%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO506_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 : n002.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 02:27:05 PM UTC 2026
% Result : Theorem 5.19s 1.69s
% Output : Refutation 5.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 8 unt; 0 typ; 1 def)
% Number of atoms : 140 ( 55 equ)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 50 ( 23 ~; 20 |; 5 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 89 ( 87 fml; 2 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 6 ( 3 usr; 4 prp; 0-2 aty)
% Number of functors : 1 ( 1 usr; 0 con; 3-3 aty)
% Number of variables : 54 ( 52 !; 2 ?; 54 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
c: ( $o * $i * $i ) > $i ).
tff(func_def_3,type,
bG0: ( $i * $i ) > $o ).
tff(f1,conjecture,
( ! [X0: $i,X1: $i] : ( c(X0 = X1,X0,X1) = X1 )
| ~ ! [X0: $i,X1: $i] : ( c($true,X0,X1) = X0 )
| ~ ! [X0: $i,X1: $i] : ( c($false,X0,X1) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',claim) ).
tff(f2,negated_conjecture,
~ ( ! [X0: $i,X1: $i] : ( c(X0 = X1,X0,X1) = X1 )
| ~ ! [X0: $i,X1: $i] : ( c($true,X0,X1) = X0 )
| ~ ! [X0: $i,X1: $i] : ( c($false,X0,X1) = X1 ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ! [X0: $i,X1: $i] : ( c(X0 = X1,X0,X1) = X1 )
| ~ ! [X2: $i,X3: $i] : ( c($true,X2,X3) = X2 )
| ~ ! [X4: $i,X5: $i] : ( c($false,X4,X5) = X5 ) ),
inference(rectify,[],[f2]) ).
tff(f4,definition,
! [X1: $i,X0: $i] :
( ( X0 = X1 )
<=> ( $true = bG0(X1,X0) ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f5,plain,
~ ( ! [X0: $i,X1: $i] : ( c(bG0(X1,X0),X0,X1) = X1 )
| ~ ! [X2: $i,X3: $i] : ( c($true,X2,X3) = X2 )
| ~ ! [X4: $i,X5: $i] : ( c($false,X4,X5) = X5 ) ),
inference(fool_elimination,[],[f3,f4]) ).
tff(f6,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
<=> ( $true = bG0(X0,X1) ) ),
inference(rectify,[],[f4]) ).
tff(f7,plain,
( ? [X0: $i,X1: $i] : ( c(bG0(X1,X0),X0,X1) != X1 )
& ! [X2: $i,X3: $i] : ( c($true,X2,X3) = X2 )
& ! [X4: $i,X5: $i] : ( c($false,X4,X5) = X5 ) ),
inference(ennf_transformation,[],[f5]) ).
tff(f8,plain,
( ( sK2 != c(bG0(sK2,sK1),sK1,sK2) )
& ! [X2: $i,X3: $i] : ( c($true,X2,X3) = X2 )
& ! [X4: $i,X5: $i] : ( c($false,X4,X5) = X5 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2]),skolemize(X0,sK1),skolemize(X1,sK2)],[f7]) ).
tff(f9,plain,
! [X0: $i,X1: $i] :
( ( ( X0 = X1 )
| ( $true != bG0(X0,X1) ) )
& ( ( $true = bG0(X0,X1) )
| ( X0 != X1 ) ) ),
inference(nnf_transformation,[],[f6]) ).
tff(f10,plain,
! [X4: $i,X5: $i] : ( c($false,X4,X5) = X5 ),
inference(cnf_transformation,[],[f8]) ).
tff(f11,plain,
! [X2: $i,X3: $i] : ( c($true,X2,X3) = X2 ),
inference(cnf_transformation,[],[f8]) ).
tff(f12,plain,
sK2 != c(bG0(sK2,sK1),sK1,sK2),
inference(cnf_transformation,[],[f8]) ).
tff(f13,plain,
! [X0: $i,X1: $i] :
( ( $true = bG0(X0,X1) )
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f9]) ).
tff(f14,plain,
! [X0: $i,X1: $i] :
( ( $true != bG0(X0,X1) )
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f9]) ).
tff(f16,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f17,plain,
! [X1: $i] : ( $true = bG0(X1,X1) ),
inference(equality_resolution,[],[f13]) ).
tff(f21,plain,
( ( sK2 != c($true,sK1,sK2) )
| ( $false = bG0(sK2,sK1) ) ),
inference(superposition,[],[f12,f16]) ).
tff(f23,plain,
( ( sK1 != sK2 )
| ( $false = bG0(sK2,sK1) ) ),
inference(forward_demodulation,[],[f21,f11]) ).
