%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYN984^1 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n007.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 : Wed Sep 30 08:41:45 AM UTC 2026
% Result : Theorem 0.24s 0.37s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 3
% Syntax : Number of formulae : 43 ( 15 unt; 0 typ; 2 def)
% Number of atoms : 226 ( 49 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 109 ( 24 ~; 21 |; 27 &; 31 @)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 0 ( 0 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 39 ( 39 sgn 0 !; 0 ?; 39 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
a: $o ).
thf(func_def_1,type,
b: $o ).
thf(func_def_2,type,
p: ( $i > $o ) > $o ).
thf(func_def_4,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_7,type,
vAND: $o > $o > $o ).
thf(f1,conjecture,
( ( ( p
@ ^ [X0: $i] : b )
& ( p
@ ^ [X0: $i] : a ) )
=> ( p
@ ^ [X0: $i] :
( a
& b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(f2,negated_conjecture,
~ ( ( ( p
@ ^ [X0: $i] : b )
& ( p
@ ^ [X0: $i] : a ) )
=> ( p
@ ^ [X0: $i] :
( a
& b ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( p
@ ^ [X0: $i] : b )
& ( p
@ ^ [X1: $i] : a ) )
=> ( p
@ ^ [X2: $i] :
( a
& b ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ( p
@ ^ [Y0: $i] : a )
= $true )
& ( ( p
@ ^ [Y0: $i] : b )
= $true ) )
=> ( $true
= ( p
@ ^ [Y0: $i] :
( b
& a ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( $true
!= ( p
@ ^ [Y0: $i] :
( b
& a ) ) )
& ( ( p
@ ^ [Y0: $i] : a )
= $true )
& ( ( p
@ ^ [Y0: $i] : b )
= $true ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( ( p
@ ^ [Y0: $i] : a )
= $true )
& ( ( p
@ ^ [Y0: $i] : b )
= $true )
& ( $true
!= ( p
@ ^ [Y0: $i] :
( b
& a ) ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( $true
!= ( p
@ ^ [Y0: $i] :
( b
& a ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( p
@ ^ [Y0: $i] : b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
( ( p
@ ^ [Y0: $i] : a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f12,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i] :
( b
& a ) )
!= ( ^ [Y0: $i] : b ) ) ),
inference(constrained_superposition,[],[f7,f8]) ).
thf(f13,plain,
( ( $true != $true )
| ( ( ^ [Y0: $i] : a )
!= ( ^ [Y0: $i] :
( b
& a ) ) ) ),
inference(constrained_superposition,[],[f7,f9]) ).
thf(f14,plain,
( ( ^ [Y0: $i] :
( b
& a ) )
!= ( ^ [Y0: $i] : b ) ),
inference(trivial_inequality_removal,[],[f12]) ).
thf(f15,plain,
( ( ^ [Y0: $i] : a )
!= ( ^ [Y0: $i] :
( b
& a ) ) ),
inference(trivial_inequality_removal,[],[f13]) ).
thf(f16,plain,
( ( ^ [Y0: $i] : b
@ sK0 )
!= ( ^ [Y0: $i] :
( b
& a )
@ sK0 ) ),
inference(negative_extensionality,[],[f14]) ).
thf(f17,plain,
( ( ( ^ [Y0: $i] :
( b
& a )
@ sK0 )
= $true )
| ( ( ^ [Y0: $i] : b
@ sK0 )
= $true ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f18,plain,
( ( $false
= ( ^ [Y0: $i] :
( b
& a )
@ sK0 ) )
| ( $false
= ( ^ [Y0: $i] : b
@ sK0 ) ) ),
inference(xor_proxy_clausification,[],[f16]) ).
thf(f19,plain,
( ( b = $false )
| ( $false
= ( b
& a ) ) ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f20,plain,
( ( b = $false )
| ( a = $false )
| ( b = $false ) ),
inference(and_proxy_clausification,[],[f19]) ).
thf(f21,plain,
( ( a = $false )
| ( b = $false ) ),
inference(duplicate_literal_removal,[],[f20]) ).
thf(f22,plain,
( ( b = $true )
| ( ( b
& a )
= $true ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f24,plain,
( ( b = $true )
| ( b = $true ) ),
inference(and_proxy_clausification,[],[f22]) ).
thf(f25,plain,
b = $true,
inference(duplicate_literal_removal,[],[f24]) ).
thf(f27,definition,
( spl1_1
<=> ( a = $false ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f29,plain,
( ( a = $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f31,definition,
( spl1_2
<=> ( b = $false ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f33,plain,
( ( b = $false )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f34,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f21,f31,f27]) ).
thf(f36,plain,
( ( $false = $true )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f33,f25]) ).
thf(f39,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f36]) ).
thf(f40,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f39]) ).
thf(f42,plain,
( ( ^ [Y0: $i] : a
@ sK2 )
!= ( ^ [Y0: $i] :
( b
& a )
@ sK2 ) ),
inference(negative_extensionality,[],[f15]) ).
thf(f43,plain,
( ( ( ^ [Y0: $i] : a
@ sK2 )
= $true )
| ( ( ^ [Y0: $i] :
( b
& a )
@ sK2 )
= $true ) ),
inference(xor_proxy_clausification,[],[f42]) ).
thf(f48,plain,
( ( a = $true )
| ( ( b
& a )
= $true ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f49,plain,
( ( a = $true )
| ( a = $true ) ),
inference(and_proxy_clausification,[],[f48]) ).
