%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SET862-1 : 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 : n007.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 8.61s 1.90s
% Output : Refutation 8.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 25
% Syntax : Number of formulae : 144 ( 27 unt; 10 def)
% Number of atoms : 485 ( 15 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 629 ( 288 ~; 335 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-3 aty)
% Number of variables : 230 ( 0 sgn 230 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f378,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(f379,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(f380,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(f381,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(f382,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2))
| X0 = X1 ),
inference(reorient_equations,[],[f381]) ).
fof(f1435,axiom,
! [X2,X3,X0,X1] :
( 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)))
| ~ c_in(X3,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| c_in(c_Zorn_Ochain__extend__1(X3,X0,X2),X3,tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
fof(f1436,axiom,
! [X2,X3,X0,X1] :
( 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)))
| ~ c_in(X3,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X3,X0,X2),X0,tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
fof(f1437,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(f1438,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(f1439,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(f1440,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f1442,negated_conjecture,
c_in(v_y,v_S,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f1443,negated_conjecture,
! [X0] :
( c_lessequals(X0,v_y,tc_set(t_a))
| ~ c_in(X0,v_c,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f1444,negated_conjecture,
! [X0] :
( c_in(v_x(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_4) ).
fof(f1445,negated_conjecture,
! [X0] :
( c_lessequals(X0,v_x(X0),tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f1446,negated_conjecture,
! [X0] :
( X0 != v_x(X0)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
fof(f1447,plain,
! [X0] :
( v_x(X0) != X0
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(reorient_equations,[],[f1446]) ).
fof(f1448,definition,
sF0 = c_Zorn_Omaxchain(v_S,t_a),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
fof(f1449,plain,
c_Zorn_Omaxchain(v_S,t_a) = sF0,
inference(reorient_equations,[],[f1448]) ).
fof(f1450,definition,
sF1 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
fof(f1451,plain,
tc_set(t_a) = sF1,
inference(reorient_equations,[],[f1450]) ).
fof(f1452,definition,
sF2 = tc_set(sF1),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
fof(f1453,plain,
tc_set(sF1) = sF2,
inference(reorient_equations,[],[f1452]) ).
fof(f1454,plain,
c_in(v_c,sF0,sF2),
inference(definition_folding,[],[f1440,f1453,f1451,f1449]) ).
fof(f1455,definition,
sF3 = c_Zorn_Ochain(v_S,t_a),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
fof(f1456,plain,
c_Zorn_Ochain(v_S,t_a) = sF3,
inference(reorient_equations,[],[f1455]) ).
fof(f1458,plain,
c_in(v_y,v_S,sF1),
inference(definition_folding,[],[f1442,f1451]) ).
fof(f1459,plain,
! [X0] :
( c_lessequals(X0,v_y,sF1)
| ~ c_in(X0,v_c,sF1) ),
inference(definition_folding,[],[f1443,f1451,f1451]) ).
fof(f1460,plain,
! [X0] :
( c_in(v_x(X0),v_S,sF1)
| ~ c_in(X0,v_S,sF1) ),
inference(definition_folding,[],[f1444,f1451,f1451]) ).
fof(f1461,plain,
! [X0] :
( c_lessequals(X0,v_x(X0),sF1)
| ~ c_in(X0,v_S,sF1) ),
inference(definition_folding,[],[f1445,f1451,f1451]) ).
fof(f1462,plain,
! [X0] :
( ~ c_in(X0,v_S,sF1)
| v_x(X0) != X0 ),
inference(definition_folding,[],[f1447,f1451]) ).
fof(f1465,plain,
c_lessequals(c_Zorn_Omaxchain(v_S,t_a),sF3,tc_set(tc_set(tc_set(t_a)))),
inference(superposition,[],[f1437,f1456]) ).
fof(f1469,plain,
c_lessequals(c_Zorn_Omaxchain(v_S,t_a),sF3,tc_set(tc_set(sF1))),
inference(forward_demodulation,[],[f1465,f1451]) ).
