%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : ALG281^5 : 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 : n019.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 0.08s 0.26s
% Output : Refutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 1
% Syntax : Number of formulae : 20 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 76 ( 40 equ; 0 cnn)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 189 ( 8 ~; 0 |; 18 &; 160 @)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 7 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 55 ( 0 ^; 52 !; 3 ?; 55 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cJ: $i > $i ).
thf(func_def_2,type,
cP: $i > $i > $i ).
thf(f1,conjecture,
( ( ! [X1: $i] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE )
& ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X0: $i,X1: $i,X2: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X3: $i] :
( ( cP @ X3 @ ( cJ @ X3 ) )
= cE ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM16_pme) ).
thf(f2,negated_conjecture,
~ ( ( ! [X1: $i] :
( ( cP @ ( cJ @ X1 ) @ X1 )
= cE )
& ! [X0: $i] :
( ( cP @ cE @ X0 )
= X0 )
& ! [X0: $i,X1: $i,X2: $i] :
( ( cP @ ( cP @ X0 @ X1 ) @ X2 )
= ( cP @ X0 @ ( cP @ X1 @ X2 ) ) ) )
=> ! [X3: $i] :
( ( cP @ X3 @ ( cJ @ X3 ) )
= cE ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ! [X0: $i] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: $i,X3: $i,X4: $i] :
( ( cP @ ( cP @ X2 @ X3 ) @ X4 )
= ( cP @ X2 @ ( cP @ X3 @ X4 ) ) ) )
=> ! [X5: $i] :
( cE
= ( cP @ X5 @ ( cJ @ X5 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ? [X5: $i] :
( cE
!= ( cP @ X5 @ ( cJ @ X5 ) ) )
& ! [X0: $i] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: $i,X3: $i,X4: $i] :
( ( cP @ ( cP @ X2 @ X3 ) @ X4 )
= ( cP @ X2 @ ( cP @ X3 @ X4 ) ) ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
( ? [X5: $i] :
( cE
!= ( cP @ X5 @ ( cJ @ X5 ) ) )
& ! [X0: $i] :
( cE
= ( cP @ ( cJ @ X0 ) @ X0 ) )
& ! [X1: $i] :
( ( cP @ cE @ X1 )
= X1 )
& ! [X2: $i,X3: $i,X4: $i] :
( ( cP @ ( cP @ X2 @ X3 ) @ X4 )
= ( cP @ X2 @ ( cP @ X3 @ X4 ) ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ? [X0: $i] :
( cE
!= ( cP @ X0 @ ( cJ @ X0 ) ) )
& ! [X1: $i] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) )
& ! [X2: $i] :
( ( cP @ cE @ X2 )
= X2 )
& ! [X3: $i,X4: $i,X5: $i] :
( ( cP @ ( cP @ X3 @ X4 ) @ X5 )
= ( cP @ X3 @ ( cP @ X4 @ X5 ) ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
( ( cE
!= ( cP @ sK0 @ ( cJ @ sK0 ) ) )
& ! [X1: $i] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) )
& ! [X2: $i] :
( ( cP @ cE @ X2 )
= X2 )
& ! [X3: $i,X4: $i,X5: $i] :
( ( cP @ ( cP @ X3 @ X4 ) @ X5 )
= ( cP @ X3 @ ( cP @ X4 @ X5 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f6]) ).
thf(f8,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( cP @ ( cP @ X3 @ X4 ) @ X5 )
= ( cP @ X3 @ ( cP @ X4 @ X5 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
! [X2: $i] :
( ( cP @ cE @ X2 )
= X2 ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
! [X1: $i] :
( cE
= ( cP @ ( cJ @ X1 ) @ X1 ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( cE
!= ( cP @ sK0 @ ( cJ @ sK0 ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
! [X0: $i,X1: $i] :
( ( cP @ cE @ X1 )
= ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f8,f10]) ).
thf(f16,plain,
! [X0: $i,X1: $i] :
( ( cP @ ( cJ @ X0 ) @ ( cP @ X0 @ X1 ) )
= X1 ),
inference(forward_demodulation,[],[f13,f9]) ).
thf(f19,plain,
! [X0: $i] :
( ( cP @ ( cJ @ ( cJ @ X0 ) ) @ cE )
= X0 ),
inference(constrained_superposition,[],[f16,f10]) ).
thf(f28,plain,
! [X0: $i] :
( cE
= ( cP @ ( cJ @ ( cJ @ ( cJ @ X0 ) ) ) @ X0 ) ),
inference(constrained_superposition,[],[f16,f19]) ).
thf(f45,plain,
! [X0: $i] :
( ( cP @ ( cJ @ ( cJ @ ( cJ @ ( cJ @ X0 ) ) ) ) @ cE )
= X0 ),
inference(constrained_superposition,[],[f16,f28]) ).
thf(f49,plain,
! [X0: $i] :
( ( cJ @ ( cJ @ X0 ) )
= X0 ),
inference(forward_demodulation,[],[f45,f19]) ).
thf(f54,plain,
! [X0: $i] :
( cE
= ( cP @ X0 @ ( cJ @ X0 ) ) ),
inference(constrained_superposition,[],[f10,f49]) ).
thf(f87,plain,
cE != cE,
inference(constrained_superposition,[],[f11,f54]) ).
thf(f88,plain,
$false,
inference(trivial_inequality_removal,[],[f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG281^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n019.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 17:36:33 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
% 0.08/0.26 % (1129994)Will run a generic schedule for satisfiability detection.
% 0.08/0.26 % (1130001)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=3442419977:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.08/0.26 % (1130001) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1129994-1130001"...
% 0.08/0.26 % (1130000)% WARNING: option uhcvi not known.
% 0.08/0.26 % (1130001)...printing done.
% 0.08/0.26 % (1130001)Refutation found. Thanks to Tanya!
% 0.08/0.26 % SZS status Theorem for theBenchmark
% 0.08/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.08/0.26 % (1130001)------------------------------
% 0.08/0.26 % (1130001)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.08/0.26 % (1130001)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.08/0.26 % (1130001)CaDiCaL version: 2.1.3
% 0.08/0.26 % (1130001)Termination reason: Refutation
% 0.08/0.26 % (1130001)Time elapsed: 0.003 s
% 0.08/0.26 % (1130001)Peak memory usage: 12 MB
% 0.08/0.26 % (1130001)Instructions burned: 8 (million)
% 0.08/0.26 % (1129994)Success in time 0.03 s
% 0.08/0.26 % Vampire exiting
%------------------------------------------------------------------------------