%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYP118^1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n004.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 08:50:41 AM UTC 2026
% Result : Theorem 0.20s 0.27s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 23 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 23 ( 22 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 306 ( 14 ~; 0 |; 0 &; 292 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 4 ( 4 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 3 con; 0-6 aty)
% Number of variables : 95 ( 16 ^; 65 !; 14 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(type_def_6,type,
sK0: $tType ).
thf(type_def_7,type,
sK1: $tType ).
thf(type_def_8,type,
sK2: $tType ).
thf(type_def_9,type,
sK3: $tType ).
thf(func_def_0,type,
o:
!>[X0: $tType,X1: $tType,X2: $tType] : ( ( X0 > X2 ) > ( X1 > X0 ) > X1 > X2 ) ).
thf(func_def_2,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_3,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_4,type,
sK4: sK1 > sK3 ).
thf(func_def_5,type,
sK5: sK2 > sK0 ).
thf(func_def_6,type,
sK6: sK0 > sK1 ).
thf(func_def_7,type,
sK7: sK2 ).
thf(func_def_8,type,
sK8: sK2 ).
thf(f1,axiom,
! [X2: $tType,X1: $tType,X0: $tType,X4: X1 > X0,X3: X0 > X2] :
( ( ^ [X5: X1] : ( X3 @ ( X4 @ X5 ) ) )
= ( o @ X0 @ X1 @ X2 @ X3 @ X4 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','trivia/o_DEF_') ).
thf(f2,conjecture,
! [X2: $tType,X0: $tType,X3: $tType,X1: $tType,X4: X1 > X0,X5: X3 > X1,X6: X2 > X3] :
( ( o @ X1 @ X2 @ X0 @ X4 @ ( o @ X3 @ X2 @ X1 @ X5 @ X6 ) )
= ( o @ X3 @ X2 @ X0 @ ( o @ X1 @ X3 @ X0 @ X4 @ X5 ) @ X6 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','trivia/o_ASSOC_') ).
thf(f3,negated_conjecture,
~ ! [X2: $tType,X0: $tType,X3: $tType,X1: $tType,X4: X1 > X0,X5: X3 > X1,X6: X2 > X3] :
( ( o @ X1 @ X2 @ X0 @ X4 @ ( o @ X3 @ X2 @ X1 @ X5 @ X6 ) )
= ( o @ X3 @ X2 @ X0 @ ( o @ X1 @ X3 @ X0 @ X4 @ X5 ) @ X6 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X2,X4: X2 > X0] :
( ( ^ [X5: X1] : ( X4 @ ( X3 @ X5 ) ) )
= ( o @ X2 @ X1 @ X0 @ X4 @ X3 ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
! [X0: $tType,X1: $tType,X2: $tType,X4: X2 > X0,X3: X1 > X2] :
( ( o @ X2 @ X1 @ X0 @ X4 @ X3 )
= ( ^ [Y0: X1] : ( X4 @ ( X3 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: X3 > X1,X5: X2 > X3,X6: X0 > X2] :
( ( o @ X2 @ X0 @ X1 @ ( o @ X3 @ X2 @ X1 @ X4 @ X5 ) @ X6 )
= ( o @ X3 @ X0 @ X1 @ X4 @ ( o @ X2 @ X0 @ X3 @ X5 @ X6 ) ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ! [X1: $tType,X0: $tType,X2: $tType,X3: $tType,X5: X2 > X3,X6: X0 > X2,X4: X3 > X1] :
( ( o @ X2 @ X0 @ X1 @ ( o @ X3 @ X2 @ X1 @ X4 @ X5 ) @ X6 )
= ( o @ X3 @ X0 @ X1 @ X4 @ ( o @ X2 @ X0 @ X3 @ X5 @ X6 ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X2: $tType,X3: $tType,X0: $tType,X1: $tType,X4: X3 > X1,X6: X0 > X2,X5: X2 > X3] :
( ( o @ X2 @ X0 @ X1 @ ( o @ X3 @ X2 @ X1 @ X4 @ X5 ) @ X6 )
!= ( o @ X3 @ X0 @ X1 @ X4 @ ( o @ X2 @ X0 @ X3 @ X5 @ X6 ) ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X2 > X0,X4: X1 > X2] :
( ( ^ [Y0: X1] : ( X3 @ ( X4 @ Y0 ) ) )
= ( o @ X2 @ X1 @ X0 @ X3 @ X4 ) ),
inference(rectify,[],[f5]) ).
thf(f10,plain,
? [X0: $tType,X1: $tType,X2: $tType,X3: $tType,X4: X1 > X3,X5: X2 > X0,X6: X0 > X1] :
( ( o @ X1 @ X2 @ X3 @ X4 @ ( o @ X0 @ X2 @ X1 @ X6 @ X5 ) )
!= ( o @ X0 @ X2 @ X3 @ ( o @ X1 @ X0 @ X3 @ X4 @ X6 ) @ X5 ) ),
inference(rectify,[],[f8]) ).
