%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET861-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n008.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 12:42:11 PM UTC 2026
% Result : Unsatisfiable 9.71s 2.24s
% Output : Refutation 10.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 19
% Syntax : Number of formulae : 124 ( 22 unt; 4 def)
% Number of atoms : 459 ( 13 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 637 ( 302 ~; 334 |; 0 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 6 con; 0-3 aty)
% Number of variables : 260 ( 0 sgn 260 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,tc_set(X2))
| ~ c_lessequals(X1,X0,tc_set(X2))
| X1 = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f2,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2))
| X0 = X1 ),
inference(reorient_equations,[],[f1]) ).
fof(f3,axiom,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2)
| c_in(X0,X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f4,axiom,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(X0,X1,X2),X0,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,X1,X2),X1,X2)
| c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X3,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,tc_set(X2))
| c_in(c_Zorn_Ochain__extend__1(X3,X0,X2),X3,tc_set(X2))
| c_in(c_union(c_insert(X0,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( ~ c_in(X3,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,tc_set(X2))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X3,X0,X2),X0,tc_set(X2))
| c_in(c_union(c_insert(X0,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
fof(f8,axiom,
! [X0,X1] : c_in(c_Zorn_OHausdorff__1(X0,X1),c_Zorn_Omaxchain(X0,X1),tc_set(tc_set(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OHausdorff_0) ).
fof(f9,axiom,
! [X0,X1] : c_lessequals(c_Zorn_Omaxchain(X0,X1),c_Zorn_Ochain(X0,X1),tc_set(tc_set(tc_set(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__subset__chain_0) ).
fof(f10,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,X2)
| c_in(X0,X5,X2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X3,X5,X2),X3,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
fof(f11,axiom,
! [X2,X3,X0,X1,X4,X5] :
( ~ c_in(c_union(c_insert(X1,c_emptyset,tc_set(X2)),X3,tc_set(X2)),c_Zorn_Ochain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_Omaxchain(X4,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,X2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X3,X5,X2),X5,tc_set(X2))
| c_in(X0,X5,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
fof(f12,negated_conjecture,
! [X0] :
( c_in(v_x(X0),v_S,tc_set(t_a))
| ~ c_in(X0,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f13,negated_conjecture,
! [X0] :
( c_in(v_xa(X0),v_S,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f14,negated_conjecture,
! [X0] :
( c_lessequals(X0,v_xa(X0),tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f15,negated_conjecture,
! [X0] :
( X0 != v_xa(X0)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f16,plain,
! [X0] :
( v_xa(X0) != X0
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(reorient_equations,[],[f15]) ).
fof(f17,negated_conjecture,
! [X0,X1] :
( c_lessequals(X0,v_x(X1),tc_set(t_a))
| ~ c_in(X0,X1,tc_set(t_a))
| ~ c_in(X1,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f18,definition,
sF0 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f19,plain,
tc_set(t_a) = sF0,
inference(reorient_equations,[],[f18]) ).
fof(f20,definition,
sF1 = c_Zorn_Ochain(v_S,t_a),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f21,plain,
c_Zorn_Ochain(v_S,t_a) = sF1,
inference(reorient_equations,[],[f20]) ).
fof(f22,definition,
sF2 = tc_set(sF0),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f23,plain,
tc_set(sF0) = sF2,
inference(reorient_equations,[],[f22]) ).
fof(f24,plain,
! [X0] :
( c_in(v_x(X0),v_S,sF0)
| ~ c_in(X0,sF1,sF2) ),
inference(definition_folding,[],[f12,f23,f19,f21,f19]) ).
fof(f25,plain,
! [X0] :
( c_in(v_xa(X0),v_S,sF0)
| ~ c_in(X0,v_S,sF0) ),
inference(definition_folding,[],[f13,f19,f19]) ).
fof(f26,plain,
! [X0] :
( c_lessequals(X0,v_xa(X0),sF0)
| ~ c_in(X0,v_S,sF0) ),
inference(definition_folding,[],[f14,f19,f19]) ).
fof(f27,plain,
! [X0] :
( v_xa(X0) != X0
| ~ c_in(X0,v_S,sF0) ),
inference(definition_folding,[],[f16,f19]) ).
fof(f28,plain,
! [X0,X1] :
( c_lessequals(X0,v_x(X1),sF0)
| ~ c_in(X0,X1,sF0)
| ~ c_in(X1,sF1,sF2) ),
inference(definition_folding,[],[f17,f23,f19,f21,f19,f19]) ).
fof(f29,plain,
! [X0,X1] :
( ~ c_in(X0,sF1,tc_set(tc_set(t_a)))
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X1,t_a),X1,tc_set(t_a))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),sF1,tc_set(tc_set(t_a))) ),
inference(superposition,[],[f7,f21]) ).
fof(f33,plain,
! [X0,X1] :
( ~ c_in(X0,sF1,tc_set(sF0))
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X1,t_a),X1,tc_set(t_a))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),sF1,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f29,f19]) ).
fof(f35,plain,
! [X0,X1] :
( ~ c_in(X0,sF1,sF2)
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X1,t_a),X1,tc_set(t_a))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),sF1,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f33,f23]) ).
fof(f36,plain,
! [X0,X1] :
( ~ c_in(X1,v_S,sF0)
| ~ c_in(X0,sF1,sF2)
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X1,t_a),X1,tc_set(t_a))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),sF1,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f35,f19]) ).
fof(f37,plain,
! [X0,X1] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X1,t_a),X1,sF0)
| ~ c_in(X1,v_S,sF0)
| ~ c_in(X0,sF1,sF2)
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),sF1,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f36,f19]) ).
