%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU956^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : Wed Sep 30 08:32:02 AM UTC 2026
% Result : Theorem 0.24s 0.30s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 1
% Syntax : Number of formulae : 16 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 95 ( 63 equ; 2 cnn)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 62 ( 15 ~; 9 |; 6 &; 16 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 5 con; 0-4 aty)
% Number of variables : 53 ( 16 ^; 33 !; 4 ?; 53 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_4,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_5,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_8,type,
vNOT: $o > $o ).
thf(f1,conjecture,
( ! [X0: $i > $o,X1: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) ) )
=> ! [X4: $i,X3: $i] :
( ( ( ^ [X5: $i] : ( X4 = X5 ) )
= ( ^ [X5: $i] : ( X3 = X5 ) ) )
=> ( X3 = X4 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM13_pme) ).
thf(f2,negated_conjecture,
~ ( ! [X0: $i > $o,X1: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) ) )
=> ! [X4: $i,X3: $i] :
( ( ( ^ [X5: $i] : ( X4 = X5 ) )
= ( ^ [X5: $i] : ( X3 = X5 ) ) )
=> ( X3 = X4 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ! [X0: $i > $o,X1: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( X1 @ X2 )
=> ( X0 @ X2 ) ) )
=> ! [X3: $i,X4: $i] :
( ( ( ^ [X5: $i] : ( X3 = X5 ) )
= ( ^ [X6: $i] : ( X4 = X6 ) ) )
=> ( X3 = X4 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ! [X1: $i > $o,X0: $i > $o] :
( ( X0 = X1 )
=> ! [X2: $i] :
( ( ( X1 @ X2 )
= $true )
=> ( ( X0 @ X2 )
= $true ) ) )
=> ! [X3: $i,X4: $i] :
( ( ( ^ [Y0: $i] : ( X4 = Y0 ) )
= ( ^ [Y0: $i] : ( X3 = Y0 ) ) )
=> ( X3 = X4 ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X1: $i > $o,X0: $i > $o] :
( ! [X2: $i] :
( ( ( X1 @ X2 )
!= $true )
| ( ( X0 @ X2 )
= $true ) )
| ( X0 != X1 ) )
& ? [X3: $i,X4: $i] :
( ( X3 != X4 )
& ( ( ^ [Y0: $i] : ( X4 = Y0 ) )
= ( ^ [Y0: $i] : ( X3 = Y0 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) )
| ( X0 != X1 ) )
& ? [X3: $i,X4: $i] :
( ( X3 != X4 )
& ( ( ^ [Y0: $i] : ( X4 = Y0 ) )
= ( ^ [Y0: $i] : ( X3 = Y0 ) ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i > $o,X1: $i > $o] :
( ! [X2: $i] :
( ( ( X0 @ X2 )
!= $true )
| ( ( X1 @ X2 )
= $true ) )
| ( X0 != X1 ) )
& ( sK1 != sK0 )
& ( ( ^ [Y0: $i] : ( sK0 = Y0 ) )
= ( ^ [Y0: $i] : ( sK1 = Y0 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0),skolemize(X4,sK1)],[f6]) ).
thf(f8,plain,
( ( ^ [Y0: $i] : ( sK0 = Y0 ) )
= ( ^ [Y0: $i] : ( sK1 = Y0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
sK1 != sK0,
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( ( (=) @ sK1 )
= ( (=) @ sK0 ) ),
inference(beta-eta_normalization,[],[f8]) ).
thf(f15,plain,
! [X1: $i] :
( ( sK0 = X1 )
= ( sK1 = X1 ) ),
inference(argument_congruence,[],[f14]) ).
thf(f17,plain,
! [X1: $i] :
( ( $false
= ( sK0 = X1 ) )
| ( $true
= ( sK1 = X1 ) ) ),
inference(iff_proxy_clausification,[],[f15]) ).
thf(f18,plain,
! [X1: $i] :
( ( sK0 != X1 )
| ( $true
= ( sK1 = X1 ) ) ),
inference(equality_proxy_clausification,[],[f17]) ).
thf(f19,plain,
! [X1: $i] :
( ( sK0 != X1 )
| ( sK1 = X1 ) ),
inference(equality_proxy_clausification,[],[f18]) ).
thf(f22,plain,
sK1 = sK0,
inference(equality_resolution,[],[f19]) ).
thf(f23,plain,
$false,
inference(forward_subsumption_resolution,[],[f22,f9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU956^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n002.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 14:53:23 UTC 2026
% 0.10/0.21 % CPUTime :
% 0.10/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.24 Running higher-order theorem proving
% 0.10/0.26 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
% 0.24/0.30 % (1395981)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.30 % (1395987)lrs+10_16_si=on:nwc=1.5:random_seed=1890049557:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.30 % (1395988)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=1590237825:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.30 % (1395989)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=481514051: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)
% 0.24/0.30 % (1395987) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1395981-1395987"...
% 0.24/0.30 % (1395988)Refutation not found, incomplete strategy
% 0.24/0.30 % (1395988)------------------------------
% 0.24/0.30 % (1395988)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (1395988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (1395988)CaDiCaL version: 2.1.3
% 0.24/0.30 % (1395988)Termination reason: Refutation not found, incomplete strategy
% 0.24/0.30 % (1395988)Time elapsed: 0.001 s
% 0.24/0.30 % (1395988)Peak memory usage: 12 MB
% 0.24/0.30 % (1395989) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1395981-1395989"...
% 0.24/0.30 % (1395988)------------------------------
% 0.24/0.30 % (1395988)------------------------------
% 0.24/0.30 % (1395987)...printing done.
% 0.24/0.30 % (1395990)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=408831999:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.30 % (1395986)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3334009423:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.30 % (1395987)Refutation found. Thanks to Tanya!
% 0.24/0.30 % SZS status Theorem for theBenchmark
% 0.24/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.30 % (1395987)------------------------------
% 0.24/0.30 % (1395987)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.30 % (1395987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.30 % (1395987)CaDiCaL version: 2.1.3
% 0.24/0.30 % (1395987)Termination reason: Refutation
% 0.24/0.30 % (1395987)Time elapsed: 0.002 s
% 0.24/0.30 % (1395987)Peak memory usage: 12 MB
% 0.24/0.30 % (1395987)Instructions burned: 1 (million)
% 0.24/0.30 % (1395981)Success in time 0.039 s
% 0.24/0.31 % Vampire exiting
%------------------------------------------------------------------------------