%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO346_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 : n026.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 02:26:01 PM UTC 2026
% Result : Theorem 5.18s 1.77s
% Output : Refutation 5.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 33 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 137 ( 22 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 79 ( 35 ~; 30 |; 10 &)
% ( 3 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 62 ( 60 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_2,type,
cP: $o > $o ).
tff(f1,conjecture,
( ( cA != cB )
| ~ cP(cA)
| cP(cB) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM621) ).
tff(f2,negated_conjecture,
~ ( ( cA != cB )
| ~ cP(cA)
| cP(cB) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,definition,
( cB
<=> ( 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,
~ ( ( cA
<~> cB )
| ~ cP(bG1)
| cP(bG0) ),
inference(fool_elimination,[],[f2,f4,f3]) ).
tff(f6,plain,
( ( cA
<=> cB )
& cP(bG1)
& ~ cP(bG0) ),
inference(ennf_transformation,[],[f5]) ).
tff(f7,plain,
( ( cA
| ~ cB )
& ( cB
| ~ cA )
& cP(bG1)
& ~ cP(bG0) ),
inference(nnf_transformation,[],[f6]) ).
tff(f8,plain,
( ( cA
| ~ cB )
& ( cB
| ~ cA )
& cP(bG1)
& ~ cP(bG0) ),
inference(flattening,[],[f7]) ).
tff(f9,plain,
( ( cB
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ~ cB ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f10,plain,
( ( cA
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ~ cA ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f11,plain,
~ cP(bG0),
inference(cnf_transformation,[],[f8]) ).
tff(f12,plain,
cP(bG1),
inference(cnf_transformation,[],[f8]) ).
tff(f13,plain,
( cB
| ~ cA ),
inference(cnf_transformation,[],[f8]) ).
tff(f14,plain,
( cA
| ~ cB ),
inference(cnf_transformation,[],[f8]) ).
tff(f15,plain,
( ( bG0 = $true )
| ~ cB ),
inference(cnf_transformation,[],[f9]) ).
tff(f16,plain,
( ( bG0 != $true )
| cB ),
inference(cnf_transformation,[],[f9]) ).
tff(f17,plain,
( ( $true = bG1 )
| ~ cA ),
inference(cnf_transformation,[],[f10]) ).
tff(f18,plain,
( ( $true != bG1 )
| cA ),
inference(cnf_transformation,[],[f10]) ).
tff(f20,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f21,plain,
( ~ cP($true)
| ~ cB ),
inference(superposition,[],[f11,f15]) ).
tff(f23,plain,
( cP($true)
| ~ cA ),
inference(superposition,[],[f12,f17]) ).
tff(f24,plain,
( ~ cA
| ~ cB ),
inference(resolution,[],[f23,f21]) ).
tff(f25,plain,
~ cB,
inference(forward_subsumption_resolution,[],[f24,f14]) ).
tff(f26,plain,
~ cA,
inference(resolution,[],[f25,f13]) ).
tff(f33,plain,
( ( $true != $true )
| cB
| ( bG0 = $false ) ),
inference(superposition,[],[f16,f20]) ).
tff(f35,plain,
( ( $true != $true )
| cA
| ( bG1 = $false ) ),
inference(superposition,[],[f18,f20]) ).
tff(f38,plain,
( cA
| ( bG1 = $false ) ),
inference(trivial_inequality_removal,[],[f35]) ).
tff(f39,plain,
( cB
| ( bG0 = $false ) ),
inference(trivial_inequality_removal,[],[f33]) ).
tff(f40,plain,
bG1 = $false,
inference(forward_subsumption_resolution,[],[f38,f26]) ).
tff(f41,plain,
bG0 = $false,
inference(forward_subsumption_resolution,[],[f39,f25]) ).
tff(f46,plain,
cP($false),
inference(superposition,[],[f12,f40]) ).
tff(f54,plain,
~ cP($false),
inference(superposition,[],[f11,f41]) ).