fof(f38,plain,
! [X0,X1] :
( c_in(c_union(c_insert(X1,c_emptyset,sF0),X0,sF0),sF1,tc_set(sF0))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X1,t_a),X1,sF0)
| ~ c_in(X1,v_S,sF0)
| ~ c_in(X0,sF1,sF2) ),
inference(forward_demodulation,[],[f37,f19]) ).
fof(f39,plain,
! [X0,X1] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X1,t_a),X1,sF0)
| c_in(c_union(c_insert(X1,c_emptyset,sF0),X0,sF0),sF1,sF2)
| ~ c_in(X1,v_S,sF0)
| ~ c_in(X0,sF1,sF2) ),
inference(forward_demodulation,[],[f38,f23]) ).
fof(f40,plain,
! [X2,X0,X1] :
( ~ c_in(X2,X0,sF0)
| ~ c_lessequals(X0,X1,sF2)
| c_in(X2,X1,sF0) ),
inference(superposition,[],[f3,f23]) ).
fof(f41,plain,
! [X2,X0,X1] :
( ~ c_in(X2,X0,t_a)
| ~ c_lessequals(X0,X1,sF0)
| c_in(X2,X1,t_a) ),
inference(superposition,[],[f3,f19]) ).
fof(f45,plain,
c_lessequals(c_Zorn_Omaxchain(v_S,t_a),sF1,tc_set(tc_set(tc_set(t_a)))),
inference(superposition,[],[f9,f21]) ).
fof(f49,plain,
c_lessequals(c_Zorn_Omaxchain(v_S,t_a),sF1,tc_set(tc_set(sF0))),
inference(forward_demodulation,[],[f45,f19]) ).
fof(f50,plain,
c_lessequals(c_Zorn_Omaxchain(v_S,t_a),sF1,tc_set(sF2)),
inference(forward_demodulation,[],[f49,f23]) ).
fof(f51,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| c_in(X0,sF1,sF2) ),
inference(resolution,[],[f50,f3]) ).
fof(f52,plain,
! [X0,X1] :
( c_lessequals(X0,X0,tc_set(X1))
| c_lessequals(X0,X0,tc_set(X1)) ),
inference(resolution,[],[f4,f5]) ).
fof(f54,plain,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
inference(duplicate_literal_removal,[],[f52]) ).
fof(f56,plain,
! [X0] : c_in(c_Zorn_OHausdorff__1(X0,t_a),c_Zorn_Omaxchain(X0,t_a),tc_set(sF0)),
inference(superposition,[],[f8,f19]) ).
fof(f57,plain,
! [X0] : c_in(c_Zorn_OHausdorff__1(X0,t_a),c_Zorn_Omaxchain(X0,t_a),sF2),
inference(forward_demodulation,[],[f56,f23]) ).
fof(f59,plain,
! [X0,X1] :
( ~ c_in(X0,sF1,tc_set(tc_set(t_a)))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(X0,X1,t_a),X0,tc_set(t_a))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),sF1,tc_set(tc_set(t_a))) ),
inference(superposition,[],[f6,f21]) ).
fof(f63,plain,
! [X0,X1] :
( ~ c_in(X0,sF1,tc_set(sF0))
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(X0,X1,t_a),X0,tc_set(t_a))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),sF1,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f59,f19]) ).
fof(f65,plain,
! [X0,X1] :
( ~ c_in(X0,sF1,sF2)
| ~ c_in(X1,v_S,tc_set(t_a))
| c_in(c_Zorn_Ochain__extend__1(X0,X1,t_a),X0,tc_set(t_a))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),sF1,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f63,f23]) ).
fof(f66,plain,
! [X0,X1] :
( ~ c_in(X1,v_S,sF0)
| ~ c_in(X0,sF1,sF2)
| c_in(c_Zorn_Ochain__extend__1(X0,X1,t_a),X0,tc_set(t_a))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),sF1,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f65,f19]) ).
fof(f67,plain,
! [X0,X1] :
( c_in(c_Zorn_Ochain__extend__1(X0,X1,t_a),X0,sF0)
| ~ c_in(X1,v_S,sF0)
| ~ c_in(X0,sF1,sF2)
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),X0,tc_set(t_a)),sF1,tc_set(tc_set(t_a))) ),
inference(forward_demodulation,[],[f66,f19]) ).
fof(f68,plain,
! [X0,X1] :
( c_in(c_union(c_insert(X1,c_emptyset,sF0),X0,sF0),sF1,tc_set(sF0))
| c_in(c_Zorn_Ochain__extend__1(X0,X1,t_a),X0,sF0)
| ~ c_in(X1,v_S,sF0)
| ~ c_in(X0,sF1,sF2) ),
inference(forward_demodulation,[],[f67,f19]) ).
fof(f69,plain,
! [X0,X1] :
( c_in(c_union(c_insert(X1,c_emptyset,sF0),X0,sF0),sF1,sF2)
| c_in(c_Zorn_Ochain__extend__1(X0,X1,t_a),X0,sF0)
| ~ c_in(X1,v_S,sF0)
| ~ c_in(X0,sF1,sF2) ),
inference(forward_demodulation,[],[f68,f23]) ).
fof(f76,plain,
! [X0,X1] :
( ~ c_lessequals(X1,X0,sF0)
| ~ c_lessequals(X0,X1,sF0)
| X0 = X1 ),
inference(superposition,[],[f2,f19]) ).