thf(f11,plain,
( ( o @ sK0 @ sK2 @ sK3 @ ( o @ sK1 @ sK0 @ sK3 @ sK4 @ sK6 ) @ sK5 )
!= ( o @ sK1 @ sK2 @ sK3 @ sK4 @ ( o @ sK0 @ sK2 @ sK1 @ sK6 @ sK5 ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6)],[f10]) ).
thf(f12,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2 > X0,X4: X1 > X2] :
( ( ^ [Y0: X1] : ( X3 @ ( X4 @ Y0 ) ) )
= ( o @ X2 @ X1 @ X0 @ X3 @ X4 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f13,plain,
( ( o @ sK0 @ sK2 @ sK3 @ ( o @ sK1 @ sK0 @ sK3 @ sK4 @ sK6 ) @ sK5 )
!= ( o @ sK1 @ sK2 @ sK3 @ sK4 @ ( o @ sK0 @ sK2 @ sK1 @ sK6 @ sK5 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f17,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2 > X0,X4: X1 > X2,X5: X1] :
( ( ^ [Y0: X1] : ( X3 @ ( X4 @ Y0 ) )
@ X5 )
= ( o @ X2 @ X1 @ X0 @ X3 @ X4 @ X5 ) ),
inference(argument_congruence,[],[f12]) ).
thf(f18,plain,
( ( o @ sK0 @ sK2 @ sK3
@ ^ [Y0: sK0] : ( sK4 @ ( sK6 @ Y0 ) )
@ sK5 )
!= ( o @ sK1 @ sK2 @ sK3 @ sK4 @ ( o @ sK0 @ sK2 @ sK1 @ sK6 @ sK5 ) ) ),
inference(constrained_superposition,[],[f13,f12]) ).
thf(f20,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X2 > X0,X4: X1 > X2,X5: X1] :
( ( o @ X2 @ X1 @ X0 @ X3 @ X4 @ X5 )
= ( X3 @ ( X4 @ X5 ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f21,plain,
( ( ^ [Y0: sK2] : ( sK4 @ ( o @ sK0 @ sK2 @ sK1 @ sK6 @ sK5 @ Y0 ) ) )
!= ( o @ sK0 @ sK2 @ sK3
@ ^ [Y0: sK0] : ( sK4 @ ( sK6 @ Y0 ) )
@ sK5 ) ),
inference(forward_demodulation,[],[f18,f12]) ).
thf(f23,plain,
( ( ^ [Y0: sK2] : ( sK4 @ ( o @ sK0 @ sK2 @ sK1 @ sK6 @ sK5 @ Y0 ) ) )
!= ( ^ [Y0: sK2] :
( ^ [Y1: sK0] : ( sK4 @ ( sK6 @ Y1 ) )
@ ( sK5 @ Y0 ) ) ) ),
inference(forward_demodulation,[],[f21,f12]) ).
thf(f24,plain,
( ( ^ [Y0: sK2] : ( sK4 @ ( o @ sK0 @ sK2 @ sK1 @ sK6 @ sK5 @ Y0 ) ) )
!= ( ^ [Y0: sK2] : ( sK4 @ ( sK6 @ ( sK5 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
( ( ^ [Y0: sK2] : ( sK4 @ ( sK6 @ ( sK5 @ Y0 ) ) )
@ sK8 )
!= ( ^ [Y0: sK2] : ( sK4 @ ( o @ sK0 @ sK2 @ sK1 @ sK6 @ sK5 @ Y0 ) )
@ sK8 ) ),
inference(negative_extensionality,[],[f24]) ).
thf(f26,plain,
( ( sK4 @ ( sK6 @ ( sK5 @ sK8 ) ) )
!= ( sK4 @ ( o @ sK0 @ sK2 @ sK1 @ sK6 @ sK5 @ sK8 ) ) ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
( ( sK4 @ ( sK6 @ ( sK5 @ sK8 ) ) )
!= ( sK4 @ ( sK6 @ ( sK5 @ sK8 ) ) ) ),
inference(forward_demodulation,[],[f26,f20]) ).
thf(f28,plain,
$false,
inference(trivial_inequality_removal,[],[f27]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYP118^1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n004.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 17:29:07 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.22 Running higher-order theorem proving
% 0.08/0.23 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.27 % (1604927)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.27 % (1604934)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2669116150:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.27 % (1604934) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1604927-1604934"...
% 0.20/0.27 % (1604934)...printing done.
% 0.20/0.27 % (1604934)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 % (1604934)------------------------------
% 0.20/0.27 % (1604934)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.27 % (1604934)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.27 % (1604934)CaDiCaL version: 2.1.3
% 0.20/0.27 % (1604934)Termination reason: Refutation
% 0.20/0.27 % (1604934)Time elapsed: 0.002 s
% 0.20/0.27 % (1604934)Peak memory usage: 12 MB
% 0.20/0.27 % (1604934)Instructions burned: 3 (million)
% 0.20/0.27 % (1604927)Success in time 0.031 s
% 0.20/0.27 % Vampire exiting
%------------------------------------------------------------------------------