%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SET794+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 12:44:38 PM UTC 2026
% Result : Theorem 0.11s 0.47s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 43 ( 7 unt; 0 def)
% Number of atoms : 146 ( 14 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 157 ( 54 ~; 64 |; 25 &)
% ( 3 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 89 ( 81 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( total_order(X0,X1)
<=> ( order(X0,X1)
& ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ( apply(X0,X2,X3)
| apply(X0,X3,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',total_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(f8,axiom,
! [X0,X1,X2] :
( min(X2,X0,X1)
<=> ( member(X2,X1)
& ! [X3] :
( ( member(X3,X1)
& apply(X0,X3,X2) )
=> X2 = X3 ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',min) ).
fof(f11,conjecture,
! [X0,X1,X2] :
( ( total_order(X0,X1)
& min(X2,X0,X1) )
=> least(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV6) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
( ( total_order(X0,X1)
& min(X2,X0,X1) )
=> least(X2,X0,X1) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( min(X2,X0,X1)
=> ( member(X2,X1)
& ! [X3] :
( ( member(X3,X1)
& apply(X0,X3,X2) )
=> X2 = X3 ) ) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) ) )
=> least(X2,X0,X1) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f16,plain,
! [X0,X1] :
( total_order(X0,X1)
=> ( order(X0,X1)
& ! [X2,X3] :
( ( member(X2,X1)
& member(X3,X1) )
=> ( apply(X0,X2,X3)
| apply(X0,X3,X2) ) ) ) ),
inference(unused_predicate_definition_removal,[],[f2]) ).
fof(f20,plain,
! [X0,X1] :
( ( order(X0,X1)
& ! [X2,X3] :
( apply(X0,X2,X3)
| apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1) ) )
| ~ total_order(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f21,plain,
! [X0,X1] :
( ( order(X0,X1)
& ! [X2,X3] :
( apply(X0,X2,X3)
| apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1) ) )
| ~ total_order(X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
| ~ member(X2,X1)
| ? [X3] :
( ~ apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f23,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
| ~ member(X2,X1)
| ? [X3] :
( ~ apply(X0,X2,X3)
& member(X3,X1) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( X2 = X3
| ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
| ~ min(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f25,plain,
! [X0,X1,X2] :
( ( member(X2,X1)
& ! [X3] :
( X2 = X3
| ~ member(X3,X1)
| ~ apply(X0,X3,X2) ) )
| ~ min(X2,X0,X1) ),
inference(flattening,[],[f24]) ).
fof(f26,plain,
? [X0,X1,X2] :
( ~ least(X2,X0,X1)
& total_order(X0,X1)
& min(X2,X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f27,plain,
? [X0,X1,X2] :
( ~ least(X2,X0,X1)
& total_order(X0,X1)
& min(X2,X0,X1) ),
inference(flattening,[],[f26]) ).
fof(f28,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
| ~ member(X2,X1)
| ( ~ apply(X0,X2,sK0(X0,X1,X2))
& member(sK0(X0,X1,X2),X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f23]) ).
fof(f29,plain,
( ~ least(sK3,sK1,sK2)
& total_order(sK1,sK2)
& min(sK3,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f27]) ).
fof(f33,plain,
! [X2,X3,X0,X1] :
( ~ total_order(X0,X1)
| apply(X0,X3,X2)
| ~ member(X2,X1)
| ~ member(X3,X1)
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f21]) ).
fof(f35,plain,
! [X2,X0,X1] :
( member(sK0(X0,X1,X2),X1)
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f36,plain,
! [X2,X0,X1] :
( ~ apply(X0,X2,sK0(X0,X1,X2))
| ~ member(X2,X1)
| least(X2,X0,X1) ),
inference(cnf_transformation,[],[f28]) ).
fof(f37,plain,
! [X2,X3,X0,X1] :
( ~ min(X2,X0,X1)
| ~ member(X3,X1)
| ~ apply(X0,X3,X2)
| X2 = X3 ),
inference(cnf_transformation,[],[f25]) ).
fof(f38,plain,
! [X2,X0,X1] :
( ~ min(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f25]) ).
fof(f39,plain,
min(sK3,sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f40,plain,
total_order(sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
~ least(sK3,sK1,sK2),
inference(cnf_transformation,[],[f29]) ).
fof(f57,plain,
member(sK3,sK2),
inference(resolution,[],[f38,f39]) ).
fof(f220,plain,
! [X0] :
( ~ apply(sK1,X0,sK3)
| ~ member(X0,sK2)
| sK3 = X0 ),
inference(resolution,[],[f37,f39]) ).