fof(f1471,plain,
c_lessequals(c_Zorn_Omaxchain(v_S,t_a),sF3,tc_set(sF2)),
inference(forward_demodulation,[],[f1469,f1453]) ).
fof(f1473,plain,
c_lessequals(sF0,sF3,tc_set(sF2)),
inference(forward_demodulation,[],[f1471,f1449]) ).
fof(f1483,plain,
! [X0,X1] :
( c_in(c_union(c_insert(X0,c_emptyset,tc_set(t_a)),X1,tc_set(t_a)),sF3,tc_set(tc_set(t_a)))
| ~ c_in(X1,sF3,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X1,X0,t_a),X0,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(superposition,[],[f1436,f1456]) ).
fof(f1487,plain,
! [X0,X1] :
( c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,tc_set(sF1))
| ~ c_in(X1,sF3,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X1,X0,t_a),X0,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_demodulation,[],[f1483,f1451]) ).
fof(f1489,plain,
! [X0,X1] :
( c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| ~ c_in(X1,sF3,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X1,X0,t_a),X0,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_demodulation,[],[f1487,f1453]) ).
fof(f1490,plain,
! [X0,X1] :
( ~ c_in(X1,sF3,tc_set(sF1))
| c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X1,X0,t_a),X0,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_demodulation,[],[f1489,f1451]) ).
fof(f1491,plain,
! [X0,X1] :
( ~ c_in(X1,sF3,sF2)
| c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X1,X0,t_a),X0,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_demodulation,[],[f1490,f1453]) ).
fof(f1492,plain,
! [X0,X1] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(X1,X0,t_a),X0,sF1)
| ~ c_in(X1,sF3,sF2)
| c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_demodulation,[],[f1491,f1451]) ).
fof(f1493,plain,
! [X0,X1] :
( c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X1,X0,t_a),X0,sF1)
| ~ c_in(X1,sF3,sF2)
| ~ c_in(X0,v_S,sF1) ),
inference(forward_demodulation,[],[f1492,f1451]) ).
fof(f1498,plain,
! [X0] :
( c_in(X0,sF3,sF2)
| ~ c_in(X0,sF0,sF2) ),
inference(resolution,[],[f378,f1473]) ).
fof(f1500,plain,
! [X2,X0,X1] :
( ~ c_lessequals(X0,X1,sF1)
| ~ c_in(X2,X0,t_a)
| c_in(X2,X1,t_a) ),
inference(superposition,[],[f378,f1451]) ).
fof(f1511,plain,
! [X0,X1] :
( c_in(X0,v_y,t_a)
| ~ c_in(X0,X1,t_a)
| ~ c_in(X1,v_c,sF1) ),
inference(resolution,[],[f1500,f1459]) ).
fof(f1512,plain,
! [X0,X1] :
( c_in(X0,v_x(X1),t_a)
| ~ c_in(X0,X1,t_a)
| ~ c_in(X1,v_S,sF1) ),
inference(resolution,[],[f1500,f1461]) ).
fof(f1517,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,tc_set(t_a)),X1,tc_set(t_a)),sF3,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,[],[f1438,f1456]) ).
fof(f1521,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,tc_set(sF1))
| ~ 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,[],[f1517,f1451]) ).
fof(f1524,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,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,[],[f1521,f1453]) ).
fof(f1525,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(sF1))
| ~ c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,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,[],[f1524,f1451]) ).
fof(f1526,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,sF1),X1,sF1),sF3,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,[],[f1525,f1453]) ).
fof(f1527,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X1,sF0,sF2)
| ~ c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,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,[],[f1526,f1449]) ).
fof(f1528,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| ~ c_in(X1,sF0,sF2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X1,sF1)
| ~ c_in(X2,X0,t_a)
| c_in(X2,X3,t_a) ),
inference(forward_demodulation,[],[f1527,f1451]) ).