fof(f86,plain,
! [X0] :
( ~ c_lessequals(v_xa(X0),X0,sF0)
| v_xa(X0) = X0
| ~ c_in(X0,v_S,sF0) ),
inference(resolution,[],[f76,f26]) ).
fof(f88,plain,
! [X0] :
( ~ c_lessequals(v_xa(X0),X0,sF0)
| ~ c_in(X0,v_S,sF0) ),
inference(forward_subsumption_resolution,[],[f86,f27]) ).
fof(f94,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,tc_set(t_a)),X1,tc_set(t_a)),sF1,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,X0,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X3,tc_set(t_a))
| c_in(X2,X3,t_a) ),
inference(superposition,[],[f11,f21]) ).
fof(f98,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF0),X1,sF0),sF1,tc_set(sF0))
| ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,X0,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X3,tc_set(t_a))
| c_in(X2,X3,t_a) ),
inference(forward_demodulation,[],[f94,f19]) ).
fof(f100,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF0),X1,sF0),sF1,sF2)
| ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,X0,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X3,tc_set(t_a))
| c_in(X2,X3,t_a) ),
inference(forward_demodulation,[],[f98,f23]) ).
fof(f101,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(sF0))
| ~ c_in(c_union(c_insert(X0,c_emptyset,sF0),X1,sF0),sF1,sF2)
| ~ c_in(X2,X0,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X3,tc_set(t_a))
| c_in(X2,X3,t_a) ),
inference(forward_demodulation,[],[f100,f19]) ).
fof(f102,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(c_union(c_insert(X0,c_emptyset,sF0),X1,sF0),sF1,sF2)
| ~ c_in(X2,X0,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X3,tc_set(t_a))
| c_in(X2,X3,t_a) ),
inference(forward_demodulation,[],[f101,f23]) ).
fof(f103,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF0),X1,sF0),sF1,sF2)
| ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X3,sF0)
| ~ c_in(X2,X0,t_a)
| c_in(X2,X3,t_a) ),
inference(forward_demodulation,[],[f102,f19]) ).
fof(f104,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,tc_set(t_a)),X1,tc_set(t_a)),sF1,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,X0,t_a)
| c_in(X2,X3,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X1,tc_set(t_a)) ),
inference(superposition,[],[f10,f21]) ).
fof(f108,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF0),X1,sF0),sF1,tc_set(sF0))
| ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,X0,t_a)
| c_in(X2,X3,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X1,tc_set(t_a)) ),
inference(forward_demodulation,[],[f104,f19]) ).
fof(f110,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF0),X1,sF0),sF1,sF2)
| ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,X0,t_a)
| c_in(X2,X3,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X1,tc_set(t_a)) ),
inference(forward_demodulation,[],[f108,f23]) ).
fof(f111,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(sF0))
| ~ c_in(c_union(c_insert(X0,c_emptyset,sF0),X1,sF0),sF1,sF2)
| ~ c_in(X2,X0,t_a)
| c_in(X2,X3,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X1,tc_set(t_a)) ),
inference(forward_demodulation,[],[f110,f19]) ).
fof(f112,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(c_union(c_insert(X0,c_emptyset,sF0),X1,sF0),sF1,sF2)
| ~ c_in(X2,X0,t_a)
| c_in(X2,X3,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X1,tc_set(t_a)) ),
inference(forward_demodulation,[],[f111,f23]) ).
fof(f113,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF0),X1,sF0),sF1,sF2)
| ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),sF2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X1,sF0)
| ~ c_in(X2,X0,t_a)
| c_in(X2,X3,t_a) ),
inference(forward_demodulation,[],[f112,f19]) ).
fof(f124,plain,
c_in(c_Zorn_OHausdorff__1(v_S,t_a),sF1,sF2),
inference(resolution,[],[f51,f57]) ).
fof(f132,plain,
! [X2,X0,X1] :
( c_in(c_union(c_insert(X2,c_emptyset,sF0),X0,sF0),sF1,sF2)
| c_in(c_Zorn_Ochain__extend__1(X0,X2,t_a),X1,sF0)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X2,v_S,sF0)
| ~ c_in(X0,sF1,sF2) ),
inference(resolution,[],[f40,f69]) ).
fof(f133,plain,
! [X0,X1] :
( c_in(v_x(X1),X0,sF0)
| ~ c_lessequals(v_S,X0,sF2)
| ~ c_in(X1,sF1,sF2) ),
inference(resolution,[],[f40,f24]) ).
fof(f136,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,sF0)
| c_in(c_Main_OsubsetI__1(X0,X2,t_a),X1,t_a)
| c_lessequals(X0,X2,tc_set(t_a)) ),
inference(resolution,[],[f41,f4]) ).
fof(f137,plain,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(X0,X2,t_a),X1,t_a)
| ~ c_lessequals(X0,X1,sF0)
| c_lessequals(X0,X2,sF0) ),
inference(forward_demodulation,[],[f136,f19]) ).
fof(f194,plain,
! [X0] : c_lessequals(X0,X0,sF2),
inference(superposition,[],[f54,f23]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(X1,X3,sF0)
| c_lessequals(X0,X2,sF0)
| ~ c_lessequals(X0,X1,sF0)
| c_in(c_Main_OsubsetI__1(X0,X2,t_a),X3,t_a) ),
inference(resolution,[],[f137,f41]) ).
fof(f216,plain,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(X0,X1,t_a),v_xa(X2),t_a)
| ~ c_lessequals(X0,X2,sF0)
| c_lessequals(X0,X1,sF0)
| ~ c_in(X2,v_S,sF0) ),
inference(resolution,[],[f215,f26]) ).
