%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET790+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n002.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 : Tue Sep 29 12:44:37 PM UTC 2026
% Result : Theorem 0.17s 0.46s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 32 ( 8 unt; 0 def)
% Number of atoms : 151 ( 15 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 182 ( 63 ~; 54 |; 39 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 87 ( 79 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X2) )
=> X2 = X3 ) )
& ! [X2,X3,X4] :
( ( member(X2,X1)
& member(X3,X1)
& member(X4,X1) )
=> ( ( apply(X0,X2,X3)
& apply(X0,X3,X4) )
=> apply(X0,X2,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',order) ).
fof(f6,axiom,
! [X0,X1,X2] :
( least(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least) ).
fof(f11,conjecture,
! [X0,X1,X2] :
( ( order(X0,X1)
& least(X2,X0,X1) )
=> ! [X3] :
( least(X3,X0,X1)
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV2) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
( ( order(X0,X1)
& least(X2,X0,X1) )
=> ! [X3] :
( least(X3,X0,X1)
=> X2 = X3 ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X1)
& member(X4,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X4,X3) )
=> X3 = X4 ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X1)
& member(X7,X1) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X6,X7) )
=> apply(X0,X5,X7) ) ) ) ),
inference(rectify,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
=> ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f15,plain,
! [X0,X1] :
( order(X0,X1)
=> ( ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X1)
& member(X4,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X4,X3) )
=> X3 = X4 ) )
& ! [X5,X6,X7] :
( ( member(X5,X1)
& member(X6,X1)
& member(X7,X1) )
=> ( ( apply(X0,X5,X6)
& apply(X0,X6,X7) )
=> apply(X0,X5,X7) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f16,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4] :
( X3 = X4
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X3)
| ~ member(X3,X1)
| ~ member(X4,X1) )
& ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) ) )
| ~ order(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X0,X2,X2)
| ~ member(X2,X1) )
& ! [X3,X4] :
( X3 = X4
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X3)
| ~ member(X3,X1)
| ~ member(X4,X1) )
& ! [X5,X6,X7] :
( apply(X0,X5,X7)
| ~ apply(X0,X5,X6)
| ~ apply(X0,X6,X7)
| ~ member(X5,X1)
| ~ member(X6,X1)
| ~ member(X7,X1) ) )
| ~ order(X0,X1) ),
inference(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( apply(X0,X2,X3)
| ~ member(X3,X1) ) )
| ~ least(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f19,plain,
? [X0,X1,X2] :
( ? [X3] :
( X2 != X3
& least(X3,X0,X1) )
& order(X0,X1)
& least(X2,X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,plain,
? [X0,X1,X2] :
( ? [X3] :
( X2 != X3
& least(X3,X0,X1) )
& order(X0,X1)
& least(X2,X0,X1) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( sK2 != sK3
& least(sK3,sK0,sK1)
& order(sK0,sK1)
& least(sK2,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f20]) ).
fof(f23,plain,
! [X3,X0,X1,X4] :
( ~ apply(X0,X4,X3)
| ~ apply(X0,X3,X4)
| X3 = X4
| ~ member(X3,X1)
| ~ member(X4,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f17]) ).
fof(f25,plain,
! [X2,X3,X0,X1] :
( ~ least(X2,X0,X1)
| ~ member(X3,X1)
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ least(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
least(sK2,sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f28,plain,
order(sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f29,plain,
least(sK3,sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
member(sK2,sK1),
inference(resolution,[],[f26,f27]) ).
fof(f32,plain,
member(sK3,sK1),
inference(resolution,[],[f26,f29]) ).
fof(f34,plain,
! [X0] :
( apply(sK0,sK2,X0)
| ~ member(X0,sK1) ),
inference(resolution,[],[f25,f27]) ).
fof(f35,plain,
! [X0] :
( apply(sK0,sK3,X0)
| ~ member(X0,sK1) ),
inference(resolution,[],[f25,f29]) ).
fof(f37,plain,
! [X0,X1] :
( ~ apply(sK0,X0,sK2)
| ~ member(X0,sK1)
| sK2 = X0
| ~ member(X0,X1)
| ~ member(sK2,X1)
| ~ order(sK0,X1) ),
inference(resolution,[],[f34,f23]) ).
fof(f50,plain,
! [X0] :
( ~ member(sK3,sK1)
| sK2 = sK3
| ~ member(sK3,X0)
| ~ member(sK2,X0)
| ~ order(sK0,X0)
| ~ member(sK2,sK1) ),
inference(resolution,[],[f37,f35]) ).
fof(f54,plain,
! [X0] :
( sK2 = sK3
| ~ member(sK3,X0)
| ~ member(sK2,X0)
| ~ order(sK0,X0)
| ~ member(sK2,sK1) ),
inference(forward_subsumption_resolution,[],[f50,f32]) ).
fof(f55,plain,
! [X0] :
( ~ member(sK3,X0)
| ~ member(sK2,X0)
| ~ order(sK0,X0)
| ~ member(sK2,sK1) ),
inference(forward_subsumption_resolution,[],[f54,f30]) ).
fof(f56,plain,
! [X0] :
( ~ member(sK3,X0)
| ~ member(sK2,X0)
| ~ order(sK0,X0) ),
inference(forward_subsumption_resolution,[],[f55,f31]) ).
fof(f57,plain,
( ~ member(sK2,sK1)
| ~ order(sK0,sK1) ),
inference(resolution,[],[f56,f32]) ).
fof(f58,plain,
~ order(sK0,sK1),
inference(forward_subsumption_resolution,[],[f57,f31]) ).
fof(f59,plain,
$false,
inference(forward_subsumption_resolution,[],[f58,f28]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET790+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.39 % Computer : n002.cluster.edu
% 0.13/0.39 % Model : x86_64 x86_64
% 0.13/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39 % Memory : 8046.5625MB
% 0.13/0.39 % OS : Linux 6.8.0-71-generic
% 0.13/0.39 % CPULimit : 300
% 0.13/0.39 % WCLimit : 300
% 0.13/0.39 % DateTime : Mon Sep 28 02:52:22 UTC 2026
% 0.13/0.39 % CPUTime :
% 0.13/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.13/0.42 Running first-order model finding
% 0.13/0.42 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
% 0.17/0.46 % (4106771)Will run a generic schedule for satisfiability detection.
% 0.17/0.46 % (4106779)dis+10_1_sil=32000:sp=arity:random_seed=401794830:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.17/0.46 % (4106779) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-4106771-4106779"...
% 0.17/0.46 % (4106779)...printing done.
% 0.17/0.46 % (4106779)Refutation found. Thanks to Tanya!
% 0.17/0.46 % SZS status Theorem for theBenchmark
% 0.17/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.17/0.46 % (4106779)------------------------------
% 0.17/0.46 % (4106779)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.17/0.46 % (4106779)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.17/0.46 % (4106779)CaDiCaL version: 2.1.3
% 0.17/0.46 % (4106779)Termination reason: Refutation
% 0.17/0.46 % (4106779)Time elapsed: 0.001 s
% 0.17/0.46 % (4106779)Peak memory usage: 11 MB
% 0.17/0.46 % (4106779)Instructions burned: 2 (million)
% 0.17/0.46 % (4106771)Success in time 0.032 s
% 0.17/0.46 % Vampire exiting
%------------------------------------------------------------------------------