fof(f1543,plain,
! [X0,X1] :
( c_in(c_union(c_insert(X0,c_emptyset,tc_set(t_a)),X1,tc_set(t_a)),sF3,tc_set(tc_set(t_a)))
| ~ c_in(X1,sF3,tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(X1,X0,t_a),X1,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(superposition,[],[f1435,f1456]) ).
fof(f1547,plain,
! [X0,X1] :
( c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,tc_set(sF1))
| ~ c_in(X1,sF3,tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(X1,X0,t_a),X1,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_demodulation,[],[f1543,f1451]) ).
fof(f1550,plain,
! [X0,X1] :
( c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| ~ c_in(X1,sF3,tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(X1,X0,t_a),X1,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_demodulation,[],[f1547,f1453]) ).
fof(f1551,plain,
! [X0,X1] :
( ~ c_in(X1,sF3,tc_set(sF1))
| c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| c_in(c_Zorn_Ochain__extend__1(X1,X0,t_a),X1,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_demodulation,[],[f1550,f1451]) ).
fof(f1552,plain,
! [X0,X1] :
( ~ c_in(X1,sF3,sF2)
| c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| c_in(c_Zorn_Ochain__extend__1(X1,X0,t_a),X1,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_demodulation,[],[f1551,f1453]) ).
fof(f1553,plain,
! [X0,X1] :
( c_in(c_Zorn_Ochain__extend__1(X1,X0,t_a),X1,sF1)
| ~ c_in(X1,sF3,sF2)
| c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(forward_demodulation,[],[f1552,f1451]) ).
fof(f1554,plain,
! [X0,X1] :
( c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| c_in(c_Zorn_Ochain__extend__1(X1,X0,t_a),X1,sF1)
| ~ c_in(X1,sF3,sF2)
| ~ c_in(X0,v_S,sF1) ),
inference(forward_demodulation,[],[f1553,f1451]) ).
fof(f1569,plain,
! [X0,X1] :
( c_lessequals(X0,v_x(X1),tc_set(t_a))
| ~ c_in(c_Main_OsubsetI__1(X0,v_x(X1),t_a),X1,t_a)
| ~ c_in(X1,v_S,sF1) ),
inference(resolution,[],[f380,f1512]) ).
fof(f1571,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(X1),t_a),X1,t_a)
| c_lessequals(X0,v_x(X1),sF1)
| ~ c_in(X1,v_S,sF1) ),
inference(forward_demodulation,[],[f1569,f1451]) ).
fof(f1573,plain,
! [X0,X1] :
( c_lessequals(X0,v_x(v_y),sF1)
| ~ c_in(v_y,v_S,sF1)
| ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_y),t_a),X1,t_a)
| ~ c_in(X1,v_c,sF1) ),
inference(resolution,[],[f1571,f1511]) ).
fof(f1576,plain,
! [X0,X1] :
( ~ c_in(c_Main_OsubsetI__1(X0,v_x(v_y),t_a),X1,t_a)
| c_lessequals(X0,v_x(v_y),sF1)
| ~ c_in(X1,v_c,sF1) ),
inference(forward_subsumption_resolution,[],[f1573,f1458]) ).
fof(f1590,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,tc_set(t_a)),X1,tc_set(t_a)),sF3,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,[],[f1439,f1456]) ).
fof(f1594,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,tc_set(sF1))
| ~ 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,[],[f1590,f1451]) ).
fof(f1598,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,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,[],[f1594,f1453]) ).
fof(f1599,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X1,c_Zorn_Omaxchain(v_S,t_a),tc_set(sF1))
| ~ c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,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,[],[f1598,f1451]) ).
fof(f1600,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,sF1),X1,sF1),sF3,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,[],[f1599,f1453]) ).
fof(f1601,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X1,sF0,sF2)
| ~ c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,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,[],[f1600,f1449]) ).