fof(f242,plain,
! [X0,X1] :
( ~ c_lessequals(X0,X1,sF0)
| c_lessequals(X0,v_xa(X1),sF0)
| ~ c_in(X1,v_S,sF0)
| c_lessequals(X0,v_xa(X1),tc_set(t_a)) ),
inference(resolution,[],[f216,f5]) ).
fof(f244,plain,
! [X0,X1] :
( c_lessequals(X0,v_xa(X1),sF0)
| ~ c_lessequals(X0,X1,sF0)
| c_lessequals(X0,v_xa(X1),sF0)
| ~ c_in(X1,v_S,sF0) ),
inference(forward_demodulation,[],[f242,f19]) ).
fof(f245,plain,
! [X0,X1] :
( c_lessequals(X0,v_xa(X1),sF0)
| ~ c_lessequals(X0,X1,sF0)
| ~ c_in(X1,v_S,sF0) ),
inference(duplicate_literal_removal,[],[f244]) ).
fof(f247,plain,
! [X0,X1] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,v_xa(X1),t_a),X1,sF0)
| ~ c_in(X1,v_S,sF0)
| c_in(c_union(c_insert(v_xa(X1),c_emptyset,sF0),X0,sF0),sF1,sF2)
| ~ c_in(v_xa(X1),v_S,sF0)
| ~ c_in(X0,sF1,sF2) ),
inference(resolution,[],[f245,f39]) ).
fof(f256,plain,
! [X0,X1] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,v_xa(X1),t_a),X1,sF0)
| ~ c_in(X1,v_S,sF0)
| c_in(c_union(c_insert(v_xa(X1),c_emptyset,sF0),X0,sF0),sF1,sF2)
| ~ c_in(X0,sF1,sF2) ),
inference(forward_subsumption_resolution,[],[f247,f25]) ).
fof(f258,plain,
! [X0,X1] :
( ~ c_in(v_x(X0),v_S,sF0)
| c_in(c_union(c_insert(v_xa(v_x(X0)),c_emptyset,sF0),X1,sF0),sF1,sF2)
| ~ c_in(X1,sF1,sF2)
| ~ c_in(c_Zorn_Ochain__extend__1(X1,v_xa(v_x(X0)),t_a),X0,sF0)
| ~ c_in(X0,sF1,sF2) ),
inference(resolution,[],[f256,f28]) ).
fof(f259,plain,
! [X0,X1] :
( ~ c_in(c_Zorn_Ochain__extend__1(X1,v_xa(v_x(X0)),t_a),X0,sF0)
| ~ c_in(X1,sF1,sF2)
| c_in(c_union(c_insert(v_xa(v_x(X0)),c_emptyset,sF0),X1,sF0),sF1,sF2)
| ~ c_in(X0,sF1,sF2) ),
inference(forward_subsumption_resolution,[],[f258,f24]) ).
fof(f262,plain,
! [X0] :
( ~ c_in(X0,sF1,sF2)
| c_in(c_union(c_insert(v_xa(v_x(X0)),c_emptyset,sF0),X0,sF0),sF1,sF2)
| ~ c_in(X0,sF1,sF2)
| c_in(c_union(c_insert(v_xa(v_x(X0)),c_emptyset,sF0),X0,sF0),sF1,sF2)
| ~ c_in(v_xa(v_x(X0)),v_S,sF0)
| ~ c_in(X0,sF1,sF2) ),
inference(resolution,[],[f259,f69]) ).
fof(f263,plain,
! [X0,X1] :
( ~ c_in(X0,sF1,sF2)
| c_in(c_union(c_insert(v_xa(v_x(X1)),c_emptyset,sF0),X0,sF0),sF1,sF2)
| ~ c_in(X1,sF1,sF2)
| c_in(c_union(c_insert(v_xa(v_x(X1)),c_emptyset,sF0),X0,sF0),sF1,sF2)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(v_xa(v_x(X1)),v_S,sF0)
| ~ c_in(X0,sF1,sF2) ),
inference(resolution,[],[f259,f132]) ).
fof(f264,plain,
! [X0,X1] :
( c_in(c_union(c_insert(v_xa(v_x(X1)),c_emptyset,sF0),X0,sF0),sF1,sF2)
| ~ c_in(X0,sF1,sF2)
| ~ c_in(X1,sF1,sF2)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(v_xa(v_x(X1)),v_S,sF0) ),
inference(duplicate_literal_removal,[],[f263]) ).
fof(f265,plain,
! [X0] :
( c_in(c_union(c_insert(v_xa(v_x(X0)),c_emptyset,sF0),X0,sF0),sF1,sF2)
| ~ c_in(X0,sF1,sF2)
| ~ c_in(v_xa(v_x(X0)),v_S,sF0) ),
inference(duplicate_literal_removal,[],[f262]) ).
fof(f267,plain,
! [X2,X0,X1] :
( ~ c_in(X0,sF1,sF2)
| ~ c_in(v_xa(v_x(X0)),v_S,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF0)
| ~ c_in(X2,v_xa(v_x(X0)),t_a)
| c_in(X2,X1,t_a) ),
inference(resolution,[],[f265,f113]) ).
fof(f271,plain,
! [X2,X0,X1] :
( ~ c_in(v_xa(v_x(X0)),v_S,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF0)
| ~ c_in(X2,v_xa(v_x(X0)),t_a)
| c_in(X2,X1,t_a) ),
inference(forward_subsumption_resolution,[],[f267,f51]) ).
