%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO369_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 : n001.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 02:26:04 PM UTC 2026
% Result : Theorem 2.86s 1.17s
% Output : Refutation 2.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 160 ( 29 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 91 ( 40 ~; 33 |; 9 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 74 ( 72 fml; 2 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 5 usr; 6 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 1 ( 1 !; 0 ?; 1 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
bG0: $o ).
tff(func_def_3,type,
bG1: $o ).
tff(pred_def_3,type,
cP: $o > $o ).
tff(f1,conjecture,
( cP(( cA
=> cB ))
=> cP(( ~ cA
| cB )) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTRIVEXT5) ).
tff(f2,negated_conjecture,
~ ( cP(( cA
=> cB ))
=> cP(( ~ cA
| cB )) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,definition,
( ( ~ cA
| cB )
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f4,definition,
( ( cA
=> cB )
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition]) ).
tff(f5,plain,
~ ( cP(bG1)
=> cP(bG0) ),
inference(fool_elimination,[],[f2,f4,f3]) ).
tff(f6,plain,
( ~ cP(bG0)
& cP(bG1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f7,plain,
( ( cB
| ~ cA )
<=> ( $true = bG1 ) ),
inference(ennf_transformation,[],[f4]) ).
tff(f8,plain,
( ( ~ cA
| cB
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ( cA
& ~ cB ) ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f9,plain,
( ( ~ cA
| cB
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ( cA
& ~ cB ) ) ),
inference(flattening,[],[f8]) ).
tff(f10,plain,
( ( cB
| ~ cA
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ( ~ cB
& cA ) ) ),
inference(nnf_transformation,[],[f7]) ).
tff(f11,plain,
( ( cB
| ~ cA
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ( ~ cB
& cA ) ) ),
inference(flattening,[],[f10]) ).
tff(f12,plain,
cP(bG1),
inference(cnf_transformation,[],[f6]) ).
tff(f13,plain,
~ cP(bG0),
inference(cnf_transformation,[],[f6]) ).
tff(f14,plain,
( ( bG0 = $true )
| ~ cB ),
inference(cnf_transformation,[],[f9]) ).
tff(f15,plain,
( ( bG0 = $true )
| cA ),
inference(cnf_transformation,[],[f9]) ).
tff(f16,plain,
( ~ cA
| cB
| ( bG0 != $true ) ),
inference(cnf_transformation,[],[f9]) ).
tff(f17,plain,
( ( $true = bG1 )
| cA ),
inference(cnf_transformation,[],[f11]) ).
tff(f18,plain,
( ( $true = bG1 )
| ~ cB ),
inference(cnf_transformation,[],[f11]) ).
tff(f19,plain,
( cB
| ~ cA
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f11]) ).
tff(f21,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f22,plain,
( ~ cP($true)
| ~ cB ),
inference(superposition,[],[f13,f14]) ).
tff(f23,plain,
( ~ cP($true)
| cA ),
inference(superposition,[],[f13,f15]) ).
tff(f24,plain,
( cP($true)
| cA ),
inference(superposition,[],[f12,f17]) ).
tff(f25,plain,
( cP($true)
| ~ cB ),
inference(superposition,[],[f12,f18]) ).
tff(f26,plain,
~ cB,
inference(forward_subsumption_resolution,[],[f25,f22]) ).
tff(f27,plain,
cA,
inference(forward_subsumption_resolution,[],[f24,f23]) ).
tff(f28,plain,
( ~ cA
| ( bG0 != $true ) ),
inference(forward_subsumption_resolution,[],[f16,f26]) ).
tff(f29,plain,
bG0 != $true,
inference(forward_subsumption_resolution,[],[f28,f27]) ).
tff(f34,plain,
( ~ cA
| ( $true != bG1 ) ),
inference(forward_subsumption_resolution,[],[f19,f26]) ).
tff(f35,plain,
$true != bG1,
inference(forward_subsumption_resolution,[],[f34,f27]) ).