fof(f1602,plain,
! [X2,X3,X0,X1] :
( ~ c_in(c_union(c_insert(X0,c_emptyset,sF1),X1,sF1),sF3,sF2)
| ~ c_in(X1,sF0,sF2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X1,X3,t_a),X3,sF1)
| ~ c_in(X2,X0,t_a)
| c_in(X2,X3,t_a) ),
inference(forward_demodulation,[],[f1601,f1451]) ).
fof(f1624,plain,
! [X0,X1] :
( ~ c_lessequals(X1,X0,sF1)
| ~ c_lessequals(X0,X1,sF1)
| X0 = X1 ),
inference(superposition,[],[f382,f1451]) ).
fof(f1635,plain,
! [X0] :
( ~ c_lessequals(v_x(X0),X0,sF1)
| v_x(X0) = X0
| ~ c_in(X0,v_S,sF1) ),
inference(resolution,[],[f1624,f1461]) ).
fof(f1637,plain,
! [X0] :
( ~ c_lessequals(v_x(X0),X0,sF1)
| ~ c_in(X0,v_S,sF1) ),
inference(forward_subsumption_resolution,[],[f1635,f1462]) ).
fof(f1658,plain,
! [X0] :
( c_lessequals(X0,v_x(v_y),tc_set(t_a))
| c_lessequals(X0,v_x(v_y),sF1)
| ~ c_in(X0,v_c,sF1) ),
inference(resolution,[],[f379,f1576]) ).
fof(f1669,plain,
! [X0] :
( c_lessequals(X0,v_x(v_y),sF1)
| c_lessequals(X0,v_x(v_y),sF1)
| ~ c_in(X0,v_c,sF1) ),
inference(forward_demodulation,[],[f1658,f1451]) ).
fof(f1670,plain,
! [X0] :
( c_lessequals(X0,v_x(v_y),sF1)
| ~ c_in(X0,v_c,sF1) ),
inference(duplicate_literal_removal,[],[f1669]) ).
fof(f1676,definition,
( spl4_3
<=> c_in(v_x(v_y),v_S,sF1) ),
introduced(definition,[new_symbols(definition,[spl4_3])],[avatar_definition]) ).
fof(f1677,plain,
( c_in(v_x(v_y),v_S,sF1)
| ~ spl4_3 ),
inference(avatar_component_clause,[],[f1676]) ).
fof(f1678,plain,
( ~ c_in(v_x(v_y),v_S,sF1)
| spl4_3 ),
inference(avatar_component_clause,[],[f1676]) ).
fof(f1723,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,sF0,sF2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF1)
| ~ c_in(X2,X3,t_a)
| c_in(X2,X1,t_a)
| c_in(c_Zorn_Ochain__extend__1(X0,X3,t_a),X0,sF1)
| ~ c_in(X0,sF3,sF2)
| ~ c_in(X3,v_S,sF1) ),
inference(resolution,[],[f1528,f1554]) ).
fof(f1724,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,sF0,sF2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF1)
| ~ c_in(X2,X3,t_a)
| c_in(X2,X1,t_a)
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X3,t_a),X3,sF1)
| ~ c_in(X0,sF3,sF2)
| ~ c_in(X3,v_S,sF1) ),
inference(resolution,[],[f1528,f1493]) ).
fof(f1726,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X3,t_a),X3,sF1)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF1)
| ~ c_in(X2,X3,t_a)
| c_in(X2,X1,t_a)
| ~ c_in(X0,sF0,sF2)
| ~ c_in(X3,v_S,sF1) ),
inference(forward_subsumption_resolution,[],[f1724,f1498]) ).
fof(f1727,plain,
! [X2,X3,X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF1)
| ~ c_in(X0,sF0,sF2)
| ~ c_in(X2,X3,t_a)
| c_in(X2,X1,t_a)
| c_in(c_Zorn_Ochain__extend__1(X0,X3,t_a),X0,sF1)
| ~ c_in(X3,v_S,sF1) ),
inference(forward_subsumption_resolution,[],[f1723,f1498]) ).
