%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV177^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% Computer : n016.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 08:39:06 AM UTC 2026
% Result : Theorem 0.23s 0.32s
% Output : Refutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 1
% Syntax : Number of formulae : 28 ( 21 unt; 0 typ; 0 def)
% Number of atoms : 139 ( 69 equ; 0 cnn)
% Maximal formula atoms : 2 ( 4 avg)
% Number of connectives : 321 ( 47 ~; 4 |; 35 &; 205 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 11 usr; 3 con; 0-4 aty)
% ( 0 !!; 26 ??; 0 @@+; 0 @@-)
% Number of variables : 73 ( 55 ^; 13 !; 5 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
vAND: $o > $o > $o ).
thf(func_def_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_5,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_7,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
sK0: ( $i > $o ) > $i ).
thf(func_def_11,type,
sK1: $i > $o ).
thf(func_def_12,type,
sK2: $i > $o ).
thf(f1,conjecture,
! [X0: ( $i > $o ) > $i,X1: $i > $o] :
( ( X1
= ( ^ [X2: $i] :
? [X3: $i > $o] :
( ( X2
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ) )
=> ( X1 @ ( X0 @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM144_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: ( $i > $o ) > $i,X1: $i > $o] :
( ( X1
= ( ^ [X2: $i] :
? [X3: $i > $o] :
( ( X2
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ) )
=> ( X1 @ ( X0 @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: ( $i > $o ) > $i,X1: $i > $o] :
( ( X1
= ( ^ [X2: $i] :
? [X3: $i > $o] :
( ( X2
= ( X0 @ X3 ) )
& ~ ( X3 @ ( X0 @ X3 ) ) ) ) )
=> ( X1 @ ( X0 @ X1 ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X0: ( $i > $o ) > $i,X1: $i > $o] :
( ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) )
= X1 )
=> ( ( X1 @ ( X0 @ X1 ) )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X0: ( $i > $o ) > $i,X1: $i > $o] :
( ( ( X1 @ ( X0 @ X1 ) )
!= $true )
& ( ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( X0 @ Y1 ) )
& ( ( X0 @ Y1 )
= Y0 ) ) ) )
= X1 ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ( $true
!= ( sK1 @ ( sK0 @ sK1 ) ) )
& ( sK1
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f5]) ).
thf(f7,plain,
( sK1
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( $true
!= ( sK1 @ ( sK0 @ sK1 ) ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
( $true
!= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) )
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(definition_unfolding,[],[f8,f7,f7]) ).
thf(f12,plain,
( $true
!= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f13,plain,
! [X1: $i > $o] :
( $false
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f12]) ).
thf(f14,plain,
! [X1: $i > $o] :
( $false
= ( ~ ( X1 @ ( sK0 @ X1 ) )
& ( ( sK0 @ X1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f15,plain,
! [X1: $i > $o] :
( ( $false
= ( ( sK0 @ X1 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) )
| ( $false
= ( ~ ( X1 @ ( sK0 @ X1 ) ) ) ) ),
inference(and_proxy_clausification,[],[f14]) ).
thf(f16,plain,
! [X1: $i > $o] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
!= ( sK0 @ X1 ) )
| ( $false
= ( ~ ( X1 @ ( sK0 @ X1 ) ) ) ) ),
inference(equality_proxy_clausification,[],[f15]) ).
thf(f17,plain,
! [X1: $i > $o] :
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
!= ( sK0 @ X1 ) )
| ( $true
= ( X1 @ ( sK0 @ X1 ) ) ) ),
inference(not_proxy_clausification,[],[f16]) ).
thf(f25,plain,
( $true
= ( ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) )
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(equality_resolution,[],[f17]) ).
thf(f26,plain,
( $true
= ( ?? @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ~ ( Y0 @ ( sK0 @ Y0 ) )
& ( ( sK0 @ Y0 )
= ( sK0
@ ^ [Y1: $i] :
( ?? @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ~ ( Y2 @ ( sK0 @ Y2 ) )
& ( ( sK0 @ Y2 )
= Y1 ) ) ) ) ) )
@ sK2 ) ),
inference(sigma_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( $true
= ( ~ ( sK2 @ ( sK0 @ sK2 ) )
& ( ( sK0 @ sK2 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
( $true
= ( ( sK0 @ sK2 )
= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( $true
= ( ~ ( sK2 @ ( sK0 @ sK2 ) ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f31,plain,
( $false
= ( sK2 @ ( sK0 @ sK2 ) ) ),
inference(not_proxy_clausification,[],[f30]) ).
thf(f32,plain,
( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
= ( sK0 @ sK2 ) ),
inference(equality_proxy_clausification,[],[f29]) ).
thf(f35,plain,
( ( ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) )
!= ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) )
| ( $true
= ( sK2
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ) ),
inference(constrained_superposition,[],[f17,f32]) ).
thf(f36,plain,
( $false
= ( sK2
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(constrained_superposition,[],[f31,f32]) ).
thf(f37,plain,
( $true
= ( sK2
@ ( sK0
@ ^ [Y0: $i] :
( ?? @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ~ ( Y1 @ ( sK0 @ Y1 ) )
& ( ( sK0 @ Y1 )
= Y0 ) ) ) ) ) ),
inference(trivial_inequality_removal,[],[f35]) ).
thf(f38,plain,
$true = $false,
inference(forward_demodulation,[],[f37,f36]) ).
thf(f39,plain,
$false,
inference(trivial_inequality_removal,[],[f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV177^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.23 % Computer : n016.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 15:23:34 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.23/0.28 Running first-order model finding
% 0.23/0.28 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.23/0.32 % (479779)Will run a generic schedule for satisfiability detection.
% 0.23/0.32 % (479788)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=162602838:i=116_3000 on theBenchmark for (3000ds/116Mi)
% 0.23/0.32 % (479788)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.23/0.32 % (479789)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=664330591:i=131_3000 on theBenchmark for (3000ds/131Mi)
% 0.23/0.32 % (479788)Refutation not found, incomplete strategy
% 0.23/0.32 % (479788)------------------------------
% 0.23/0.32 % (479788)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (479788)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (479788)CaDiCaL version: 2.1.3
% 0.23/0.32 % (479788)Termination reason: Refutation not found, incomplete strategy
% 0.23/0.32 % (479788)Time elapsed: 0.003 s
% 0.23/0.32 % (479788)Peak memory usage: 12 MB
% 0.23/0.32 % (479788)Instructions burned: 4 (million)
% 0.23/0.32 % (479788)------------------------------
% 0.23/0.32 % (479788)------------------------------
% 0.23/0.32 % (479789) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-479779-479789"...
% 0.23/0.32 % (479785)% WARNING: option uhcvi not known.
% 0.23/0.32 % (479789)...printing done.
% 0.23/0.32 % (479789)Refutation found. Thanks to Tanya!
% 0.23/0.32 % SZS status Theorem for theBenchmark
% 0.23/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.23/0.32 % (479789)------------------------------
% 0.23/0.32 % (479789)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.23/0.32 % (479789)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.23/0.32 % (479789)CaDiCaL version: 2.1.3
% 0.23/0.32 % (479789)Termination reason: Refutation
% 0.23/0.32 % (479789)Time elapsed: 0.004 s
% 0.23/0.32 % (479789)Peak memory usage: 12 MB
% 0.23/0.32 % (479789)Instructions burned: 4 (million)
% 0.23/0.32 % (479779)Success in time 0.029 s
% 0.23/0.32 % Vampire exiting
%------------------------------------------------------------------------------