fof(f274,plain,
! [X2,X0,X1] :
( ~ c_in(X2,v_xa(v_x(X0)),t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| c_in(X2,X1,t_a)
| ~ c_in(v_x(X0),v_S,sF0) ),
inference(resolution,[],[f271,f25]) ).
fof(f278,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,sF1,sF2)
| ~ c_in(X1,sF1,sF2)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(v_xa(v_x(X1)),v_S,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X0,X2,t_a),X2,sF0)
| ~ c_in(X3,v_xa(v_x(X1)),t_a)
| c_in(X3,X2,t_a) ),
inference(resolution,[],[f264,f103]) ).
fof(f280,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X0,X2,t_a),X2,sF0)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(v_xa(v_x(X1)),v_S,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(X1,sF1,sF2)
| ~ c_in(X3,v_xa(v_x(X1)),t_a)
| c_in(X3,X2,t_a) ),
inference(forward_subsumption_resolution,[],[f278,f51]) ).
fof(f283,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X0,v_x(X3),t_a),X3,sF0)
| ~ c_in(v_xa(v_x(X1)),v_S,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(X1,sF1,sF2)
| ~ c_in(X2,v_xa(v_x(X1)),t_a)
| c_in(X2,v_x(X3),t_a)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X3,sF1,sF2) ),
inference(resolution,[],[f280,f28]) ).
fof(f319,plain,
! [X2,X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| c_in(c_Main_OsubsetI__1(v_xa(v_x(X0)),X2,t_a),X1,t_a)
| ~ c_in(v_x(X0),v_S,sF0)
| c_lessequals(v_xa(v_x(X0)),X2,tc_set(t_a)) ),
inference(resolution,[],[f274,f4]) ).
fof(f322,plain,
! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(v_xa(v_x(X0)),X2,t_a),X1,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| c_lessequals(v_xa(v_x(X0)),X2,sF0)
| ~ c_in(v_x(X0),v_S,sF0) ),
inference(forward_demodulation,[],[f319,f19]) ).
fof(f947,plain,
! [X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| c_lessequals(v_xa(v_x(X0)),X1,sF0)
| ~ c_in(v_x(X0),v_S,sF0)
| c_lessequals(v_xa(v_x(X0)),X1,tc_set(t_a)) ),
inference(resolution,[],[f322,f5]) ).
fof(f984,plain,
! [X0,X1] :
( c_lessequals(v_xa(v_x(X0)),X1,sF0)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| c_lessequals(v_xa(v_x(X0)),X1,sF0)
| ~ c_in(v_x(X0),v_S,sF0) ),
inference(forward_demodulation,[],[f947,f19]) ).
fof(f985,plain,
! [X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF0)
| c_lessequals(v_xa(v_x(X0)),X1,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(v_x(X0),v_S,sF0) ),
inference(duplicate_literal_removal,[],[f984]) ).
fof(f999,plain,
! [X2,X0,X1] :
( c_lessequals(v_xa(v_x(X0)),v_x(X0),sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(v_x(X0),v_S,sF0)
| ~ c_in(v_xa(v_x(X1)),v_S,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(X1,sF1,sF2)
| ~ c_in(X2,v_xa(v_x(X1)),t_a)
| c_in(X2,v_x(X0),t_a)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X0,sF1,sF2) ),
inference(resolution,[],[f985,f283]) ).
fof(f1017,plain,
! [X2,X0,X1] :
( c_lessequals(v_xa(v_x(X0)),v_x(X0),sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(v_x(X0),v_S,sF0)
| ~ c_in(v_xa(v_x(X1)),v_S,sF0)
| ~ c_in(X1,sF1,sF2)
| ~ c_in(X2,v_xa(v_x(X1)),t_a)
| c_in(X2,v_x(X0),t_a)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X0,sF1,sF2) ),
inference(duplicate_literal_removal,[],[f999]) ).
fof(f1064,plain,
! [X2,X0,X1] :
( ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(v_x(X0),v_S,sF0)
| ~ c_in(v_xa(v_x(X1)),v_S,sF0)
| ~ c_in(X1,sF1,sF2)
| ~ c_in(X2,v_xa(v_x(X1)),t_a)
| c_in(X2,v_x(X0),t_a)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X0,sF1,sF2) ),
inference(forward_subsumption_resolution,[],[f1017,f88]) ).
fof(f1073,plain,
! [X2,X0,X1] :
( ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(v_xa(v_x(X1)),v_S,sF0)
| ~ c_in(X1,sF1,sF2)
| ~ c_in(X2,v_xa(v_x(X1)),t_a)
| c_in(X2,v_x(X0),t_a)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X0,sF1,sF2) ),
inference(forward_subsumption_resolution,[],[f1064,f24]) ).
fof(f1081,plain,
! [X2,X0,X1] :
( ~ c_in(v_xa(v_x(X1)),v_S,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(X1,sF1,sF2)
| ~ c_in(X2,v_xa(v_x(X1)),t_a)
| c_in(X2,v_x(X0),t_a)
| ~ c_lessequals(X0,X1,sF2) ),
inference(forward_subsumption_resolution,[],[f1073,f51]) ).
fof(f1102,plain,
! [X2,X0,X1] :
( ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(X1,sF1,sF2)
| ~ c_in(X2,v_xa(v_x(X1)),t_a)
| c_in(X2,v_x(X0),t_a)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(v_x(X1),v_S,sF0) ),
inference(resolution,[],[f1081,f25]) ).