tff(f24,plain,
! [X0: $i,X1: $i] :
( ( $true != $true )
| ( X0 = X1 )
| ( $false = bG0(X0,X1) ) ),
inference(superposition,[],[f14,f16]) ).
tff(f25,plain,
! [X0: $i,X1: $i] :
( ( $false = bG0(X0,X1) )
| ( X0 = X1 ) ),
inference(trivial_inequality_removal,[],[f24]) ).
tff(f28,plain,
( ( sK2 != c($false,sK1,sK2) )
| ( sK1 = sK2 ) ),
inference(superposition,[],[f12,f25]) ).
tff(f32,plain,
sK1 = sK2,
inference(forward_subsumption_resolution,[],[f28,f10]) ).
tff(f33,plain,
( ( sK1 != sK1 )
| ( $false = bG0(sK1,sK1) ) ),
inference(superposition,[],[f23,f32]) ).
tff(f35,plain,
$false = bG0(sK1,sK1),
inference(trivial_inequality_removal,[],[f33]) ).
tff(f37,plain,
$false = $true,
inference(forward_demodulation,[],[f35,f17]) ).
tff(f38,plain,
$false,
inference(trivial_inequality_removal,[],[f37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO506_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.21 % Computer : n002.cluster.edu
% 0.10/0.21 % Model : x86_64 x86_64
% 0.10/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.21 % Memory : 8046.5625MB
% 0.10/0.21 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Mon Sep 28 17:49:37 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.25/0.27 Running first-order theorem proving
% 0.25/0.27 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
% 5.19/1.69 % (587866)Detected formulas, will run a generic FOF schedule.
% 5.19/1.69 % (587968)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=773195524:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 5.19/1.69 % (587968)Refutation not found, incomplete strategy
% 5.19/1.69 % (587968)------------------------------
% 5.19/1.69 % (587968)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.69 % (587968)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.69 % (587968)CaDiCaL version: 2.1.3
% 5.19/1.69 % (587968)Termination reason: Refutation not found, incomplete strategy
% 5.19/1.69 % (587968)Time elapsed: 0.001 s
% 5.19/1.69 % (587968)Peak memory usage: 88 MB
% 5.19/1.69 % (587966)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=2306164943:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 5.19/1.69 % (587965)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=3845506644:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 5.19/1.69 % (587969)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=1756074671:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 5.19/1.69 % (587969)First to succeed.
% 5.19/1.69 % (587969)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-587866"
% 5.19/1.69 % (587971)dis-21_1_sil=8000:lcm=predicate:random_seed=1444636240: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)
% 5.19/1.69 % (587970)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3871080441:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 5.19/1.69 % (587971)Refutation not found, incomplete strategy
% 5.19/1.69 % (587971)------------------------------
% 5.19/1.69 % (587971)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.69 % (587971)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.69 % (587971)CaDiCaL version: 2.1.3
% 5.19/1.69 % (587971)Termination reason: Refutation not found, incomplete strategy
% 5.19/1.69 % (587971)Time elapsed: 0.002 s
% 5.19/1.69 % (587971)Peak memory usage: 88 MB
% 5.19/1.69 % (587970)Also succeeded, but the first one will report.
% 5.19/1.69 % (587967)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=3774340718:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 5.19/1.69 % (587968)------------------------------
% 5.19/1.69 % (587968)------------------------------
% 5.19/1.69 % (588002)lrs+10_1_sil=8000:sp=occurrence:random_seed=4269516461:i=285:sd=3:ss=axioms:sgt=8_2996 on theBenchmark for (2996ds/285Mi)
% 5.19/1.69 % (588002)Also succeeded, but the first one will report.
% 5.19/1.69 % (587969)Refutation found. Thanks to Tanya!
% 5.19/1.69 % SZS status Theorem for theBenchmark
% 5.19/1.69 % SZS output start Proof for theBenchmark
% See solution above
% 5.19/1.69 % (587969)------------------------------
% 5.19/1.69 % (587969)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 5.19/1.69 % (587969)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 5.19/1.69 % (587969)CaDiCaL version: 2.1.3
% 5.19/1.69 % (587969)Termination reason: Refutation
% 5.19/1.69 % (587969)Time elapsed: 0.004 s
% 5.19/1.69 % (587969)Peak memory usage: 88 MB
% 5.19/1.69 % (587969)Instructions burned: 2 (million)
% 5.19/1.69 % (587969)------------------------------
% 5.19/1.69 % (587969)------------------------------
% 5.19/1.69 % (587866)Success in time 0.636 s
% 5.19/1.69 % Vampire exiting
%------------------------------------------------------------------------------