%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET791+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 : n016.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 0.11s 0.45s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 41 ( 7 unt; 0 def)
% Number of atoms : 179 ( 15 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 200 ( 62 ~; 64 |; 46 &)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 118 ( 110 !; 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(f5,axiom,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',greatest) ).
fof(f7,axiom,
! [X0,X1,X2] :
( max(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( ( member(X3,X1)
& apply(X0,X2,X3) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',max) ).
fof(f11,conjecture,
! [X0,X1,X2] :
( ( order(X0,X1)
& greatest(X2,X0,X1) )
=> max(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV3) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
( ( order(X0,X1)
& greatest(X2,X0,X1) )
=> max(X2,X0,X1) ),
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] :
( ( member(X2,X1)
& ! [X3] :
( ( member(X3,X1)
& apply(X0,X2,X3) )
=> X2 = X3 ) )
=> max(X2,X0,X1) ),
inference(unused_predicate_definition_removal,[],[f7]) ).
fof(f15,plain,
! [X0,X1,X2] :
( greatest(X2,X0,X1)
=> ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X3,X2) ) ) ),
inference(unused_predicate_definition_removal,[],[f5]) ).
fof(f16,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(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(ennf_transformation,[],[f16]) ).
fof(f18,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,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( apply(X0,X3,X2)
| ~ member(X3,X1) ) )
| ~ greatest(X2,X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0,X1,X2] :
( max(X2,X0,X1)
| ~ member(X2,X1)
| ? [X3] :
( X2 != X3
& member(X3,X1)
& apply(X0,X2,X3) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0,X1,X2] :
( max(X2,X0,X1)
| ~ member(X2,X1)
| ? [X3] :
( X2 != X3
& member(X3,X1)
& apply(X0,X2,X3) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
? [X0,X1,X2] :
( ~ max(X2,X0,X1)
& order(X0,X1)
& greatest(X2,X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f23,plain,
? [X0,X1,X2] :
( ~ max(X2,X0,X1)
& order(X0,X1)
& greatest(X2,X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( max(X2,X0,X1)
| ~ member(X2,X1)
| ( sK0(X0,X1,X2) != X2
& member(sK0(X0,X1,X2),X1)
& apply(X0,X2,sK0(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f21]) ).
fof(f25,plain,
( ~ max(sK3,sK1,sK2)
& order(sK1,sK2)
& greatest(sK3,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f23]) ).
fof(f27,plain,
! [X3,X0,X1,X4] :
( ~ member(X3,X1)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X4,X3)
| X3 = X4
| ~ member(X4,X1)
| ~ order(X0,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X2,X3,X0,X1] :
( ~ member(X3,X1)
| apply(X0,X3,X2)
| ~ greatest(X2,X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ greatest(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| max(X2,X0,X1)
| apply(X0,X2,sK0(X0,X1,X2)) ),
inference(cnf_transformation,[],[f24]) ).
fof(f32,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| max(X2,X0,X1)
| member(sK0(X0,X1,X2),X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X2,X0,X1] :
( ~ member(X2,X1)
| max(X2,X0,X1)
| sK0(X0,X1,X2) != X2 ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
greatest(sK3,sK1,sK2),
inference(cnf_transformation,[],[f25]) ).
fof(f35,plain,
order(sK1,sK2),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
~ max(sK3,sK1,sK2),
inference(cnf_transformation,[],[f25]) ).
fof(f37,plain,
member(sK3,sK2),
inference(resolution,[],[f30,f34]) ).
fof(f41,plain,
! [X0] :
( member(sK0(X0,sK2,sK3),sK2)
| max(sK3,X0,sK2) ),
inference(resolution,[],[f32,f37]) ).
fof(f43,plain,
! [X0] :
( sK3 != sK0(X0,sK2,sK3)
| max(sK3,X0,sK2) ),
inference(resolution,[],[f33,f37]) ).
fof(f46,plain,
! [X2,X0,X1] :
( ~ greatest(X2,X1,sK2)
| apply(X1,sK0(X0,sK2,sK3),X2)
| max(sK3,X0,sK2) ),
inference(resolution,[],[f41,f29]) ).
fof(f48,plain,
! [X0] :
( max(sK3,X0,sK2)
| apply(X0,sK3,sK0(X0,sK2,sK3)) ),
inference(resolution,[],[f31,f37]) ).
fof(f50,plain,
! [X0,X1] :
( ~ member(X1,sK2)
| ~ apply(X0,X1,sK3)
| sK3 = X1
| ~ apply(X0,sK3,X1)
| ~ order(X0,sK2) ),
inference(resolution,[],[f27,f37]) ).
fof(f52,plain,
apply(sK1,sK3,sK0(sK1,sK2,sK3)),
inference(resolution,[],[f48,f36]) ).
fof(f56,plain,
! [X0,X1] :
( ~ apply(X0,sK0(X1,sK2,sK3),sK3)
| sK3 = sK0(X1,sK2,sK3)
| ~ apply(X0,sK3,sK0(X1,sK2,sK3))
| ~ order(X0,sK2)
| max(sK3,X1,sK2) ),
inference(resolution,[],[f50,f41]) ).
fof(f58,plain,
! [X0,X1] :
( ~ order(X0,sK2)
| ~ apply(X0,sK3,sK0(X1,sK2,sK3))
| ~ apply(X0,sK0(X1,sK2,sK3),sK3)
| max(sK3,X1,sK2) ),
inference(forward_subsumption_resolution,[],[f56,f43]) ).
fof(f59,plain,
! [X0] :
( max(sK3,X0,sK2)
| apply(sK1,sK0(X0,sK2,sK3),sK3) ),
inference(resolution,[],[f46,f34]) ).
fof(f74,plain,
! [X0] :
( ~ apply(sK1,sK3,sK0(X0,sK2,sK3))
| ~ apply(sK1,sK0(X0,sK2,sK3),sK3)
| max(sK3,X0,sK2) ),
inference(resolution,[],[f58,f35]) ).
fof(f75,plain,
! [X0] :
( ~ apply(sK1,sK3,sK0(X0,sK2,sK3))
| max(sK3,X0,sK2) ),
inference(forward_subsumption_resolution,[],[f74,f59]) ).
fof(f76,plain,
max(sK3,sK1,sK2),
inference(resolution,[],[f75,f52]) ).
fof(f77,plain,
$false,
inference(forward_subsumption_resolution,[],[f76,f36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET791+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.38 % Computer : n016.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Mon Sep 28 02:54:33 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.41 Running first-order model finding
% 0.11/0.41 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
% 0.11/0.45 % (3213476)Will run a generic schedule for satisfiability detection.
% 0.11/0.45 % (3213486)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=945438737:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.11/0.45 % (3213486) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3213476-3213486"...
% 0.11/0.45 % (3213482)% WARNING: option uhcvi not known.
% 0.11/0.45 % (3213486)...printing done.
% 0.11/0.45 % (3213486)Refutation found. Thanks to Tanya!
% 0.11/0.45 % SZS status Theorem for theBenchmark
% 0.11/0.45 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.45 % (3213486)------------------------------
% 0.11/0.45 % (3213486)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.45 % (3213486)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.45 % (3213486)CaDiCaL version: 2.1.3
% 0.11/0.45 % (3213486)Termination reason: Refutation
% 0.11/0.45 % (3213486)Time elapsed: 0.002 s
% 0.11/0.45 % (3213486)Peak memory usage: 11 MB
% 0.11/0.45 % (3213486)Instructions burned: 4 (million)
% 0.11/0.45 % (3213476)Success in time 0.032 s
% 0.11/0.45 % Vampire exiting
%------------------------------------------------------------------------------