%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG286^5 : TPTP v9.3.1. Released v4.0.0.
% 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 07:45:31 AM UTC 2026
% Result : Theorem 0.09s 0.25s
% Output : Refutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 1
% Syntax : Number of formulae : 26 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 72 ( 71 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 188 ( 19 ~; 4 |; 31 &; 123 @)
% ( 5 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 36 ( 0 ^; 36 !; 0 ?; 36 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cZ: a ).
thf(func_def_1,type,
u: a ).
thf(func_def_2,type,
y: a ).
thf(func_def_3,type,
x: a ).
thf(func_def_4,type,
cP: a > a > a ).
thf(func_def_5,type,
cR: a > a ).
thf(func_def_6,type,
cL: a > a ).
thf(f1,conjecture,
( ( ! [X2: a] :
( ( X2 != cZ )
<=> ( X2
= ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) ) ) )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ( ( cR @ cZ )
= cZ )
& ( ( cL @ cZ )
= cZ ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( u != cZ ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cPU_PAIR_NOT_ZERO_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X2: a] :
( ( X2 != cZ )
<=> ( X2
= ( cP @ ( cL @ X2 ) @ ( cR @ X2 ) ) ) )
& ! [X0: a,X1: a] :
( ( cR @ ( cP @ X0 @ X1 ) )
= X1 )
& ! [X0: a,X1: a] :
( ( cL @ ( cP @ X0 @ X1 ) )
= X0 )
& ( ( cR @ cZ )
= cZ )
& ( ( cL @ cZ )
= cZ ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( u != cZ ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: a] :
( ( cZ != X0 )
<=> ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
= X0 ) )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 )
& ! [X3: a,X4: a] :
( ( cL @ ( cP @ X3 @ X4 ) )
= X3 )
& ( ( cR @ cZ )
= cZ )
& ( ( cL @ cZ )
= cZ ) )
=> ( ( u
= ( cP @ x @ y ) )
=> ( u != cZ ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( cZ = u )
& ( u
= ( cP @ x @ y ) )
& ! [X0: a] :
( ( cZ != X0 )
<=> ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
= X0 ) )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 )
& ! [X3: a,X4: a] :
( ( cL @ ( cP @ X3 @ X4 ) )
= X3 )
& ( ( cR @ cZ )
= cZ )
& ( ( cL @ cZ )
= cZ ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
( ( cZ = u )
& ( u
= ( cP @ x @ y ) )
& ! [X0: a] :
( ( cZ != X0 )
<=> ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
= X0 ) )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 )
& ! [X3: a,X4: a] :
( ( cL @ ( cP @ X3 @ X4 ) )
= X3 )
& ( ( cR @ cZ )
= cZ )
& ( ( cL @ cZ )
= cZ ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( cZ = u )
& ( u
= ( cP @ x @ y ) )
& ! [X0: a] :
( ( ( cZ != X0 )
| ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
!= X0 ) )
& ( ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
= X0 )
| ( cZ = X0 ) ) )
& ! [X1: a,X2: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 )
& ! [X3: a,X4: a] :
( ( cL @ ( cP @ X3 @ X4 ) )
= X3 )
& ( ( cR @ cZ )
= cZ )
& ( ( cL @ cZ )
= cZ ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
( cZ
= ( cL @ cZ ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( cZ
= ( cR @ cZ ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
! [X3: a,X4: a] :
( ( cL @ ( cP @ X3 @ X4 ) )
= X3 ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
! [X2: a,X1: a] :
( ( cR @ ( cP @ X1 @ X2 ) )
= X2 ),
inference(cnf_transformation,[],[f6]) ).
thf(f12,plain,
! [X0: a] :
( ( cZ != X0 )
| ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
!= X0 ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,plain,
( u
= ( cP @ x @ y ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f14,plain,
cZ = u,
inference(cnf_transformation,[],[f6]) ).