tff(f58,plain,
$false,
inference(forward_subsumption_resolution,[],[f54,f46]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SYO346_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.07 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.10/0.26 % Computer : n026.cluster.edu
% 0.10/0.26 % Model : x86_64 x86_64
% 0.10/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.26 % Memory : 8046.5625MB
% 0.10/0.26 % OS : Linux 6.8.0-71-generic
% 0.10/0.26 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Mon Sep 28 17:38:12 UTC 2026
% 0.10/0.27 % CPUTime :
% 0.10/0.27 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.28/0.32 Running first-order theorem proving
% 0.28/0.32 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
% 5.18/1.77 % (4062016)Detected formulas, will run a generic FOF schedule.
% 5.18/1.77 % (4062022)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=4246191525:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_3000 on theBenchmark for (3000ds/134677Mi)
% 5.18/1.77 % (4062025)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=2289288473:i=119:av=off:ss=axioms_3000 on theBenchmark for (3000ds/119Mi)
% 5.18/1.77 % (4062025)First to succeed.
% 5.18/1.77 % (4062025)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-4062016"
% 5.18/1.77 % (4062024)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=4189252634:i=109:sd=1:ins=1:gsp=on:ss=axioms_3000 on theBenchmark for (3000ds/109Mi)
% 5.18/1.77 % (4062023)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=2929376914:i=141695:sd=1:nm=32:gsp=on:ss=included_3000 on theBenchmark for (3000ds/141695Mi)
% 5.18/1.77 % (4062021)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=1472807951:i=141193_3000 on theBenchmark for (3000ds/141193Mi)
% 5.18/1.77 % (4062024)Refutation not found, incomplete strategy
% 5.18/1.77 % (4062024)------------------------------
% 5.18/1.77 % (4062024)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.77 % (4062024)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.77 % (4062024)CaDiCaL version: 2.1.3
% 5.18/1.77 % (4062024)Termination reason: Refutation not found, incomplete strategy
% 5.18/1.77 % (4062024)Time elapsed: 0.003 s
% 5.18/1.77 % (4062024)Peak memory usage: 88 MB
% 5.18/1.77 % (4062024)Instructions burned: 1 (million)
% 5.18/1.77 % (4062027)dis-21_1_sil=8000:lcm=predicate:random_seed=3283614457:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_3000 on theBenchmark for (3000ds/129Mi)
% 5.18/1.77 % (4062026)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3495984437:s2a=on:i=139:gtg=position_3000 on theBenchmark for (3000ds/139Mi)
% 5.18/1.77 % (4062027)Refutation not found, incomplete strategy
% 5.18/1.77 % (4062027)------------------------------
% 5.18/1.77 % (4062027)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.77 % (4062027)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.77 % (4062027)CaDiCaL version: 2.1.3
% 5.18/1.77 % (4062027)Termination reason: Refutation not found, incomplete strategy
% 5.18/1.77 % (4062027)Time elapsed: 0.002 s
% 5.18/1.77 % (4062027)Peak memory usage: 89 MB
% 5.18/1.77 % (4062026)Also succeeded, but the first one will report.
% 5.18/1.77 % (4062025)Refutation found. Thanks to Tanya!
% 5.18/1.77 % SZS status Theorem for theBenchmark
% 5.18/1.77 % SZS output start Proof for theBenchmark
% See solution above
% 5.18/1.77 % (4062025)------------------------------
% 5.18/1.77 % (4062025)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.18/1.77 % (4062025)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.18/1.77 % (4062025)CaDiCaL version: 2.1.3
% 5.18/1.77 % (4062025)Termination reason: Refutation
% 5.18/1.77 % (4062025)Time elapsed: 0.004 s
% 5.18/1.77 % (4062025)Peak memory usage: 88 MB
% 5.18/1.77 % (4062025)Instructions burned: 1 (million)
% 5.18/1.77 % (4062025)------------------------------
% 5.18/1.77 % (4062025)------------------------------
% 5.18/1.77 % (4062016)Success in time 0.602 s
% 5.18/1.77 % Vampire exiting
%------------------------------------------------------------------------------