tff(f44,plain,
( ( $true != $true )
| ( bG1 = $false ) ),
inference(superposition,[],[f35,f21]) ).
tff(f46,plain,
( ( $true != $true )
| ( bG0 = $false ) ),
inference(superposition,[],[f29,f21]) ).
tff(f49,plain,
bG0 = $false,
inference(trivial_inequality_removal,[],[f46]) ).
tff(f50,plain,
bG1 = $false,
inference(trivial_inequality_removal,[],[f44]) ).
tff(f57,plain,
~ cP($false),
inference(superposition,[],[f13,f49]) ).
tff(f69,plain,
cP($false),
inference(superposition,[],[f12,f50]) ).
tff(f75,plain,
$false,
inference(forward_subsumption_resolution,[],[f69,f57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO369_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.18 % Computer : n001.cluster.edu
% 0.11/0.18 % Model : x86_64 x86_64
% 0.11/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.18 % Memory : 8046.5625MB
% 0.11/0.18 % OS : Linux 6.8.0-71-generic
% 0.11/0.18 % CPULimit : 300
% 0.11/0.18 % WCLimit : 300
% 0.11/0.18 % DateTime : Mon Sep 28 17:42:33 UTC 2026
% 0.11/0.18 % CPUTime :
% 0.11/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.21 Running first-order theorem proving
% 0.11/0.21 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
% 2.86/1.17 % (542582)Detected formulas, will run a generic FOF schedule.
% 2.86/1.17 % (542710)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3420727110:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.86/1.17 % (542710)First to succeed.
% 2.86/1.17 % (542710)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-542582"
% 2.86/1.17 % (542708)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=3275200932:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.86/1.17 % (542712)dis-21_1_sil=8000:lcm=predicate:random_seed=2108338232: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)
% 2.86/1.17 % (542707)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=2615089359:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.86/1.17 % (542711)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2791005070:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.86/1.17 % (542709)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=2624746108:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.86/1.17 % (542706)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=2887751380:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.86/1.17 % (542712)Refutation not found, incomplete strategy
% 2.86/1.17 % (542712)------------------------------
% 2.86/1.17 % (542712)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.17 % (542712)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.17 % (542712)CaDiCaL version: 2.1.3
% 2.86/1.17 % (542712)Termination reason: Refutation not found, incomplete strategy
% 2.86/1.17 % (542712)Time elapsed: 0.001 s
% 2.86/1.17 % (542712)Peak memory usage: 88 MB
% 2.86/1.17 % (542709)Refutation not found, incomplete strategy
% 2.86/1.17 % (542709)------------------------------
% 2.86/1.17 % (542709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.17 % (542709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.17 % (542709)CaDiCaL version: 2.1.3
% 2.86/1.17 % (542709)Termination reason: Refutation not found, incomplete strategy
% 2.86/1.17 % (542709)Time elapsed: 0.002 s
% 2.86/1.17 % (542709)Peak memory usage: 88 MB
% 2.86/1.17 % (542709)Instructions burned: 1 (million)
% 2.86/1.17 % (542711)Also succeeded, but the first one will report.
% 2.86/1.17 % (542710)Refutation found. Thanks to Tanya!
% 2.86/1.17 % SZS status Theorem for theBenchmark
% 2.86/1.17 % SZS output start Proof for theBenchmark
% See solution above
% 2.86/1.17 % (542710)------------------------------
% 2.86/1.17 % (542710)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.86/1.17 % (542710)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.86/1.17 % (542710)CaDiCaL version: 2.1.3
% 2.86/1.17 % (542710)Termination reason: Refutation
% 2.86/1.17 % (542710)Time elapsed: 0.002 s
% 2.86/1.17 % (542710)Peak memory usage: 88 MB
% 2.86/1.17 % (542710)Instructions burned: 1 (million)
% 2.86/1.17 % (542710)------------------------------
% 2.86/1.17 % (542710)------------------------------
% 2.86/1.17 % (542582)Success in time 0.316 s
% 2.86/1.17 % Vampire exiting
%------------------------------------------------------------------------------