%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN983_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 : 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 02:06:07 PM UTC 2026
% Result : Theorem 3.50s 1.26s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 43 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 190 ( 30 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 100 ( 40 ~; 38 |; 16 &)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 89 ( 87 fml; 2 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 6 usr; 7 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(func_def_4,type,
bG2: $o ).
tff(pred_def_3,type,
p: $o > $o ).
tff(f1,conjecture,
( ( p(a)
& p(b) )
=> p(( a
& b )) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thm) ).
tff(f2,negated_conjecture,
~ ( ( p(a)
& p(b) )
=> p(( a
& b )) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
tff(f3,definition,
( ( a
& b )
<=> ( bG0 = $true ) ),
introduced(definition,[new_symbols(definition,[bG0])],[fool_formula_definition]) ).
tff(f4,definition,
( b
<=> ( $true = bG1 ) ),
introduced(definition,[new_symbols(definition,[bG1])],[fool_formula_definition]) ).
tff(f5,definition,
( a
<=> ( $true = bG2 ) ),
introduced(definition,[new_symbols(definition,[bG2])],[fool_formula_definition]) ).
tff(f6,plain,
~ ( ( p(bG2)
& p(bG1) )
=> p(bG0) ),
inference(fool_elimination,[],[f2,f5,f4,f3]) ).
tff(f7,plain,
( ~ p(bG0)
& p(bG2)
& p(bG1) ),
inference(ennf_transformation,[],[f6]) ).
tff(f8,plain,
( ~ p(bG0)
& p(bG2)
& p(bG1) ),
inference(flattening,[],[f7]) ).
tff(f9,plain,
( ( ( a
& b )
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ~ a
| ~ b ) ),
inference(nnf_transformation,[],[f3]) ).
tff(f10,plain,
( ( ( a
& b )
| ( bG0 != $true ) )
& ( ( bG0 = $true )
| ~ a
| ~ b ) ),
inference(flattening,[],[f9]) ).
tff(f11,plain,
( ( b
| ( $true != bG1 ) )
& ( ( $true = bG1 )
| ~ b ) ),
inference(nnf_transformation,[],[f4]) ).
tff(f12,plain,
( ( a
| ( $true != bG2 ) )
& ( ( $true = bG2 )
| ~ a ) ),
inference(nnf_transformation,[],[f5]) ).
tff(f13,plain,
p(bG1),
inference(cnf_transformation,[],[f8]) ).
tff(f14,plain,
p(bG2),
inference(cnf_transformation,[],[f8]) ).
tff(f15,plain,
~ p(bG0),
inference(cnf_transformation,[],[f8]) ).
tff(f16,plain,
( ( bG0 = $true )
| ~ a
| ~ b ),
inference(cnf_transformation,[],[f10]) ).
tff(f17,plain,
( ( bG0 != $true )
| b ),
inference(cnf_transformation,[],[f10]) ).
tff(f19,plain,
( ( $true = bG1 )
| ~ b ),
inference(cnf_transformation,[],[f11]) ).
tff(f20,plain,
( ( $true != bG1 )
| b ),
inference(cnf_transformation,[],[f11]) ).
tff(f21,plain,
( ( $true = bG2 )
| ~ a ),
inference(cnf_transformation,[],[f12]) ).
tff(f22,plain,
( ( $true != bG2 )
| a ),
inference(cnf_transformation,[],[f12]) ).
tff(f24,plain,
! [X0: $o] :
( ( $true = (X0) )
| ( $false = (X0) ) ),
introduced(definition,[],[fool_exhaustiveness_axiom]) ).
tff(f25,plain,
( p($true)
| ~ b ),
inference(superposition,[],[f13,f19]) ).
tff(f27,plain,
( p($true)
| ~ a ),
inference(superposition,[],[f14,f21]) ).
tff(f31,plain,
( ~ p($true)
| ~ a
| ~ b ),
inference(superposition,[],[f15,f16]) ).
tff(f32,plain,
( ~ b
| ~ a ),
inference(forward_subsumption_resolution,[],[f31,f27]) ).
tff(f38,plain,
( ( $true != $true )
| b
| ( bG0 = $false ) ),
inference(superposition,[],[f17,f24]) ).
tff(f39,plain,
( ( bG0 = $false )
| ~ p($true) ),
inference(superposition,[],[f15,f24]) ).
tff(f40,plain,
( ( $true != $true )
| b
| ( bG1 = $false ) ),
inference(superposition,[],[f20,f24]) ).
tff(f42,plain,
( ( $true != $true )
| a
| ( bG2 = $false ) ),
inference(superposition,[],[f22,f24]) ).