fof(f1107,plain,
! [X2,X0,X1] :
( ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(X1,sF1,sF2)
| ~ c_in(X2,v_xa(v_x(X1)),t_a)
| c_in(X2,v_x(X0),t_a)
| ~ c_lessequals(X0,X1,sF2) ),
inference(forward_subsumption_resolution,[],[f1102,f24]) ).
fof(f1110,definition,
( spl3_33
<=> ! [X2,X0,X1] :
( ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X1,sF1,sF2)
| c_in(X2,v_x(X0),t_a)
| ~ c_in(X2,v_xa(v_x(X1)),t_a) ) ),
introduced(definition,[new_symbols(definition,[spl3_33])],[avatar_definition]) ).
fof(f1111,plain,
( ! [X2,X0,X1] :
( ~ c_in(X2,v_xa(v_x(X1)),t_a)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X1,sF1,sF2)
| c_in(X2,v_x(X0),t_a)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2) )
| ~ spl3_33 ),
inference(avatar_component_clause,[],[f1110]) ).
fof(f1113,plain,
spl3_33,
inference(avatar_split_clause,[],[f1107,f1110]) ).
fof(f1115,plain,
( ! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X1,sF1,sF2)
| c_in(c_Main_OsubsetI__1(v_xa(v_x(X1)),X2,t_a),v_x(X0),t_a)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| c_lessequals(v_xa(v_x(X1)),X2,tc_set(t_a)) )
| ~ spl3_33 ),
inference(resolution,[],[f1111,f4]) ).
fof(f1118,plain,
( ! [X2,X0,X1] :
( c_in(c_Main_OsubsetI__1(v_xa(v_x(X1)),X2,t_a),v_x(X0),t_a)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X1,sF1,sF2)
| c_lessequals(v_xa(v_x(X1)),X2,sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2) )
| ~ spl3_33 ),
inference(forward_demodulation,[],[f1115,f19]) ).
fof(f1284,plain,
( ! [X0,X1] :
( ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X1,sF1,sF2)
| c_lessequals(v_xa(v_x(X1)),v_x(X0),sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| c_lessequals(v_xa(v_x(X1)),v_x(X0),tc_set(t_a)) )
| ~ spl3_33 ),
inference(resolution,[],[f1118,f5]) ).
fof(f1290,plain,
( ! [X0,X1] :
( c_lessequals(v_xa(v_x(X1)),v_x(X0),sF0)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X1,sF1,sF2)
| c_lessequals(v_xa(v_x(X1)),v_x(X0),sF0)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2) )
| ~ spl3_33 ),
inference(forward_demodulation,[],[f1284,f19]) ).
fof(f1291,plain,
( ! [X0,X1] :
( c_lessequals(v_xa(v_x(X1)),v_x(X0),sF0)
| ~ c_lessequals(X0,X1,sF2)
| ~ c_in(X1,sF1,sF2)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2) )
| ~ spl3_33 ),
inference(duplicate_literal_removal,[],[f1290]) ).
fof(f1292,plain,
( ! [X0] :
( ~ c_lessequals(X0,X0,sF2)
| ~ c_in(X0,sF1,sF2)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(v_x(X0),v_S,sF0) )
| ~ spl3_33 ),
inference(resolution,[],[f1291,f88]) ).
fof(f1297,plain,
( ! [X0] :
( ~ c_in(X0,sF1,sF2)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(v_x(X0),v_S,sF0) )
| ~ spl3_33 ),
inference(forward_subsumption_resolution,[],[f1292,f194]) ).
fof(f1298,plain,
( ! [X0] :
( ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),sF2)
| ~ c_in(v_x(X0),v_S,sF0) )
| ~ spl3_33 ),
inference(forward_subsumption_resolution,[],[f1297,f51]) ).
fof(f1299,plain,
( ~ c_in(v_x(c_Zorn_OHausdorff__1(v_S,t_a)),v_S,sF0)
| ~ spl3_33 ),
inference(resolution,[],[f1298,f57]) ).
fof(f1353,plain,
( ~ c_lessequals(v_S,v_S,sF2)
| ~ c_in(c_Zorn_OHausdorff__1(v_S,t_a),sF1,sF2)
| ~ spl3_33 ),
inference(resolution,[],[f1299,f133]) ).
fof(f1354,plain,
( ~ c_in(c_Zorn_OHausdorff__1(v_S,t_a),sF1,sF2)
| ~ spl3_33 ),
inference(forward_subsumption_resolution,[],[f1353,f194]) ).
fof(f1357,plain,
( $false
| ~ spl3_33 ),
inference(forward_subsumption_resolution,[],[f1354,f124]) ).
fof(f1358,plain,
~ spl3_33,
inference(avatar_contradiction_clause,[],[f1357]) ).
cnf(s48,plain,
spl3_33,
inference(sat_conversion,[],[f1113]) ).
cnf(s62,plain,
~ spl3_33,
inference(sat_conversion,[],[f1358]) ).
cnf(s63,plain,
$false,
inference(rat,[],[s48,s62]) ).
fof(f1359,plain,
$false,
inference(avatar_sat_refutation,[],[s63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET861-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.37 % Computer : n008.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Mon Sep 28 03:04:39 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.12/0.41 Running first-order theorem proving
% 0.12/0.41 Running: /export/starexec/sandbox2/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.71/2.24 % (1825887)Input is clausal, will run a generic CNF schedule.
% 9.71/2.24 % (1825898)dis-21_1_sil=8000:lcm=predicate:random_seed=4103120256:st=5:avsq=on:i=117:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/117Mi)
% 9.71/2.24 % (1825898)Instruction limit reached!