fof(f235,plain,
! [X0,X1] :
( apply(sK1,X1,X0)
| apply(sK1,X0,X1)
| ~ member(X0,sK2)
| ~ member(X1,sK2) ),
inference(resolution,[],[f33,f40]) ).
fof(f240,plain,
! [X0] :
( apply(sK1,sK3,X0)
| ~ member(X0,sK2)
| ~ member(sK3,sK2)
| ~ member(X0,sK2)
| sK3 = X0 ),
inference(resolution,[],[f235,f220]) ).
fof(f241,plain,
! [X0] :
( apply(sK1,X0,X0)
| ~ member(X0,sK2)
| ~ member(X0,sK2) ),
inference(factoring,[],[f235]) ).
fof(f242,plain,
! [X0] :
( apply(sK1,X0,X0)
| ~ member(X0,sK2) ),
inference(duplicate_literal_removal,[],[f241]) ).
fof(f243,plain,
! [X0] :
( apply(sK1,sK3,X0)
| ~ member(X0,sK2)
| ~ member(sK3,sK2)
| sK3 = X0 ),
inference(duplicate_literal_removal,[],[f240]) ).
fof(f245,plain,
! [X0] :
( apply(sK1,sK3,X0)
| ~ member(X0,sK2)
| sK3 = X0 ),
inference(forward_subsumption_resolution,[],[f243,f57]) ).
fof(f256,plain,
! [X0] :
( ~ member(sK0(sK1,X0,sK3),sK2)
| sK3 = sK0(sK1,X0,sK3)
| ~ member(sK3,X0)
| least(sK3,sK1,X0) ),
inference(resolution,[],[f245,f36]) ).
fof(f282,plain,
( sK3 = sK0(sK1,sK2,sK3)
| ~ member(sK3,sK2)
| least(sK3,sK1,sK2)
| ~ member(sK3,sK2)
| least(sK3,sK1,sK2) ),
inference(resolution,[],[f256,f35]) ).
fof(f283,plain,
( sK3 = sK0(sK1,sK2,sK3)
| ~ member(sK3,sK2)
| least(sK3,sK1,sK2) ),
inference(duplicate_literal_removal,[],[f282]) ).
fof(f284,plain,
( sK3 = sK0(sK1,sK2,sK3)
| least(sK3,sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f283,f57]) ).
fof(f286,plain,
sK3 = sK0(sK1,sK2,sK3),
inference(forward_subsumption_resolution,[],[f284,f41]) ).
fof(f327,plain,
( ~ apply(sK1,sK3,sK3)
| ~ member(sK3,sK2)
| least(sK3,sK1,sK2) ),
inference(superposition,[],[f36,f286]) ).
fof(f337,plain,
( ~ member(sK3,sK2)
| least(sK3,sK1,sK2) ),
inference(forward_subsumption_resolution,[],[f327,f242]) ).
fof(f338,plain,
least(sK3,sK1,sK2),
inference(forward_subsumption_resolution,[],[f337,f57]) ).
fof(f339,plain,
$false,
inference(forward_subsumption_resolution,[],[f338,f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET794+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.39 % Computer : n016.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Mon Sep 28 02:55:03 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.11/0.42 Running first-order model finding
% 0.11/0.42 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
% 0.11/0.47 % (3214308)Will run a generic schedule for satisfiability detection.
% 0.11/0.47 % (3214315)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=2976114858:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.11/0.47 % (3214314)% WARNING: option uhcvi not known.
% 0.11/0.47 % (3214315) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3214308-3214315"...
% 0.11/0.47 % (3214315)...printing done.
% 0.11/0.47 % (3214315)Refutation found. Thanks to Tanya!
% 0.11/0.47 % SZS status Theorem for theBenchmark
% 0.11/0.47 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.47 % (3214315)------------------------------
% 0.11/0.47 % (3214315)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.11/0.47 % (3214315)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.11/0.47 % (3214315)CaDiCaL version: 2.1.3
% 0.11/0.47 % (3214315)Termination reason: Refutation
% 0.11/0.47 % (3214315)Time elapsed: 0.005 s
% 0.11/0.47 % (3214315)Peak memory usage: 12 MB
% 0.11/0.47 % (3214315)Instructions burned: 9 (million)
% 0.11/0.47 % (3214308)Success in time 0.034 s
% 0.11/0.47 % Vampire exiting
%------------------------------------------------------------------------------