fof(f1738,plain,
! [X2,X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF1)
| ~ c_in(X2,v_x(v_y),t_a)
| c_in(X2,X1,t_a)
| ~ c_in(X0,sF0,sF2)
| ~ c_in(v_x(v_y),v_S,sF1)
| ~ c_in(c_Zorn_Ochain__extend__1(X0,v_x(v_y),t_a),v_c,sF1) ),
inference(resolution,[],[f1726,f1670]) ).
fof(f1746,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,sF0,sF2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X1,sF1)
| ~ c_in(X2,X3,t_a)
| c_in(X2,X1,t_a)
| c_in(c_Zorn_Ochain__extend__1(X0,X3,t_a),X0,sF1)
| ~ c_in(X0,sF3,sF2)
| ~ c_in(X3,v_S,sF1) ),
inference(resolution,[],[f1602,f1554]) ).
fof(f1747,plain,
! [X2,X3,X0,X1] :
( ~ c_in(X0,sF0,sF2)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X1,sF1)
| ~ c_in(X2,X3,t_a)
| c_in(X2,X1,t_a)
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X3,t_a),X3,sF1)
| ~ c_in(X0,sF3,sF2)
| ~ c_in(X3,v_S,sF1) ),
inference(resolution,[],[f1602,f1493]) ).
fof(f1749,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X1,sF1)
| ~ c_in(X0,sF0,sF2)
| ~ c_in(X2,X3,t_a)
| c_in(X2,X1,t_a)
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X3,t_a),X3,sF1)
| ~ c_in(X3,v_S,sF1) ),
inference(forward_subsumption_resolution,[],[f1747,f1498]) ).
fof(f1750,plain,
! [X2,X3,X0,X1] :
( ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X1,sF1)
| ~ c_in(X0,sF0,sF2)
| ~ c_in(X2,X3,t_a)
| c_in(X2,X1,t_a)
| c_in(c_Zorn_Ochain__extend__1(X0,X3,t_a),X0,sF1)
| ~ c_in(X3,v_S,sF1) ),
inference(forward_subsumption_resolution,[],[f1746,f1498]) ).
fof(f1751,plain,
! [X2,X0,X1] :
( c_in(c_Zorn_Ochain__extend__1(X0,X2,t_a),X0,sF1)
| ~ c_in(X1,X2,t_a)
| c_in(X1,v_y,t_a)
| ~ c_in(X0,sF0,sF2)
| ~ c_in(X2,v_S,sF1)
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X0,v_y,t_a),v_c,sF1) ),
inference(resolution,[],[f1750,f1459]) ).
fof(f1755,plain,
! [X2,X0,X1] :
( ~ c_lessequals(c_Zorn_Ochain__extend__1(X0,X2,t_a),X2,sF1)
| ~ c_in(X1,X2,t_a)
| c_in(X1,v_y,t_a)
| ~ c_in(X0,sF0,sF2)
| ~ c_in(X2,v_S,sF1)
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X0,v_y,t_a),v_c,sF1) ),
inference(resolution,[],[f1749,f1459]) ).
fof(f1760,plain,
! [X0,X1] :
( ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,v_y,t_a)
| ~ c_in(X1,sF0,sF2)
| ~ c_in(v_x(v_y),v_S,sF1)
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X1,v_y,t_a),v_c,sF1)
| ~ c_in(c_Zorn_Ochain__extend__1(X1,v_x(v_y),t_a),v_c,sF1) ),
inference(resolution,[],[f1755,f1670]) ).
fof(f1827,definition,
( spl4_18
<=> ! [X0] :
( ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,v_y,t_a) ) ),
introduced(definition,[new_symbols(definition,[spl4_18])],[avatar_definition]) ).