% 9.71/2.24 % (1825898)------------------------------
% 9.71/2.24 % (1825898)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825898)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825898)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825898)Termination reason: Instruction limit
% 9.71/2.24 % (1825898)Termination phase: Saturation
% 9.71/2.24 % (1825898)Time elapsed: 0.038 s
% 9.71/2.24 % (1825898)Peak memory usage: 88 MB
% 9.71/2.24 % (1825898)Instructions burned: 118 (million)
% 9.71/2.24 % (1825896)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=3695233190:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 9.71/2.24 % (1825897)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=2280168128:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 9.71/2.24 % (1825894)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=2765655708:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 9.71/2.24 % (1825892)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=1353695505:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 9.71/2.24 % (1825895)lrs+10_1_sil=8000:sp=occurrence:random_seed=903008712:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 9.71/2.24 % (1825893)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=366606889:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 9.71/2.24 % (1825896)Refutation not found, incomplete strategy
% 9.71/2.24 % (1825896)------------------------------
% 9.71/2.24 % (1825896)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825896)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825896)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825896)Termination reason: Refutation not found, incomplete strategy
% 9.71/2.24 % (1825896)Time elapsed: 0.001 s
% 9.71/2.24 % (1825896)Peak memory usage: 88 MB
% 9.71/2.24 % (1825896)Instructions burned: 1 (million)
% 9.71/2.24 % (1825895)Instruction limit reached!
% 9.71/2.24 % (1825895)------------------------------
% 9.71/2.24 % (1825895)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825895)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825895)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825895)Termination reason: Instruction limit
% 9.71/2.24 % (1825895)Termination phase: Saturation
% 9.71/2.24 % (1825895)Time elapsed: 0.063 s
% 9.71/2.24 % (1825895)Peak memory usage: 89 MB
% 9.71/2.24 % (1825895)Instructions burned: 109 (million)
% 9.71/2.24 % (1825897)Instruction limit reached!
% 9.71/2.24 % (1825897)------------------------------
% 9.71/2.24 % (1825897)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825897)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825897)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825897)Termination reason: Instruction limit
% 9.71/2.24 % (1825897)Termination phase: Saturation
% 9.71/2.24 % (1825897)Time elapsed: 0.117 s
% 9.71/2.24 % (1825897)Peak memory usage: 89 MB
% 9.71/2.24 % (1825897)Instructions burned: 181 (million)
% 9.71/2.24 % (1825906)dis+1010_3_sil=8000:plsq=on:drc=off:fde=none:plsqc=1:bsd=on:plsqr=7,2:sos=on:spb=goal_then_units:random_seed=4218673758:i=143:sd=2:aac=none:ss=axioms:sgt=16_2998 on theBenchmark for (2998ds/143Mi)
% 9.71/2.24 % (1825906)Instruction limit reached!
% 9.71/2.24 % (1825906)------------------------------
% 9.71/2.24 % (1825906)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825906)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825906)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825906)Termination reason: Instruction limit
% 9.71/2.24 % (1825906)Termination phase: Saturation
% 9.71/2.24 % (1825906)Time elapsed: 0.042 s
% 9.71/2.24 % (1825906)Peak memory usage: 88 MB
% 9.71/2.24 % (1825906)Instructions burned: 145 (million)
% 9.71/2.24 % (1825907)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=3449783956:st=3:avsq=on:s2a=on:i=189:s2at=1.2:avsqr=1,16:sd=2:bd=all:nm=64:ss=axioms:sgt=30_2997 on theBenchmark for (2997ds/189Mi)
% 9.71/2.24 % (1825907)Refutation not found, incomplete strategy
% 9.71/2.24 % (1825907)------------------------------
% 9.71/2.24 % (1825907)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825907)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825907)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825907)Termination reason: Refutation not found, incomplete strategy
% 9.71/2.24 % (1825907)Time elapsed: 0.002 s
% 9.71/2.24 % (1825907)Peak memory usage: 88 MB
% 9.71/2.24 % (1825907)Instructions burned: 2 (million)
% 9.71/2.24 % (1825896)------------------------------
% 9.71/2.24 % (1825896)------------------------------
% 9.71/2.24 % (1825909)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=801261049:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 9.71/2.24 % (1825909)Refutation not found, incomplete strategy
% 9.71/2.24 % (1825909)------------------------------
% 9.71/2.24 % (1825909)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825909)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825909)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825909)Termination reason: Refutation not found, incomplete strategy
% 9.71/2.24 % (1825909)Time elapsed: 0.003 s
% 9.71/2.24 % (1825909)Peak memory usage: 87 MB
% 9.71/2.24 % (1825909)Instructions burned: 4 (million)
% 9.71/2.24 % (1825910)lrs+10_64_to=lpo:sil=8000:random_seed=816126731:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 9.71/2.24 % (1825910)Instruction limit reached!
% 9.71/2.24 % (1825910)------------------------------
% 9.71/2.24 % (1825910)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825910)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825910)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825910)Termination reason: Instruction limit
% 9.71/2.24 % (1825910)Termination phase: Saturation
% 9.71/2.24 % (1825910)Time elapsed: 0.038 s
% 9.71/2.24 % (1825910)Peak memory usage: 88 MB
% 9.71/2.24 % (1825910)Instructions burned: 128 (million)
% 9.71/2.24 % (1825912)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=2435708841:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 9.71/2.24 % (1825915)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=2910958803:i=157:gtg=all_2995 on theBenchmark for (2995ds/157Mi)
% 9.71/2.24 % (1825907)------------------------------
% 9.71/2.24 % (1825907)------------------------------
% 9.71/2.24 % (1825915)Instruction limit reached!
