%------------------------------------------------------------------------------
% File : Vampire-SAT---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 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 08:50:42 AM UTC 2026
% Result : Theorem 0.19s 0.27s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 2
% Syntax : Number of formulae : 19 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 19 ( 18 equ; 0 cnn)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 238 ( 11 ~; 0 |; 0 &; 227 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 4 ( 4 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 10 usr; 4 con; 0-6 aty)
% Number of variables : 66 ( 13 ^; 46 !; 7 ?; 66 :)
% 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 > sK0 ).
thf(func_def_5,type,
sK5: sK3 > sK1 ).
thf(func_def_6,type,
sK6: sK2 > sK3 ).
thf(func_def_7,type,
sK7: sK2 ).
thf(func_def_8,type,
sK8: sK2 ).
thf(func_def_9,type,
sK9: sK2 ).
thf(f1,axiom,
! [X2: $tType,X0: $tType,X1: $tType,X3: X0 > X2,X4: X1 > X0] :
( ( o @ X0 @ X1 @ X2 @ X3 @ X4 )
= ( ^ [X5: X1] : ( X3 @ ( X4 @ X5 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p','trivia/o_DEF_') ).
thf(f2,conjecture,
! [X0: $tType,X1: $tType,X2: $tType,X3: $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,
~ ! [X0: $tType,X1: $tType,X2: $tType,X3: $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 > X0,X4: X2 > X1] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 )
= ( ^ [X5: X2] : ( X3 @ ( X4 @ X5 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
! [X0: $tType,X1: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 )
= ( ^ [Y0: X2] : ( X3 @ ( X4 @ Y0 ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
? [X0: $tType,X1: $tType,X2: $tType,X3: $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(ennf_transformation,[],[f3]) ).
thf(f7,plain,
( ( o @ sK1 @ sK2 @ sK0 @ sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 ) )
!= ( o @ sK3 @ sK2 @ sK0 @ ( o @ sK1 @ sK3 @ sK0 @ sK4 @ sK5 ) @ sK6 ) ),
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)],[f6]) ).
thf(f8,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 )
= ( ^ [Y0: X2] : ( X3 @ ( X4 @ Y0 ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( ( o @ sK1 @ sK2 @ sK0 @ sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 ) )
!= ( o @ sK3 @ sK2 @ sK0 @ ( o @ sK1 @ sK3 @ sK0 @ sK4 @ sK5 ) @ sK6 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1,X5: X2] :
( ( o @ X1 @ X2 @ X0 @ X3 @ X4 @ X5 )
= ( ^ [Y0: X2] : ( X3 @ ( X4 @ Y0 ) )
@ X5 ) ),
inference(argument_congruence,[],[f8]) ).
thf(f13,plain,
( ( o @ sK1 @ sK2 @ sK0 @ sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 ) )
!= ( o @ sK3 @ sK2 @ sK0
@ ^ [Y0: sK3] : ( sK4 @ ( sK5 @ Y0 ) )
@ sK6 ) ),
inference(constrained_superposition,[],[f9,f8]) ).
thf(f15,plain,
! [X1: $tType,X0: $tType,X2: $tType,X3: X1 > X0,X4: X2 > X1,X5: X2] :
( ( X3 @ ( X4 @ X5 ) )
= ( o @ X1 @ X2 @ X0 @ X3 @ X4 @ X5 ) ),
inference(beta-eta_normalization,[],[f11]) ).
thf(f17,plain,
( ( o @ sK1 @ sK2 @ sK0 @ sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 ) )
!= ( ^ [Y0: sK2] :
( ^ [Y1: sK3] : ( sK4 @ ( sK5 @ Y1 ) )
@ ( sK6 @ Y0 ) ) ) ),
inference(forward_demodulation,[],[f13,f8]) ).
thf(f18,plain,
( ( o @ sK1 @ sK2 @ sK0 @ sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 ) )
!= ( ^ [Y0: sK2] : ( sK4 @ ( sK5 @ ( sK6 @ Y0 ) ) ) ) ),
inference(beta-eta_normalization,[],[f17]) ).
thf(f20,plain,
( ( ^ [Y0: sK2] : ( sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0 ) ) )
!= ( ^ [Y0: sK2] : ( sK4 @ ( sK5 @ ( sK6 @ Y0 ) ) ) ) ),
inference(forward_demodulation,[],[f18,f8]) ).
thf(f21,plain,
( ( ^ [Y0: sK2] : ( sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ Y0 ) )
@ sK8 )
!= ( ^ [Y0: sK2] : ( sK4 @ ( sK5 @ ( sK6 @ Y0 ) ) )
@ sK8 ) ),
inference(negative_extensionality,[],[f20]) ).
thf(f22,plain,
( ( sK4 @ ( o @ sK3 @ sK2 @ sK1 @ sK5 @ sK6 @ sK8 ) )
!= ( sK4 @ ( sK5 @ ( sK6 @ sK8 ) ) ) ),
inference(beta-eta_normalization,[],[f21]) ).
thf(f29,plain,
( ( sK4 @ ( sK5 @ ( sK6 @ sK8 ) ) )
!= ( sK4 @ ( sK5 @ ( sK6 @ sK8 ) ) ) ),
inference(constrained_superposition,[],[f22,f15]) ).
thf(f30,plain,
$false,
inference(trivial_inequality_removal,[],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % 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 SAT
% 0.09/0.19 % Computer : n001.cluster.edu
% 0.09/0.19 % Model : x86_64 x86_64
% 0.09/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.19 % Memory : 8046.5625MB
% 0.09/0.19 % OS : Linux 6.8.0-71-generic
% 0.09/0.19 % CPULimit : 300
% 0.09/0.19 % WCLimit : 300
% 0.09/0.19 % DateTime : Tue Sep 29 17:35:06 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 SAT
% 0.09/0.22 Running first-order model finding
% 0.09/0.22 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
% 0.19/0.27 % (1565733)Will run a generic schedule for satisfiability detection.
% 0.19/0.27 % (1565751)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2569312030:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.19/0.27 % (1565751) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-1565733-1565751"...
% 0.19/0.27 % (1565751)...printing done.
% 0.19/0.27 % (1565751)Refutation found. Thanks to Tanya!
% 0.19/0.27 % SZS status Theorem for theBenchmark
% 0.19/0.27 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.27 % (1565751)------------------------------
% 0.19/0.27 % (1565751)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.27 % (1565751)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.27 % (1565751)CaDiCaL version: 2.1.3
% 0.19/0.27 % (1565751)Termination reason: Refutation
% 0.19/0.27 % (1565751)Time elapsed: 0.002 s
% 0.19/0.27 % (1565751)Peak memory usage: 12 MB
% 0.19/0.27 % (1565751)Instructions burned: 4 (million)
% 0.19/0.27 % (1565733)Success in time 0.037 s
% 0.19/0.27 % Vampire exiting
%------------------------------------------------------------------------------