%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET766+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n003.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 12:44:34 PM UTC 2026
% Result : Theorem 0.12s 0.46s
% Output : Refutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 20 ( 5 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 13 ( 4 avg)
% Number of connectives : 112 ( 34 ~; 28 |; 29 &)
% ( 3 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 66 ( 60 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X2,X3] :
( ( member(X2,X0)
& member(X3,X0) )
=> ( apply(X1,X2,X3)
=> apply(X1,X3,X2) ) )
& ! [X2,X3,X4] :
( ( member(X2,X0)
& member(X3,X0)
& member(X4,X0) )
=> ( ( apply(X1,X2,X3)
& apply(X1,X3,X4) )
=> apply(X1,X2,X4) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( member(X3,equivalence_class(X2,X1,X0))
<=> ( member(X3,X1)
& apply(X0,X2,X3) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+2.ax',equivalence_class) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( equivalence(X1,X0)
& member(X2,X0) )
=> member(X2,equivalence_class(X2,X0,X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIII02) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( equivalence(X1,X0)
& member(X2,X0) )
=> member(X2,equivalence_class(X2,X0,X1)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( equivalence(X1,X0)
<=> ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X5,X6,X7] :
( ( member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X1,X6,X7) )
=> apply(X1,X5,X7) ) ) ) ),
inference(rectify,[],[f14]) ).
fof(f22,plain,
! [X0,X1] :
( equivalence(X1,X0)
=> ( ! [X2] :
( member(X2,X0)
=> apply(X1,X2,X2) )
& ! [X3,X4] :
( ( member(X3,X0)
& member(X4,X0) )
=> ( apply(X1,X3,X4)
=> apply(X1,X4,X3) ) )
& ! [X5,X6,X7] :
( ( member(X5,X0)
& member(X6,X0)
& member(X7,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X1,X6,X7) )
=> apply(X1,X5,X7) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f20]) ).
fof(f25,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X1,X2,X2)
| ~ member(X2,X0) )
& ! [X3,X4] :
( apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X3,X0)
| ~ member(X4,X0) )
& ! [X5,X6,X7] :
( apply(X1,X5,X7)
| ~ apply(X1,X5,X6)
| ~ apply(X1,X6,X7)
| ~ member(X5,X0)
| ~ member(X6,X0)
| ~ member(X7,X0) ) )
| ~ equivalence(X1,X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( ( ! [X2] :
( apply(X1,X2,X2)
| ~ member(X2,X0) )
& ! [X3,X4] :
( apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| ~ member(X3,X0)
| ~ member(X4,X0) )
& ! [X5,X6,X7] :
( apply(X1,X5,X7)
| ~ apply(X1,X5,X6)
| ~ apply(X1,X6,X7)
| ~ member(X5,X0)
| ~ member(X6,X0)
| ~ member(X7,X0) ) )
| ~ equivalence(X1,X0) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
? [X0,X1,X2] :
( ~ member(X2,equivalence_class(X2,X0,X1))
& equivalence(X1,X0)
& member(X2,X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f28,plain,
? [X0,X1,X2] :
( ~ member(X2,equivalence_class(X2,X0,X1))
& equivalence(X1,X0)
& member(X2,X0) ),
inference(flattening,[],[f27]) ).
fof(f55,plain,
! [X2,X0,X1] :
( ~ equivalence(X1,X0)
| ~ member(X2,X0)
| apply(X1,X2,X2) ),
inference(cnf_transformation,[],[f26]) ).
fof(f60,plain,
! [X2,X3,X0,X1] :
( ~ apply(X0,X2,X3)
| ~ member(X3,X1)
| member(X3,equivalence_class(X2,X1,X0)) ),
inference(cnf_transformation,[],[f15]) ).
fof(f61,plain,
member(sK5,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f62,plain,
equivalence(sK4,sK3),
inference(cnf_transformation,[],[f28]) ).
fof(f63,plain,
~ member(sK5,equivalence_class(sK5,sK3,sK4)),
inference(cnf_transformation,[],[f28]) ).
fof(f151,plain,
! [X0] :
( apply(sK4,X0,X0)
| ~ member(X0,sK3) ),
inference(resolution,[],[f55,f62]) ).
fof(f202,plain,
! [X0,X1] :
( member(X0,equivalence_class(X0,X1,sK4))
| ~ member(X0,X1)
| ~ member(X0,sK3) ),
inference(resolution,[],[f60,f151]) ).
fof(f204,plain,
( ~ member(sK5,sK3)
| ~ member(sK5,sK3) ),
inference(resolution,[],[f202,f63]) ).
fof(f210,plain,
~ member(sK5,sK3),
inference(duplicate_literal_removal,[],[f204]) ).
fof(f211,plain,
$false,
inference(forward_subsumption_resolution,[],[f210,f61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET766+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.38 % Computer : n003.cluster.edu
% 0.12/0.38 % Model : x86_64 x86_64
% 0.12/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.38 % Memory : 8046.5625MB
% 0.12/0.38 % OS : Linux 6.8.0-71-generic
% 0.12/0.38 % CPULimit : 300
% 0.12/0.38 % WCLimit : 300
% 0.12/0.38 % DateTime : Mon Sep 28 02:47:13 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.12/0.42 Running first-order model finding
% 0.12/0.42 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
% 0.12/0.46 % (1135467)Will run a generic schedule for satisfiability detection.
% 0.12/0.46 % (1135476)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3741798699:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.12/0.46 % (1135473)% WARNING: option uhcvi not known.
% 0.12/0.46 % (1135476) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1135467-1135476"...
% 0.12/0.46 % (1135476)...printing done.
% 0.12/0.46 % (1135476)Refutation found. Thanks to Tanya!
% 0.12/0.46 % SZS status Theorem for theBenchmark
% 0.12/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.46 % (1135476)------------------------------
% 0.12/0.46 % (1135476)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.12/0.46 % (1135476)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.12/0.46 % (1135476)CaDiCaL version: 2.1.3
% 0.12/0.46 % (1135476)Termination reason: Refutation
% 0.12/0.46 % (1135476)Time elapsed: 0.004 s
% 0.12/0.46 % (1135476)Peak memory usage: 12 MB
% 0.12/0.46 % (1135476)Instructions burned: 10 (million)
% 0.12/0.46 % (1135467)Success in time 0.029 s
% 0.12/0.46 % Vampire exiting
%------------------------------------------------------------------------------