%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG285^5 : 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 : n017.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 0.19s 0.28s
% Output : Refutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 16 unt; 0 typ; 3 def)
% Number of atoms : 93 ( 63 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 351 ( 40 ~; 24 |; 24 &; 257 @)
% ( 3 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 10 con; 0-2 aty)
% Number of variables : 104 ( 0 sgn 83 !; 21 ?; 104 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cP: a > a > a ).
thf(func_def_1,type,
cE: a ).
thf(func_def_2,type,
cJ: a > a ).
thf(func_def_4,type,
sK0: a ).
thf(func_def_5,type,
sK1: a ).
thf(func_def_6,type,
sK2: a ).
thf(func_def_7,type,
sK3: a ).
thf(func_def_8,type,
sK4: a ).
thf(f1,conjecture,
( ( ! [X1: a] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE )
& ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X0: a,X1: a,X2: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) )
=> ( ! [X3: a,X4: a] :
( ? [X6: a] :
( ( cP @ X6 @ X3 )
= X4 )
& ? [X5: a] :
( ( cP @ X3 @ X5 )
= X4 ) )
& ! [X0: a,X1: a,X2: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM22_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: a] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE )
& ! [X0: a] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X0: a,X1: a,X2: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) )
=> ( ! [X3: a,X4: a] :
( ? [X6: a] :
( ( cP @ X6 @ X3 )
= X4 )
& ? [X5: a] :
( ( cP @ X3 @ X5 )
= X4 ) )
& ! [X0: a,X1: a,X2: a] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X2 @ X3 ) @ X4 )
= ( cP @ X2 @ ( cP @ X3 @ X4 ) ) ) )
=> ( ! [X5: a,X6: a] :
( ? [X7: a] :
( ( cP @ X7 @ X5 )
= X6 )
& ? [X8: a] :
( ( cP @ X5 @ X8 )
= X6 ) )
& ! [X9: a,X10: a,X11: a] :
( ( cP @ ( cP @ X9 @ X10 ) @ X11 )
= ( cP @ X9 @ ( cP @ X10 @ X11 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ? [X5: a,X6: a] :
( ! [X7: a] :
( ( cP @ X7 @ X5 )
!= X6 )
| ! [X8: a] :
( ( cP @ X5 @ X8 )
!= X6 ) )
| ? [X9: a,X10: a,X11: a] :
( ( cP @ ( cP @ X9 @ X10 ) @ X11 )
!= ( cP @ X9 @ ( cP @ X10 @ X11 ) ) ) )
& ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X2 @ X3 ) @ X4 )
= ( cP @ X2 @ ( cP @ X3 @ X4 ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
( ( ? [X5: a,X6: a] :
( ! [X7: a] :
( ( cP @ X7 @ X5 )
!= X6 )
| ! [X8: a] :
( ( cP @ X5 @ X8 )
!= X6 ) )
| ? [X9: a,X10: a,X11: a] :
( ( cP @ ( cP @ X9 @ X10 ) @ X11 )
!= ( cP @ X9 @ ( cP @ X10 @ X11 ) ) ) )
& ! [X0: a] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X1: a] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: a,X3: a,X4: a] :
( ( cP @ ( cP @ X2 @ X3 ) @ X4 )
= ( cP @ X2 @ ( cP @ X3 @ X4 ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ? [X0: a,X1: a] :
( ! [X2: a] :
( ( cP @ X2 @ X0 )
!= X1 )
| ! [X3: a] :
( ( cP @ X0 @ X3 )
!= X1 ) )
| ? [X4: a,X5: a,X6: a] :
( ( cP @ ( cP @ X4 @ X5 ) @ X6 )
!= ( cP @ X4 @ ( cP @ X5 @ X6 ) ) ) )
& ! [X7: a] :
( cE
= ( cP @ ( cJ @ X7 ) @ X7 ) )
& ! [X8: a] :
( ( cP @ cE @ X8 )
= X8 )
& ! [X9: a,X10: a,X11: a] :
( ( cP @ ( cP @ X9 @ X10 ) @ X11 )
= ( cP @ X9 @ ( cP @ X10 @ X11 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( ! [X2: a] :
( sK1
!= ( cP @ X2 @ sK0 ) )
| ! [X3: a] :
( sK1
!= ( cP @ sK0 @ X3 ) )
| ( ( cP @ ( cP @ sK2 @ sK3 ) @ sK4 )
!= ( cP @ sK2 @ ( cP @ sK3 @ sK4 ) ) ) )
& ! [X7: a] :
( cE
= ( cP @ ( cJ @ X7 ) @ X7 ) )
& ! [X8: a] :
( ( cP @ cE @ X8 )
= X8 )
& ! [X9: a,X10: a,X11: a] :
( ( cP @ ( cP @ X9 @ X10 ) @ X11 )
= ( cP @ X9 @ ( cP @ X10 @ X11 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2),skolemize(X5,sK3),skolemize(X6,sK4)],[f6]) ).
thf(f8,plain,
! [X10: a,X11: a,X9: a] :
( ( cP @ ( cP @ X9 @ X10 ) @ X11 )
= ( cP @ X9 @ ( cP @ X10 @ X11 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X8: a] :
( ( cP @ cE @ X8 )
= X8 ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X7: a] :
( cE
= ( cP @ ( cJ @ X7 ) @ X7 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
! [X2: a,X3: a] :
( ( sK1
!= ( cP @ X2 @ sK0 ) )
| ( sK1
!= ( cP @ sK0 @ X3 ) )
| ( ( cP @ ( cP @ sK2 @ sK3 ) @ sK4 )
!= ( cP @ sK2 @ ( cP @ sK3 @ sK4 ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,definition,
( spl5_1
<=> ( ( cP @ ( cP @ sK2 @ sK3 ) @ sK4 )
= ( cP @ sK2 @ ( cP @ sK3 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl5_1])],[avatar_definition]) ).
