%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG278^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 : Wed Sep 30 07:45:30 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 50 ( 44 unt; 0 typ; 0 def)
% Number of atoms : 191 ( 87 equ; 0 cnn)
% Maximal formula atoms : 2 ( 3 avg)
% Number of connectives : 431 ( 7 ~; 0 |; 17 &; 355 @)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 52 ( 52 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 19 usr; 6 con; 0-4 aty)
% ( 40 !!; 8 ??; 0 @@+; 0 @@-)
% Number of variables : 143 ( 91 ^; 48 !; 4 ?; 143 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cGROUP2: ( g > g > g ) > g > $o ).
thf(func_def_1,type,
cGRP_ASSOC: ( g > g > g ) > $o ).
thf(func_def_2,type,
cGRP_LEFT_INVERSE: ( g > g > g ) > g > $o ).
thf(func_def_3,type,
cGRP_LEFT_UNIT: ( g > g > g ) > g > $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
db3:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_12,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_13,type,
vAND: $o > $o > $o ).
thf(func_def_16,type,
sK0: g > g > g ).
thf(func_def_17,type,
sK1: g ).
thf(func_def_18,type,
sK2: g ).
thf(func_def_19,type,
vNOT: $o > $o ).
thf(func_def_20,type,
sK3: g > g ).
thf(f1,axiom,
( cGRP_ASSOC
= ( ^ [X0: g > g > g] :
! [X1: g,X2: g,X3: g] :
( ( X0 @ ( X0 @ X1 @ X2 ) @ X3 )
= ( X0 @ X1 @ ( X0 @ X2 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_ASSOC_def) ).
thf(f2,axiom,
( cGRP_LEFT_INVERSE
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
? [X3: g] :
( ( X0 @ X3 @ X2 )
= X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_LEFT_INVERSE_def) ).
thf(f3,axiom,
( cGRP_LEFT_UNIT
= ( ^ [X0: g > g > g,X1: g] :
! [X2: g] :
( ( X0 @ X1 @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGRP_LEFT_UNIT_def) ).
thf(f4,axiom,
( cGROUP2
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_LEFT_INVERSE @ X0 @ X1 )
& ( cGRP_LEFT_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cGROUP2_def) ).
thf(f5,conjecture,
! [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
=> ! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cE12A1) ).
thf(f6,negated_conjecture,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
=> ! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) ),
inference(negated_conjecture,[status(cth)],[f5]) ).
thf(f7,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f1]) ).
thf(f8,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(fool_elimination,[],[f2]) ).
thf(f9,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f10,plain,
( cGROUP2
= ( ^ [X0: g > g > g,X1: g] :
( ( cGRP_LEFT_INVERSE @ X0 @ X1 )
& ( cGRP_LEFT_UNIT @ X0 @ X1 )
& ( cGRP_ASSOC @ X0 ) ) ) ),
inference(rectify,[],[f4]) ).
thf(f11,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_LEFT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(fool_elimination,[],[f10]) ).
thf(f12,plain,
~ ! [X0: g > g > g,X1: g] :
( ( cGROUP2 @ X0 @ X1 )
=> ! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) ),
inference(rectify,[],[f6]) ).
thf(f13,plain,
~ ! [X0: g > g > g,X1: g] :
( ( ( cGROUP2 @ X0 @ X1 )
= $true )
=> ! [X2: g] :
( ( X0 @ X2 @ X1 )
= X2 ) ),
inference(fool_elimination,[],[f12]) ).
thf(f14,plain,
? [X0: g > g > g,X1: g] :
( ? [X2: g] :
( ( X0 @ X2 @ X1 )
!= X2 )
& ( ( cGROUP2 @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[],[f13]) ).
thf(f15,plain,
( ( sK2
!= ( sK0 @ sK2 @ sK1 ) )
& ( $true
= ( cGROUP2 @ sK0 @ sK1 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f14]) ).
