%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO501_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 : 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 02:27:05 PM UTC 2026
% Result : Theorem 0.19s 1.20s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 28 ( 9 unt; 0 typ; 2 def)
% Number of atoms : 122 ( 20 equ)
% Maximal formula atoms : 4 ( 4 avg)
% Number of connectives : 49 ( 25 ~; 19 |; 3 &)
% ( 2 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 72 ( 70 fml; 2 var)
% Number of types : 2 ( 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 : 1 ( 1 usr; 0 con; 2-2 aty)
% Number of variables : 1 ( 1 !; 0 ?; 1 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_1,type,
f: ( $i * $o ) > $i ).
tff(func_def_2,type,
bG0: $o ).
tff(func_def_5,type,
bG1: $o ).
tff(f1,conjecture,
( ~ p(f(x,y))
| p(f(x,y)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',claim) ).
tff(f2,negated_conjecture,
~ ( ~ p(f(x,y))
| p(f(x,y)) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,plain,
~ ( ~ p(f(x,y))
| p(f(x,y)) ),
inference(rectify,[],[f2]) ).
tff(f4,definition,
( y
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f5,definition,
( y
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition]) ).
tff(f6,plain,
~ ( ~ p(f(x,bG1))
| p(f(x,bG0)) ),
inference(fool_elimination,[],[f3,f5,f4]) ).
tff(f7,plain,
( p(f(x,bG1))
& ~ p(f(x,bG0)) ),
inference(ennf_transformation,[],[f6]) ).
tff(f8,plain,
( ( y
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ~ y ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f9,plain,
( ( y
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ~ y ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f10,plain,
~ p(f(x,bG0)),
inference(cnf_transformation,[],[f7]) ).
tff(f11,plain,
p(f(x,bG1)),
inference(cnf_transformation,[],[f7]) ).
tff(f12,plain,
( ( bG0 = $true )
| ~ y ),
inference(cnf_transformation,[],[f8]) ).
tff(f13,plain,
( ( bG0 != $true )
| y ),
inference(cnf_transformation,[],[f8]) ).
tff(f14,plain,
( ( $true = bG1 )
| ~ y ),
inference(cnf_transformation,[],[f9]) ).
tff(f15,plain,
( y
| ( $true != bG1 ) ),
inference(cnf_transformation,[],[f9]) ).
tff(f17,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f18,plain,
( ~ p(f(x,$true))
| ~ y ),
inference(superposition,[],[f10,f12]) ).
tff(f20,plain,
( p(f(x,$true))
| ~ y ),
inference(superposition,[],[f11,f14]) ).
tff(f21,plain,
~ y,
inference(forward_subsumption_resolution,[],[f20,f18]) ).
tff(f22,plain,
$true != bG1,
inference(forward_subsumption_resolution,[],[f15,f21]) ).
tff(f28,plain,
( ( $true != $true )
| y
| ( bG0 = $false ) ),
inference(superposition,[],[f13,f17]) ).
tff(f30,plain,
( ( $true != $true )
| ( bG1 = $false ) ),
inference(superposition,[],[f22,f17]) ).
tff(f33,plain,
bG1 = $false,
inference(trivial_inequality_removal,[],[f30]) ).
tff(f34,plain,
( y
| ( bG0 = $false ) ),
inference(trivial_inequality_removal,[],[f28]) ).
tff(f35,plain,
bG0 = $false,
inference(forward_subsumption_resolution,[],[f34,f21]) ).
tff(f40,plain,
p(f(x,$false)),
inference(superposition,[],[f11,f33]) ).
tff(f48,plain,
~ p(f(x,$false)),
inference(superposition,[],[f10,f35]) ).
tff(f52,plain,
$false,
inference(forward_subsumption_resolution,[],[f48,f40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO501_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n001.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Mon Sep 28 17:52:33 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 0.19/1.20 % (565960)Detected formulas, will run a generic FOF schedule.
% 0.19/1.20 % (566013)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=1497553850:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 0.19/1.20 % (566018)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=3419373937:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 0.19/1.20 % (566017)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=982404884:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 0.19/1.20 % (566014)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=1503108639:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 0.19/1.20 % (566016)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=1655407705:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 0.19/1.20 % (566015)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=3338194006:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 0.19/1.20 % (566019)dis-21_1_sil=8000:lcm=predicate:random_seed=1401634977: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)
% 0.19/1.20 % (566019)Refutation not found, incomplete strategy
% 0.19/1.20 % (566019)------------------------------
% 0.19/1.20 % (566019)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (566019)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (566019)CaDiCaL version: 2.1.3
% 0.19/1.20 % (566019)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.20 % (566019)Time elapsed: 0.001 s
% 0.19/1.20 % (566019)Peak memory usage: 88 MB
% 0.19/1.20 % (566016)Refutation not found, incomplete strategy
% 0.19/1.20 % (566016)------------------------------
% 0.19/1.20 % (566016)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (566016)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (566016)CaDiCaL version: 2.1.3
% 0.19/1.20 % (566016)Termination reason: Refutation not found, incomplete strategy
% 0.19/1.20 % (566016)Time elapsed: 0.002 s
% 0.19/1.20 % (566016)Peak memory usage: 88 MB
% 0.19/1.20 % (566017)First to succeed.
% 0.19/1.20 % (566018)Also succeeded, but the first one will report.
% 0.19/1.20 % (566017)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-565960"
% 0.19/1.20 [W928 17:52:34.634193984 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 17:52:34.634221906 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 17:52:34.634242138 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 17:52:34.634248222 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 17:52:34.634261465 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 [W928 17:52:34.634266908 register_special_ops.cpp:225] Warning: Creating a tensor from an empty intlist will create a tensor of default floating point type (currently Float) in python but a tensor of type int in torchscript.
% 0.19/1.20 Pass in a dtype argument to ensure consistent behavior (function createTensorFromList)
% 0.19/1.20 % (566019)------------------------------
% 0.19/1.20 % (566019)------------------------------
% 0.19/1.20 % (566016)------------------------------
% 0.19/1.20 % (566016)------------------------------
% 0.19/1.20 % (566017)Refutation found. Thanks to Tanya!
% 0.19/1.20 % SZS status Theorem for theBenchmark
% 0.19/1.20 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/1.20 % (566017)------------------------------
% 0.19/1.20 % (566017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 0.19/1.20 % (566017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/1.20 % (566017)CaDiCaL version: 2.1.3
% 0.19/1.20 % (566017)Termination reason: Refutation
% 0.19/1.20 % (566017)Time elapsed: 0.002 s
% 0.19/1.20 % (566017)Peak memory usage: 88 MB
% 0.19/1.20 % (566017)Instructions burned: 1 (million)
% 0.19/1.20 % (566017)------------------------------
% 0.19/1.20 % (566017)------------------------------
% 0.19/1.20 % (565960)Success in time 0.435 s
% 0.19/1.20 % Vampire exiting
%------------------------------------------------------------------------------