thf(f15,plain,
! [X0: a] :
( ( u != X0 )
| ( ( cP @ ( cL @ X0 ) @ ( cR @ X0 ) )
!= X0 ) ),
inference(definition_unfolding,[],[f12,f14]) ).
thf(f17,plain,
( u
= ( cR @ u ) ),
inference(definition_unfolding,[],[f8,f14,f14]) ).
thf(f18,plain,
( u
= ( cL @ u ) ),
inference(definition_unfolding,[],[f7,f14,f14]) ).
thf(f19,plain,
( u
!= ( cP @ ( cL @ u ) @ ( cR @ u ) ) ),
inference(equality_resolution,[],[f15]) ).
thf(f22,plain,
( u
!= ( cP @ u @ ( cR @ u ) ) ),
inference(constrained_superposition,[],[f19,f18]) ).
thf(f23,plain,
( u
!= ( cP @ u @ u ) ),
inference(forward_demodulation,[],[f22,f17]) ).
thf(f24,plain,
( x
= ( cL @ u ) ),
inference(constrained_superposition,[],[f9,f13]) ).
thf(f25,plain,
u = x,
inference(forward_demodulation,[],[f24,f18]) ).
thf(f26,plain,
( u
= ( cP @ u @ y ) ),
inference(constrained_superposition,[],[f13,f25]) ).
thf(f28,plain,
( y
= ( cR @ u ) ),
inference(constrained_superposition,[],[f10,f13]) ).
thf(f31,plain,
u = y,
inference(forward_demodulation,[],[f28,f17]) ).
thf(f32,plain,
( u
= ( cP @ u @ u ) ),
inference(constrained_superposition,[],[f26,f31]) ).
thf(f35,plain,
$false,
inference(forward_subsumption_resolution,[],[f32,f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG286^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.17 % Computer : n001.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 17:43:36 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.21 Running first-order model finding
% 0.09/0.21 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
% 0.09/0.25 % (1580614)Will run a generic schedule for satisfiability detection.
% 0.09/0.25 % (1580619)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=384610708_2999 on theBenchmark for (2999ds/0Mi)
% 0.09/0.25 % Exception at run slice level
% 0.09/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.25 % (1580622)dis+10_1_sil=32000:sp=arity:random_seed=703998927:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.09/0.25 % (1580621)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=23348276:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.09/0.25 % (1580625)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=2917757649:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.09/0.25 % (1580623)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=1195398466:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.09/0.25 % (1580627)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=1066603647:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.09/0.25 % (1580622) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1580614-1580622"...
% 0.09/0.25 % (1580623)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.09/0.25 % Exception at run slice level
% 0.09/0.25 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.09/0.25 % (1580624)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2485017772:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.09/0.25 % (1580621) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1580614-1580621"...
% 0.09/0.25 % (1580625) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1580614-1580625"...
% 0.09/0.25 % (1580623) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1580614-1580623"...
% 0.09/0.25 % (1580622)...printing done.
% 0.09/0.25 % (1580621)...printing done.
% 0.09/0.25 % (1580624) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1580614-1580624"...
% 0.09/0.25 % (1580625)...printing done.
% 0.09/0.25 % (1580623)...printing done.
% 0.09/0.25 % (1580621)Refutation found. Thanks to Tanya!
% 0.09/0.25 % SZS status Theorem for theBenchmark
% 0.09/0.25 % SZS output start Proof for theBenchmark
% See solution above
% 0.09/0.25 % (1580621)------------------------------
% 0.09/0.25 % (1580621)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.09/0.25 % (1580621)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.09/0.25 % (1580621)CaDiCaL version: 2.1.3
% 0.09/0.25 % (1580621)Termination reason: Refutation
% 0.09/0.25 % (1580621)Time elapsed: 0.003 s
% 0.09/0.25 % (1580621)Peak memory usage: 12 MB
% 0.09/0.25 % (1580621)Instructions burned: 3 (million)
% 0.09/0.25 % (1580614)Success in time 0.036 s
% 0.09/0.25 % Vampire exiting
%------------------------------------------------------------------------------