fof(f1828,plain,
( ! [X0] :
( ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,v_y,t_a) )
| ~ spl4_18 ),
inference(avatar_component_clause,[],[f1827]) ).
fof(f1840,plain,
( ~ c_in(v_y,v_S,sF1)
| spl4_3 ),
inference(resolution,[],[f1678,f1460]) ).
fof(f1841,plain,
( $false
| spl4_3 ),
inference(forward_subsumption_resolution,[],[f1840,f1458]) ).
fof(f1842,plain,
spl4_3,
inference(avatar_contradiction_clause,[],[f1841]) ).
fof(f1844,plain,
( ! [X2,X0,X1] :
( ~ c_in(c_Zorn_Ochain__extend__1(X0,v_x(v_y),t_a),v_c,sF1)
| ~ c_in(X2,v_x(v_y),t_a)
| c_in(X2,X1,t_a)
| ~ c_in(X0,sF0,sF2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X0,X1,t_a),X0,sF1) )
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f1738,f1677]) ).
fof(f1845,plain,
( ! [X0,X1] :
( ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,v_y,t_a)
| ~ c_in(X1,sF0,sF2)
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X1,v_y,t_a),v_c,sF1)
| ~ c_in(c_Zorn_Ochain__extend__1(X1,v_x(v_y),t_a),v_c,sF1) )
| ~ spl4_3 ),
inference(forward_subsumption_resolution,[],[f1760,f1677]) ).
fof(f1847,definition,
( spl4_21
<=> ! [X1] :
( ~ c_in(X1,sF0,sF2)
| ~ c_in(c_Zorn_Ochain__extend__1(X1,v_x(v_y),t_a),v_c,sF1)
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X1,v_y,t_a),v_c,sF1) ) ),
introduced(definition,[new_symbols(definition,[spl4_21])],[avatar_definition]) ).
fof(f1848,plain,
( ! [X1] :
( ~ c_in(c_Zorn_Ochain__extend__1(X1,v_x(v_y),t_a),v_c,sF1)
| ~ c_in(X1,sF0,sF2)
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(X1,v_y,t_a),v_c,sF1) )
| ~ spl4_21 ),
inference(avatar_component_clause,[],[f1847]) ).
fof(f1849,plain,
( spl4_21
| spl4_18
| ~ spl4_3 ),
inference(avatar_split_clause,[],[f1845,f1676,f1827,f1847]) ).
fof(f1853,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(v_x(v_y),X0,t_a),v_y,t_a)
| c_lessequals(v_x(v_y),X0,tc_set(t_a)) )
| ~ spl4_18 ),
inference(resolution,[],[f1828,f379]) ).
fof(f1854,plain,
( ! [X0] :
( c_in(c_Main_OsubsetI__1(v_x(v_y),X0,t_a),v_y,t_a)
| c_lessequals(v_x(v_y),X0,sF1) )
| ~ spl4_18 ),
inference(forward_demodulation,[],[f1853,f1451]) ).
fof(f1863,plain,
( c_lessequals(v_x(v_y),v_y,sF1)
| c_lessequals(v_x(v_y),v_y,tc_set(t_a))
| ~ spl4_18 ),
inference(resolution,[],[f1854,f380]) ).
fof(f1869,plain,
( c_lessequals(v_x(v_y),v_y,sF1)
| c_lessequals(v_x(v_y),v_y,sF1)
| ~ spl4_18 ),
inference(forward_demodulation,[],[f1863,f1451]) ).
fof(f1870,plain,
( c_lessequals(v_x(v_y),v_y,sF1)
| ~ spl4_18 ),
inference(duplicate_literal_removal,[],[f1869]) ).
fof(f1872,definition,
( spl4_22
<=> c_lessequals(v_x(v_y),v_y,sF1) ),
introduced(definition,[new_symbols(definition,[spl4_22])],[avatar_definition]) ).
