%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO367_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 : n008.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 2.64s 1.05s
% Output : Refutation 2.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 102 ( 20 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 43 ( 20 ~; 15 |; 3 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 54 ( 52 fml; 2 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 4 usr; 5 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_2,type,
cC: $o > $o ).
tff(f1,conjecture,
( cC(cA)
=> cC(cA) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cEXT2) ).
tff(f2,negated_conjecture,
~ ( cC(cA)
=> cC(cA) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,definition,
( cA
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f4,definition,
( cA
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition]) ).
tff(f5,plain,
~ ( cC(bG1)
=> cC(bG0) ),
inference(fool_elimination,[],[f2,f4,f3]) ).
tff(f6,plain,
( ~ cC(bG0)
& cC(bG1) ),
inference(ennf_transformation,[],[f5]) ).
tff(f7,plain,
( ( cA
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ~ cA ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f8,plain,
( ( cA
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ~ cA ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f9,plain,
cC(bG1),
inference(cnf_transformation,[],[f6]) ).
tff(f10,plain,
~ cC(bG0),
inference(cnf_transformation,[],[f6]) ).
tff(f11,plain,
( ( bG0 = $true )
| ~ cA ),
inference(cnf_transformation,[],[f7]) ).
tff(f12,plain,
( ( bG0 != $true )
| cA ),
inference(cnf_transformation,[],[f7]) ).
tff(f13,plain,
( ( $true = bG1 )
| ~ cA ),
inference(cnf_transformation,[],[f8]) ).
tff(f14,plain,
( cA
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f8]) ).
tff(f16,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f17,plain,
( ~ cC($true)
| ~ cA ),
inference(superposition,[],[f10,f11]) ).
tff(f19,plain,
( cC($true)
| ~ cA ),
inference(superposition,[],[f9,f13]) ).
tff(f20,plain,
~ cA,
inference(forward_subsumption_resolution,[],[f19,f17]) ).
tff(f21,plain,
$true != bG1,
inference(forward_subsumption_resolution,[],[f14,f20]) ).
tff(f27,plain,
( ( $true != $true )
| ( bG1 = $false ) ),
inference(superposition,[],[f21,f16]) ).
tff(f29,plain,
( ( $true != $true )
| cA
| ( bG0 = $false ) ),
inference(superposition,[],[f12,f16]) ).
tff(f32,plain,
( cA
| ( bG0 = $false ) ),
inference(trivial_inequality_removal,[],[f29]) ).
tff(f33,plain,
bG1 = $false,
inference(trivial_inequality_removal,[],[f27]) ).
tff(f34,plain,
bG0 = $false,
inference(forward_subsumption_resolution,[],[f32,f20]) ).
tff(f39,plain,
cC($false),
inference(superposition,[],[f9,f33]) ).
tff(f47,plain,
~ cC($false),
inference(superposition,[],[f10,f34]) ).
tff(f51,plain,
$false,
inference(forward_subsumption_resolution,[],[f47,f39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO367_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.19 % Computer : n008.cluster.edu
% 0.10/0.19 % Model : x86_64 x86_64
% 0.10/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.19 % Memory : 8046.5625MB
% 0.10/0.19 % OS : Linux 6.8.0-71-generic
% 0.10/0.19 % CPULimit : 300
% 0.10/0.19 % WCLimit : 300
% 0.10/0.19 % DateTime : Mon Sep 28 17:37:09 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 2.64/1.05 % (2443752)Detected formulas, will run a generic FOF schedule.
% 2.64/1.05 % (2443761)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2752749368:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.64/1.05 % (2443761)First to succeed.
% 2.64/1.05 % (2443761)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-2443752"
% 2.64/1.05 % (2443758)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=1346794645:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.64/1.05 % (2443757)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=2733174053:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.64/1.05 % (2443762)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2500234050:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.64/1.05 % (2443763)dis-21_1_sil=8000:lcm=predicate:random_seed=2726643232: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)
% 2.64/1.05 % (2443760)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=614581461:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.64/1.05 % (2443759)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=2939723908:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.64/1.05 % (2443763)Refutation not found, incomplete strategy
% 2.64/1.05 % (2443763)------------------------------
% 2.64/1.05 % (2443763)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.05 % (2443763)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.05 % (2443763)CaDiCaL version: 2.1.3
% 2.64/1.05 % (2443763)Termination reason: Refutation not found, incomplete strategy
% 2.64/1.05 % (2443763)Time elapsed: 0.001 s
% 2.64/1.05 % (2443763)Peak memory usage: 88 MB
% 2.64/1.05 % (2443760)Refutation not found, incomplete strategy
% 2.64/1.05 % (2443760)------------------------------
% 2.64/1.05 % (2443760)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.05 % (2443760)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.05 % (2443760)CaDiCaL version: 2.1.3
% 2.64/1.05 % (2443760)Termination reason: Refutation not found, incomplete strategy
% 2.64/1.05 % (2443760)Time elapsed: 0.002 s
% 2.64/1.05 % (2443760)Peak memory usage: 88 MB
% 2.64/1.05 % (2443762)Also succeeded, but the first one will report.
% 2.64/1.05 % (2443761)Refutation found. Thanks to Tanya!
% 2.64/1.05 % SZS status Theorem for theBenchmark
% 2.64/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 2.64/1.05 % (2443761)------------------------------
% 2.64/1.05 % (2443761)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.64/1.05 % (2443761)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.64/1.05 % (2443761)CaDiCaL version: 2.1.3
% 2.64/1.05 % (2443761)Termination reason: Refutation
% 2.64/1.05 % (2443761)Time elapsed: 0.001 s
% 2.64/1.05 % (2443761)Peak memory usage: 88 MB
% 2.64/1.05 % (2443761)Instructions burned: 1 (million)
% 2.64/1.05 % (2443761)------------------------------
% 2.64/1.05 % (2443761)------------------------------
% 2.64/1.05 % (2443752)Success in time 0.291 s
% 2.64/1.05 % Vampire exiting
%------------------------------------------------------------------------------