tff(f45,plain,
( ( bG2 = $false )
| a ),
inference(trivial_inequality_removal,[],[f42]) ).
tff(f46,plain,
( ( bG1 = $false )
| b ),
inference(trivial_inequality_removal,[],[f40]) ).
tff(f47,plain,
( b
| ( bG0 = $false ) ),
inference(trivial_inequality_removal,[],[f38]) ).
tff(f54,plain,
( ~ p($true)
| ~ p($false) ),
inference(superposition,[],[f15,f39]) ).
tff(f67,plain,
( ~ p($false)
| ~ b ),
inference(resolution,[],[f54,f25]) ).
tff(f81,plain,
( p($false)
| a ),
inference(superposition,[],[f14,f45]) ).
tff(f84,plain,
( a
| ~ b ),
inference(resolution,[],[f81,f67]) ).
tff(f86,plain,
~ b,
inference(forward_subsumption_resolution,[],[f84,f32]) ).
tff(f91,plain,
( p($false)
| b ),
inference(superposition,[],[f13,f46]) ).
tff(f94,plain,
p($false),
inference(forward_subsumption_resolution,[],[f91,f86]) ).
tff(f95,plain,
bG0 = $false,
inference(forward_subsumption_resolution,[],[f47,f86]) ).
tff(f103,plain,
~ p($false),
inference(superposition,[],[f15,f95]) ).
tff(f107,plain,
$false,
inference(forward_subsumption_resolution,[],[f103,f94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN983_8 : TPTP v9.3.1. Released v8.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.19 % Computer : n002.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 17:21:58 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running first-order theorem proving
% 0.08/0.22 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
% 3.50/1.26 % (526879)Detected formulas, will run a generic FOF schedule.
% 3.50/1.26 % (526886)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=2915654952:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 3.50/1.26 % (526888)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=453176974:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 3.50/1.26 % (526884)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=794640804:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 3.50/1.26 % (526887)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=477186863:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 3.50/1.26 % (526890)dis-21_1_sil=8000:lcm=predicate:random_seed=454627167: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)
% 3.50/1.26 % (526885)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=4159771637:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 3.50/1.26 % (526889)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=592616714:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 3.50/1.26 % (526890)Refutation not found, incomplete strategy
% 3.50/1.26 % (526890)------------------------------
% 3.50/1.26 % (526890)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.26 % (526890)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.26 % (526890)CaDiCaL version: 2.1.3
% 3.50/1.26 % (526890)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.26 % (526890)Time elapsed: 0.001 s
% 3.50/1.26 % (526890)Peak memory usage: 89 MB
% 3.50/1.26 % (526887)Refutation not found, incomplete strategy
% 3.50/1.26 % (526887)------------------------------
% 3.50/1.26 % (526887)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.26 % (526887)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.26 % (526887)CaDiCaL version: 2.1.3
% 3.50/1.26 % (526887)Termination reason: Refutation not found, incomplete strategy
% 3.50/1.26 % (526887)Time elapsed: 0.002 s
% 3.50/1.26 % (526887)Peak memory usage: 88 MB
% 3.50/1.26 % (526887)Instructions burned: 1 (million)
% 3.50/1.26 % (526888)First to succeed.
% 3.50/1.26 % (526889)Also succeeded, but the first one will report.
% 3.50/1.26 % (526888)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-526879"
% 3.50/1.26 % (526890)------------------------------
% 3.50/1.26 % (526890)------------------------------
% 3.50/1.26 % (526887)------------------------------
% 3.50/1.26 % (526887)------------------------------
% 3.50/1.26 % (526888)Refutation found. Thanks to Tanya!
% 3.50/1.26 % SZS status Theorem for theBenchmark
% 3.50/1.26 % SZS output start Proof for theBenchmark
% See solution above
% 3.50/1.26 % (526888)------------------------------
% 3.50/1.26 % (526888)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.50/1.26 % (526888)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.50/1.26 % (526888)CaDiCaL version: 2.1.3
% 3.50/1.26 % (526888)Termination reason: Refutation
% 3.50/1.26 % (526888)Time elapsed: 0.003 s
% 3.50/1.26 % (526888)Peak memory usage: 88 MB
% 3.50/1.26 % (526888)Instructions burned: 2 (million)
% 3.50/1.26 % (526888)------------------------------
% 3.50/1.26 % (526888)------------------------------
% 3.50/1.26 % (526879)Success in time 0.408 s
% 3.50/1.26 % Vampire exiting
%------------------------------------------------------------------------------