thf(f15,plain,
( ( ( cP @ ( cP @ sK2 @ sK3 ) @ sK4 )
!= ( cP @ sK2 @ ( cP @ sK3 @ sK4 ) ) )
| spl5_1 ),
inference(avatar_component_clause,[],[f13]) ).
thf(f17,definition,
( spl5_2
<=> ! [X3: a] :
( sK1
!= ( cP @ sK0 @ X3 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_2])],[avatar_definition]) ).
thf(f18,plain,
( ! [X3: a] :
( sK1
!= ( cP @ sK0 @ X3 ) )
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f17]) ).
thf(f20,definition,
( spl5_3
<=> ! [X2: a] :
( sK1
!= ( cP @ X2 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl5_3])],[avatar_definition]) ).
thf(f21,plain,
( ! [X2: a] :
( sK1
!= ( cP @ X2 @ sK0 ) )
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f20]) ).
thf(f22,plain,
( ~ spl5_1
| spl5_2
| spl5_3 ),
inference(avatar_split_clause,[],[f11,f20,f17,f13]) ).
thf(f24,plain,
! [X0: a,X1: a] :
( ( cP @ cE @ X1 )
= ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f8,f10]) ).
thf(f27,plain,
! [X0: a,X1: a] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[],[f24,f9]) ).
thf(f29,plain,
( $false
| spl5_1 ),
inference(forward_subsumption_resolution,[],[f15,f8]) ).
thf(f30,plain,
spl5_1,
inference(avatar_contradiction_clause,[],[f29]) ).
thf(f33,plain,
( ! [X0: a,X1: a] :
( sK1
!= ( cP @ X0 @ ( cP @ X1 @ sK0 ) ) )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f21,f8]) ).
thf(f35,plain,
( ! [X0: a] :
( sK1
!= ( cP @ X0 @ cE ) )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f33,f10]) ).
thf(f41,plain,
! [X0: a] :
( ( cP @ ( cJ @ ( cJ @ X0 ) ) @ cE )
= X0 ),
inference(constrained_superposition,[],[f27,f10]) ).
thf(f43,plain,
! [X0: a,X1: a] :
( ( cP @ X1 @ X0 )
= ( cP @ ( cJ @ ( cJ @ X1 ) ) @ X0 ) ),
inference(constrained_superposition,[],[f27,f27]) ).
thf(f60,plain,
( ! [X0: a] : ( sK1 != X0 )
| ~ spl5_3 ),
inference(constrained_superposition,[],[f35,f41]) ).
thf(f64,plain,
! [X0: a,X1: a] :
( ( cP @ X1 @ ( cP @ ( cJ @ X1 ) @ X0 ) )
= X0 ),
inference(constrained_superposition,[],[f43,f27]) ).
thf(f92,plain,
( $false
| ~ spl5_3 ),
inference(equality_resolution,[],[f60]) ).
thf(f93,plain,
~ spl5_3,
inference(avatar_contradiction_clause,[],[f92]) ).
thf(f224,plain,
( ! [X0: a] : ( sK1 != X0 )
| ~ spl5_2 ),
inference(constrained_superposition,[],[f18,f64]) ).
thf(f238,plain,
( $false
| ~ spl5_2 ),
inference(equality_resolution,[],[f224]) ).
thf(f239,plain,
~ spl5_2,
inference(avatar_contradiction_clause,[],[f238]) ).
cnf(s1,plain,
( ~ spl5_1
| spl5_2
| spl5_3 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
spl5_1,
inference(sat_conversion,[],[f30]) ).
cnf(s3,plain,
~ spl5_3,
inference(sat_conversion,[],[f93]) ).
cnf(s4,plain,
~ spl5_2,
inference(sat_conversion,[],[f239]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s3,s4,s2]) ).
thf(f240,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG285^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.18 % Computer : n017.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 17:33:07 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.07/0.21 Running first-order model finding
% 0.07/0.21 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
% 0.19/0.28 % (650432)Will run a generic schedule for satisfiability detection.
% 0.19/0.28 % (650438)% WARNING: option uhcvi not known.
% 0.19/0.28 % (650437)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=4212176316_2999 on theBenchmark for (2999ds/0Mi)
% 0.19/0.28 % (650438)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=1896657654:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.19/0.28 % (650438)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.19/0.28 % (650438)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.19/0.28 % Exception at run slice level
% 0.19/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.19/0.28 % (650438) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-650432-650438"...
% 0.19/0.28 % (650440)dis+10_1_sil=32000:sp=arity:random_seed=2813540412:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.19/0.28 % (650438)...printing done.
% 0.19/0.28 % (650438)Refutation found. Thanks to Tanya!
% 0.19/0.28 % SZS status Theorem for theBenchmark
% 0.19/0.28 % SZS output start Proof for theBenchmark
% See solution above
% 0.19/0.28 % (650438)------------------------------
% 0.19/0.28 % (650438)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.19/0.28 % (650438)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.19/0.28 % (650438)CaDiCaL version: 2.1.3
% 0.19/0.28 % (650438)Termination reason: Refutation
% 0.19/0.28 % (650438)Time elapsed: 0.012 s
% 0.19/0.28 % (650438)Peak memory usage: 12 MB
% 0.19/0.28 % (650438)Instructions burned: 19 (million)
% 0.19/0.28 % (650432)Success in time 0.054 s
% 0.19/0.28 % Vampire exiting
%------------------------------------------------------------------------------