thf(f51,plain,
a = $true,
inference(duplicate_literal_removal,[],[f49]) ).
thf(f52,plain,
( ( $false = $true )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f51,f29]) ).
thf(f53,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f52]) ).
thf(f54,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f53]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f34]) ).
cnf(s3,plain,
~ spl1_2,
inference(sat_conversion,[],[f40]) ).
cnf(s4,plain,
~ spl1_1,
inference(sat_conversion,[],[f54]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4]) ).
thf(f55,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN984^1 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.23 % Computer : n007.cluster.edu
% 0.09/0.23 % Model : x86_64 x86_64
% 0.09/0.23 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.23 % Memory : 8046.5625MB
% 0.09/0.23 % OS : Linux 6.8.0-71-generic
% 0.09/0.23 % CPULimit : 300
% 0.09/0.23 % WCLimit : 300
% 0.09/0.23 % DateTime : Tue Sep 29 16:17:41 UTC 2026
% 0.09/0.24 % CPUTime :
% 0.09/0.24 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.24/0.29 Running higher-order theorem proving
% 0.24/0.31 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.24/0.37 % (3571302)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.37 % (3571310)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=1475468048:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.24/0.37 % (3571310)Refutation not found, incomplete strategy
% 0.24/0.37 % (3571310)------------------------------
% 0.24/0.37 % (3571310)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (3571310)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (3571310)CaDiCaL version: 2.1.3
% 0.24/0.37 % (3571310)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.37 % (3571310)Time elapsed: 0.001 s
% 0.24/0.37 % (3571310)Peak memory usage: 12 MB
% 0.24/0.37 % (3571310)Instructions burned: 1 (million)
% 0.24/0.37 % (3571310)------------------------------
% 0.24/0.37 % (3571310)------------------------------
% 0.24/0.37 % (3571313)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.37 % (3571313)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.24/0.37 % (3571307)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3811821554:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.37 % (3571308)lrs+10_16_si=on:nwc=1.5:random_seed=472516983:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.37 % (3571309)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2064273745:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.37 % (3571311)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=4145266926:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.37 % (3571312)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=1178415532:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.37 % (3571313)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=2196419412:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.37 % (3571307)Refutation not found, incomplete strategy
% 0.24/0.37 % (3571307)------------------------------
% 0.24/0.37 % (3571307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (3571309)Refutation not found, incomplete strategy
% 0.24/0.37 % (3571309)------------------------------
% 0.24/0.37 % (3571309)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (3571307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (3571309)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (3571307)CaDiCaL version: 2.1.3
% 0.24/0.37 % (3571307)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.37 % (3571307)Time elapsed: 0.001 s
% 0.24/0.37 % (3571309)CaDiCaL version: 2.1.3
% 0.24/0.37 % (3571307)Peak memory usage: 12 MB
% 0.24/0.37 % (3571309)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.37 % (3571309)Time elapsed: 0.001 s
% 0.24/0.37 % (3571309)Peak memory usage: 12 MB
% 0.24/0.37 % (3571311)Refutation not found, incomplete strategy
% 0.24/0.37 % (3571311)------------------------------
% 0.24/0.37 % (3571311)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (3571311)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (3571311)CaDiCaL version: 2.1.3
% 0.24/0.37 % (3571311)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.37 % (3571311)Time elapsed: 0.002 s
% 0.24/0.37 % (3571311)Peak memory usage: 11 MB
% 0.24/0.37 % (3571311)Instructions burned: 1 (million)
% 0.24/0.37 % (3571307)------------------------------
% 0.24/0.37 % (3571307)------------------------------
% 0.24/0.37 % (3571309)------------------------------
% 0.24/0.37 % (3571309)------------------------------
% 0.24/0.37 % (3571308) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3571302-3571308"...
% 0.24/0.37 % (3571311)------------------------------
% 0.24/0.37 % (3571311)------------------------------
% 0.24/0.37 % (3571312) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3571302-3571312"...
% 0.24/0.37 % (3571313)Refutation not found, incomplete strategy
% 0.24/0.37 % (3571313)------------------------------
% 0.24/0.37 % (3571313)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (3571313)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (3571313)CaDiCaL version: 2.1.3
% 0.24/0.37 % (3571313)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.37 % (3571313)Time elapsed: 0.003 s
% 0.24/0.37 % (3571313)Peak memory usage: 12 MB
% 0.24/0.37 % (3571313)Instructions burned: 2 (million)
% 0.24/0.37 % (3571308)...printing done.
% 0.24/0.37 % (3571313)------------------------------
% 0.24/0.37 % (3571313)------------------------------
% 0.24/0.37 % (3571312)...printing done.
% 0.24/0.37 % (3571308)Refutation found. Thanks to Tanya!
% 0.24/0.37 % SZS status Theorem for theBenchmark
% 0.24/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.37 % (3571308)------------------------------
% 0.24/0.37 % (3571308)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.37 % (3571308)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.37 % (3571308)CaDiCaL version: 2.1.3
% 0.24/0.37 % (3571308)Termination reason: Refutation
% 0.24/0.37 % (3571308)Time elapsed: 0.004 s
% 0.24/0.37 % (3571308)Peak memory usage: 13 MB
% 0.24/0.37 % (3571308)Instructions burned: 2 (million)
% 0.24/0.37 % (3571302)Success in time 0.052 s
% 0.24/0.37 % Vampire exiting
%------------------------------------------------------------------------------