% 9.71/2.24 % (1825915)------------------------------
% 9.71/2.24 % (1825915)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825915)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825915)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825915)Termination reason: Instruction limit
% 9.71/2.24 % (1825915)Termination phase: Saturation
% 9.71/2.24 % (1825915)Time elapsed: 0.051 s
% 9.71/2.24 % (1825915)Peak memory usage: 89 MB
% 9.71/2.24 % (1825915)Instructions burned: 159 (million)
% 9.71/2.24 % (1825909)------------------------------
% 9.71/2.24 % (1825909)------------------------------
% 9.71/2.24 % (1825912)Instruction limit reached!
% 9.71/2.24 % (1825912)------------------------------
% 9.71/2.24 % (1825912)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825912)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825912)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825912)Termination reason: Instruction limit
% 9.71/2.24 % (1825912)Termination phase: Saturation
% 9.71/2.24 % (1825912)Time elapsed: 0.116 s
% 9.71/2.24 % (1825912)Peak memory usage: 90 MB
% 9.71/2.24 % (1825912)Instructions burned: 195 (million)
% 9.71/2.24 % (1825919)lrs+1011_5_to=lpo:sil=8000:tgt=full:plsq=on:prc=on:drc=off:plsqr=31,4:sp=occurrence:urr=on:nwc=0.8:s2agt=16:br=off:random_seed=3880495712:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 9.71/2.24 % (1825918)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=3721050990:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 9.71/2.24 % (1825919)Instruction limit reached!
% 9.71/2.24 % (1825919)------------------------------
% 9.71/2.24 % (1825919)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825919)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825919)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825919)Termination reason: Instruction limit
% 9.71/2.24 % (1825919)Termination phase: Saturation
% 9.71/2.24 % (1825919)Time elapsed: 0.030 s
% 9.71/2.24 % (1825919)Peak memory usage: 88 MB
% 9.71/2.24 % (1825919)Instructions burned: 109 (million)
% 9.71/2.24 % (1825920)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=2582276146:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 9.71/2.24 % (1825921)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=887251934:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 9.71/2.24 % (1825920)Instruction limit reached!
% 9.71/2.24 % (1825920)------------------------------
% 9.71/2.24 % (1825920)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825920)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825920)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825920)Termination reason: Instruction limit
% 9.71/2.24 % (1825920)Termination phase: Saturation
% 9.71/2.24 % (1825920)Time elapsed: 0.049 s
% 9.71/2.24 % (1825920)Peak memory usage: 87 MB
% 9.71/2.24 % (1825920)Instructions burned: 110 (million)
% 9.71/2.24 % (1825924)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=3757296758:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 9.71/2.24 % (1825921)Instruction limit reached!
% 9.71/2.24 % (1825921)------------------------------
% 9.71/2.24 % (1825921)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825921)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825921)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825921)Termination reason: Instruction limit
% 9.71/2.24 % (1825921)Termination phase: Saturation
% 9.71/2.24 % (1825921)Time elapsed: 0.152 s
% 9.71/2.24 % (1825921)Peak memory usage: 89 MB
% 9.71/2.24 % (1825921)Instructions burned: 243 (million)
% 9.71/2.24 % (1825927)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=1743640887:i=134:sd=2:doe=on:ss=axioms:sgt=14_2991 on theBenchmark for (2991ds/134Mi)
% 9.71/2.24 % (1825892)First to succeed.
% 9.71/2.24 % (1825892)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1825887"
% 9.71/2.24 % (1825927)Instruction limit reached!
% 9.71/2.24 % (1825927)------------------------------
% 9.71/2.24 % (1825927)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 9.71/2.24 % (1825927)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 9.71/2.24 % (1825927)CaDiCaL version: 2.1.3
% 9.71/2.24 % (1825927)Termination reason: Instruction limit
% 9.71/2.24 % (1825927)Termination phase: Saturation
% 9.71/2.24 % (1825927)Time elapsed: 0.084 s
% 9.71/2.24 % (1825927)Peak memory usage: 89 MB
% 9.71/2.24 % (1825927)Instructions burned: 134 (million)
% 9.71/2.24 % (1825929)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=267010509:i=499:bd=all_2989 on theBenchmark for (2989ds/499Mi)
% 9.71/2.24 % (1825931)lrs+10_64_to=lpo:sil=8000:prc=on:sp=reverse_frequency:nwc=5:alpa=false:flr=on:random_seed=3250905586:i=191:fgj=on:bd=all_2988 on theBenchmark for (2988ds/191Mi)
% 9.71/2.24 % (1825892)Refutation found. Thanks to Tanya!
% 9.71/2.24 % SZS status Unsatisfiable for theBenchmark
% 9.71/2.24 % SZS output start Proof for theBenchmark
% See solution above
% 10.37/2.44 % (1825892)------------------------------
% 10.37/2.44 % (1825892)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 10.37/2.44 % (1825892)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 10.37/2.44 % (1825892)CaDiCaL version: 2.1.3
% 10.37/2.44 % (1825892)Termination reason: Refutation
% 10.37/2.44 % (1825892)Time elapsed: 0.952 s
% 10.37/2.44 % (1825892)Peak memory usage: 131 MB
% 10.37/2.44 % (1825892)Instructions burned: 1405 (million)
% 10.37/2.44 % (1825892)------------------------------
% 10.37/2.44 % (1825892)------------------------------
% 10.37/2.44 % (1825887)Success in time 1.381 s
% 10.37/2.44 % Vampire exiting
%------------------------------------------------------------------------------