peak memory usage: 88 MB
% 3.12/1.18 % (2482872)Refutation not found, incomplete strategy
% 3.12/1.18 % (2482872)------------------------------
% 3.12/1.18 % (2482872)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.18 % (2482872)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.18 % (2482872)CaDiCaL version: 2.1.3
% 3.12/1.18 % (2482872)Termination reason: Refutation not found, incomplete strategy
% 3.12/1.18 % (2482872)Time elapsed: 0.001 s
% 3.12/1.18 % (2482872)Peak memory usage: 88 MB
% 3.12/1.18 % (2482872)Instructions burned: 1 (million)
% 3.12/1.18 % (2482871)First to succeed.
% 3.12/1.18 % (2482871)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2482861"
% 3.12/1.18 % (2482870)Instruction limit reached!
% 3.12/1.18 % (2482870)------------------------------
% 3.12/1.18 % (2482870)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.18 % (2482870)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.18 % (2482870)CaDiCaL version: 2.1.3
% 3.12/1.18 % (2482870)Termination reason: Instruction limit
% 3.12/1.18 % (2482870)Termination phase: Saturation
% 3.12/1.18 % (2482870)Time elapsed: 0.053 s
% 3.12/1.18 % (2482870)Peak memory usage: 87 MB
% 3.12/1.18 % (2482870)Instructions burned: 120 (million)
% 3.12/1.18 % (2482880)lrs+10_1_sil=8000:sp=occurrence:random_seed=1835807828:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 3.12/1.18 % (2482880)Also succeeded, but the first one will report.
% 3.12/1.18 % (2482869)------------------------------
% 3.12/1.18 % (2482869)------------------------------
% 3.12/1.18 % (2482872)------------------------------
% 3.12/1.18 % (2482872)------------------------------
% 3.12/1.18 % (2482871)Refutation found. Thanks to Tanya!
% 3.12/1.18 % SZS status Theorem for theBenchmark
% 3.12/1.18 % SZS output start Proof for theBenchmark
% See solution above
% 3.12/1.18 % (2482871)------------------------------
% 3.12/1.18 % (2482871)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.12/1.18 % (2482871)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.12/1.18 % (2482871)CaDiCaL version: 2.1.3
% 3.12/1.18 % (2482871)Termination reason: Refutation
% 3.12/1.18 % (2482871)Time elapsed: 0.004 s
% 3.12/1.18 % (2482871)Peak memory usage: 90 MB
% 3.12/1.18 % (2482871)Instructions burned: 3 (million)
% 3.12/1.18 % (2482871)------------------------------
% 3.12/1.18 % (2482871)------------------------------
% 3.12/1.18 % (2482861)Success in time 0.388 s
% 3.12/1.18 % Vampire exiting
%------------------------------------------------------------------------------