thf(f16,plain,
( cGRP_ASSOC
= ( ^ [Y0: g > g > g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( !! @ g
@ ^ [Y3: g] :
( ( Y0 @ ( Y0 @ Y3 @ Y2 ) @ Y1 )
= ( Y0 @ Y3 @ ( Y0 @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f17,plain,
( cGRP_LEFT_INVERSE
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ?? @ g
@ ^ [Y3: g] :
( ( Y0 @ Y3 @ Y2 )
= Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,plain,
( cGRP_LEFT_UNIT
= ( ^ [Y0: g > g > g,Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( Y0 @ Y1 @ Y2 )
= Y2 ) ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( cGRP_ASSOC @ Y0 )
& ( cGRP_LEFT_UNIT @ Y0 @ Y1 )
& ( cGRP_LEFT_INVERSE @ Y0 @ Y1 ) ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f20,plain,
( $true
= ( cGROUP2 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f21,plain,
( sK2
!= ( sK0 @ sK2 @ sK1 ) ),
inference(cnf_transformation,[],[f15]) ).
thf(f24,plain,
( cGROUP2
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 ) ) ) ),
inference(definition_unfolding,[],[f19,f16,f18,f17]) ).
thf(f25,plain,
( $true
= ( ^ [Y0: g > g > g,Y1: g] :
( ( ^ [Y2: g > g > g] :
( !! @ g
@ ^ [Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( !! @ g
@ ^ [Y5: g] :
( ( Y2 @ ( Y2 @ Y5 @ Y4 ) @ Y3 )
= ( Y2 @ Y5 @ ( Y2 @ Y4 @ Y3 ) ) ) ) ) )
@ Y0 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ( Y2 @ Y3 @ Y4 )
= Y4 ) )
@ Y0
@ Y1 )
& ( ^ [Y2: g > g > g,Y3: g] :
( !! @ g
@ ^ [Y4: g] :
( ?? @ g
@ ^ [Y5: g] :
( ( Y2 @ Y5 @ Y4 )
= Y3 ) ) )
@ Y0
@ Y1 ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f20,f24]) ).
thf(f26,plain,
( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) )
& ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) ) ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( $true
= ( ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) )
& ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) ) ),
inference(and_proxy_clausification,[],[f26]) ).
thf(f29,plain,
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f28]) ).
thf(f31,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( !! @ g
@ ^ [Y2: g] :
( ( sK0 @ ( sK0 @ Y2 @ Y1 ) @ Y0 )
= ( sK0 @ Y2 @ ( sK0 @ Y1 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f30]) ).
thf(f32,plain,
! [X1: g] :
( $true
= ( !! @ g
@ ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X1 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X1 ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
! [X2: g,X1: g] :
( $true
= ( ^ [Y0: g] :
( !! @ g
@ ^ [Y1: g] :
( ( sK0 @ ( sK0 @ Y1 @ Y0 ) @ X1 )
= ( sK0 @ Y1 @ ( sK0 @ Y0 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_proxy_clausification,[],[f32]) ).
thf(f34,plain,
! [X2: g,X1: g] :
( $true
= ( !! @ g
@ ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X2 ) @ X1 )
= ( sK0 @ Y0 @ ( sK0 @ X2 @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f35,plain,
! [X2: g,X3: g,X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK0 @ ( sK0 @ Y0 @ X2 ) @ X1 )
= ( sK0 @ Y0 @ ( sK0 @ X2 @ X1 ) ) )
@ X3 ) ),
inference(pi_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X2: g,X3: g,X1: g] :
( $true
= ( ( sK0 @ ( sK0 @ X3 @ X2 ) @ X1 )
= ( sK0 @ X3 @ ( sK0 @ X2 @ X1 ) ) ) ),
inference(beta-eta_normalization,[],[f35]) ).
