%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO039_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 : 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 02:24:48 PM UTC 2026
% Result : Theorem 3.58s 1.19s
% Output : Refutation 3.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 96 ( 33 equ)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 28 ( 16 ~; 9 |; 1 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 69 ( 67 fml; 2 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 2 usr; 4 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 1-1 aty)
% Number of variables : 1 ( 1 !; 0 ?; 1 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
h: $o > $i ).
tff(func_def_3,type,
bG0: $o ).
tff(func_def_4,type,
bG1: $o ).
tff(f1,conjecture,
h(h($false) = h(~ $false)) = h($false),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',1) ).
tff(f2,negated_conjecture,
( ( ~ h(h($false) = h(~ $false)) ) = h($false) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
( ( ~ h(h($false) = h(~ $false)) ) = h($false) ),
inference(rectify,[],[f2]) ).
tff(f4,definition,
( ~ $false
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f5,definition,
( ( h($false) = h(bG0) )
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition]) ).
tff(f6,plain,
( ( ~ h($false) ) = h(bG1) ),
inference(fool_elimination,[],[f3,f5,f4]) ).
tff(f7,plain,
h($false) != h(bG1),
inference(flattening,[],[f6]) ).
tff(f8,plain,
bG0 = $true,
inference(true_and_false_elimination,[],[f4]) ).
tff(f9,plain,
( ( ( h($false) = h(bG0) )
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ( h($false) != h(bG0) ) ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f10,plain,
h($false) != h(bG1),
inference(cnf_transformation,[],[f7]) ).
tff(f12,plain,
( ( h($false) = h(bG0) )
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f9]) ).
tff(f13,plain,
bG0 = $true,
inference(cnf_transformation,[],[f8]) ).
tff(f15,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f16,plain,
( ( $true != bG1 )
| ( h($false) = h($true) ) ),
inference(definition_unfolding,[],[f12,f13]) ).
tff(f20,plain,
( ( h($false) != h($true) )
| ( $false = bG1 ) ),
inference(superposition,[],[f10,f15]) ).
tff(f22,plain,
( ( $true != $true )
| ( h($false) = h($true) )
| ( $false = bG1 ) ),
inference(superposition,[],[f16,f15]) ).
tff(f23,plain,
( ( h($false) = h($true) )
| ( $false = bG1 ) ),
inference(trivial_inequality_removal,[],[f22]) ).
tff(f27,plain,
$false = bG1,
inference(forward_subsumption_resolution,[],[f23,f20]) ).
tff(f30,plain,
h($false) != h($false),
inference(superposition,[],[f10,f27]) ).
tff(f31,plain,
$false,
inference(trivial_inequality_removal,[],[f30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO039_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.18 % Computer : n008.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Mon Sep 28 17:22:54 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.22 Running first-order theorem proving
% 0.10/0.22 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
% 3.58/1.19 % (2411586)Detected formulas, will run a generic FOF schedule.
% 3.58/1.19 % (2411704)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=1770095947:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.58/1.19 % (2411708)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2231872655:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.58/1.19 % (2411705)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=1892183861:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.58/1.19 % (2411707)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2167973611:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.58/1.19 % (2411703)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=120996474:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.58/1.19 % (2411706)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=303061821:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.58/1.19 % (2411709)dis-21_1_sil=8000:lcm=predicate:random_seed=2903880417: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)
% 3.58/1.19 % (2411709)Refutation not found, incomplete strategy
% 3.58/1.19 % (2411709)------------------------------
% 3.58/1.19 % (2411709)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.19 % (2411709)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.19 % (2411707)First to succeed.
% 3.58/1.19 % (2411709)CaDiCaL version: 2.1.3
% 3.58/1.19 % (2411709)Termination reason: Refutation not found, incomplete strategy
% 3.58/1.19 % (2411709)Time elapsed: 0.001 s
% 3.58/1.19 % (2411709)Peak memory usage: 88 MB
% 3.58/1.19 % (2411706)Refutation not found, incomplete strategy
% 3.58/1.19 % (2411706)------------------------------
% 3.58/1.19 % (2411706)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.19 % (2411706)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.19 % (2411706)CaDiCaL version: 2.1.3
% 3.58/1.19 % (2411706)Termination reason: Refutation not found, incomplete strategy
% 3.58/1.19 % (2411706)Time elapsed: 0.002 s
% 3.58/1.19 % (2411706)Peak memory usage: 88 MB
% 3.58/1.19 % (2411708)Also succeeded, but the first one will report.
% 3.58/1.19 % (2411707)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-2411586"
% 3.58/1.19 % (2411706)------------------------------
% 3.58/1.19 % (2411706)------------------------------
% 3.58/1.19 % (2411709)------------------------------
% 3.58/1.19 % (2411709)------------------------------
% 3.58/1.19 % (2411707)Refutation found. Thanks to Tanya!
% 3.58/1.19 % SZS status Theorem for theBenchmark
% 3.58/1.19 % SZS output start Proof for theBenchmark
% See solution above
% 3.58/1.19 % (2411707)------------------------------
% 3.58/1.19 % (2411707)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.58/1.19 % (2411707)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.58/1.19 % (2411707)CaDiCaL version: 2.1.3
% 3.58/1.19 % (2411707)Termination reason: Refutation
% 3.58/1.19 % (2411707)Time elapsed: 0.002 s
% 3.58/1.19 % (2411707)Peak memory usage: 88 MB
% 3.58/1.19 % (2411707)Instructions burned: 1 (million)
% 3.58/1.19 % (2411707)------------------------------
% 3.58/1.19 % (2411707)------------------------------
% 3.58/1.19 % (2411586)Success in time 0.436 s
% 3.58/1.19 % Vampire exiting
%------------------------------------------------------------------------------