thf(f37,plain,
! [X2: g,X3: g,X1: g] :
( ( sK0 @ ( sK0 @ X3 @ X2 ) @ X1 )
= ( sK0 @ X3 @ ( sK0 @ X2 @ X1 ) ) ),
inference(equality_proxy_clausification,[],[f36]) ).
thf(f38,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK0 @ sK1 @ Y0 )
= Y0 )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f39,plain,
! [X1: g] :
( $true
= ( ( sK0 @ sK1 @ X1 )
= X1 ) ),
inference(beta-eta_normalization,[],[f38]) ).
thf(f40,plain,
! [X1: g] :
( ( sK0 @ sK1 @ X1 )
= X1 ),
inference(equality_proxy_clausification,[],[f39]) ).
thf(f41,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ?? @ g
@ ^ [Y1: g] :
( ( sK0 @ Y1 @ Y0 )
= sK1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f27]) ).
thf(f42,plain,
! [X1: g] :
( $true
= ( ?? @ g
@ ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X1: g] :
( $true
= ( ^ [Y0: g] :
( ( sK0 @ Y0 @ X1 )
= sK1 )
@ ( sK3 @ X1 ) ) ),
inference(sigma_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X1: g] :
( $true
= ( ( sK0 @ ( sK3 @ X1 ) @ X1 )
= sK1 ) ),
inference(beta-eta_normalization,[],[f43]) ).
thf(f45,plain,
! [X1: g] :
( sK1
= ( sK0 @ ( sK3 @ X1 ) @ X1 ) ),
inference(equality_proxy_clausification,[],[f44]) ).
thf(f54,plain,
! [X0: g,X1: g] :
( ( sK0 @ sK1 @ X1 )
= ( sK0 @ ( sK3 @ X0 ) @ ( sK0 @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f37,f45]) ).
thf(f57,plain,
! [X0: g,X1: g] :
( ( sK0 @ ( sK3 @ X0 ) @ ( sK0 @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[],[f54,f40]) ).
thf(f60,plain,
! [X0: g] :
( ( sK0 @ ( sK3 @ ( sK3 @ X0 ) ) @ sK1 )
= X0 ),
inference(constrained_superposition,[],[f57,f45]) ).
thf(f62,plain,
! [X0: g,X1: g] :
( ( sK0 @ X1 @ X0 )
= ( sK0 @ ( sK3 @ ( sK3 @ X1 ) ) @ X0 ) ),
inference(constrained_superposition,[],[f57,f57]) ).
thf(f65,plain,
! [X0: g] :
( ( sK0 @ X0 @ sK1 )
= X0 ),
inference(forward_demodulation,[],[f60,f62]) ).
thf(f72,plain,
sK2 != sK2,
inference(constrained_superposition,[],[f21,f65]) ).
thf(f73,plain,
$false,
inference(trivial_inequality_removal,[],[f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG278^5 : TPTP v9.3.1. Bugfixed v5.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 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 : Tue Sep 29 17:42:06 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.22 Running first-order model finding
% 0.08/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.27 % (1577684)Will run a generic schedule for satisfiability detection.
% 0.20/0.27 % (1577693)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1708438034:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.27 % (1577693)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.27 % (1577693) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1577684-1577693"...
% 0.20/0.27 % (1577690)% WARNING: option uhcvi not known.
% 0.20/0.27 % (1577693)...printing done.
% 0.20/0.27 % (1577693)Refutation found. Thanks to Tanya!
% 0.20/0.27 % SZS status Theorem for theBenchmark
% 0.20/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.27 % (1577693)------------------------------
% 0.20/0.27 % (1577693)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1577693)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1577693)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1577693)Termination reason: Refutation
% 0.20/0.27 % (1577693)Time elapsed: 0.003 s
% 0.20/0.27 % (1577693)Peak memory usage: 12 MB
% 0.20/0.27 % (1577693)Instructions burned: 8 (million)
% 0.20/0.27 % (1577684)Success in time 0.038 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------