fof(f1874,plain,
( c_lessequals(v_x(v_y),v_y,sF1)
| ~ spl4_22 ),
inference(avatar_component_clause,[],[f1872]) ).
fof(f1882,plain,
( spl4_22
| ~ spl4_18 ),
inference(avatar_split_clause,[],[f1870,f1827,f1872]) ).
fof(f1885,plain,
( ! [X0] :
( ~ c_in(v_c,sF0,sF2)
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,sF1)
| ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,v_y,t_a)
| ~ c_in(v_c,sF0,sF2)
| ~ c_in(v_x(v_y),v_S,sF1)
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,sF1) )
| ~ spl4_21 ),
inference(resolution,[],[f1848,f1751]) ).
fof(f1886,plain,
( ! [X0] :
( ~ c_in(v_c,sF0,sF2)
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,sF1)
| ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,v_y,t_a)
| ~ c_in(v_x(v_y),v_S,sF1) )
| ~ spl4_21 ),
inference(duplicate_literal_removal,[],[f1885]) ).
fof(f1888,plain,
( ! [X0] :
( ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,sF1)
| ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,v_y,t_a)
| ~ c_in(v_x(v_y),v_S,sF1) )
| ~ spl4_21 ),
inference(forward_subsumption_resolution,[],[f1886,f1454]) ).
fof(f1890,plain,
( ! [X0] :
( ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,sF1)
| ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,v_y,t_a) )
| ~ spl4_3
| ~ spl4_21 ),
inference(forward_subsumption_resolution,[],[f1888,f1677]) ).
fof(f1895,definition,
( spl4_25
<=> c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,sF1) ),
introduced(definition,[new_symbols(definition,[spl4_25])],[avatar_definition]) ).
fof(f1897,plain,
( ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,sF1)
| spl4_25 ),
inference(avatar_component_clause,[],[f1895]) ).
fof(f1899,plain,
( spl4_18
| ~ spl4_25
| ~ spl4_3
| ~ spl4_21 ),
inference(avatar_split_clause,[],[f1890,f1847,f1676,f1895,f1827]) ).
fof(f1972,plain,
( ! [X0,X1] :
( ~ c_in(v_c,sF0,sF2)
| ~ c_in(X0,X1,t_a)
| c_in(X0,v_y,t_a)
| c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,sF1)
| ~ c_in(X1,v_S,sF1) )
| spl4_25 ),
inference(resolution,[],[f1897,f1727]) ).
fof(f1973,plain,
( ! [X0,X1] :
( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,sF1)
| c_in(X0,v_y,t_a)
| ~ c_in(X0,X1,t_a)
| ~ c_in(X1,v_S,sF1) )
| spl4_25 ),
inference(forward_subsumption_resolution,[],[f1972,f1454]) ).
fof(f2245,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,X1,t_a)
| ~ c_in(v_c,sF0,sF2)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,sF1)
| c_in(X2,v_y,t_a)
| ~ c_in(X2,v_x(v_y),t_a)
| ~ c_in(v_x(v_y),v_S,sF1) )
| ~ spl4_3
| spl4_25 ),
inference(resolution,[],[f1844,f1973]) ).
fof(f2250,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,X1,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,sF1)
| c_in(X2,v_y,t_a)
| ~ c_in(X2,v_x(v_y),t_a)
| ~ c_in(v_x(v_y),v_S,sF1) )
| ~ spl4_3
| spl4_25 ),
inference(forward_subsumption_resolution,[],[f2245,f1454]) ).
fof(f2251,plain,
( ! [X2,X0,X1] :
( ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,X1,t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,sF1)
| c_in(X2,v_y,t_a)
| ~ c_in(X2,v_x(v_y),t_a) )
| ~ spl4_3
| spl4_25 ),
inference(forward_subsumption_resolution,[],[f2250,f1677]) ).
fof(f2253,definition,
( spl4_44
<=> ! [X0,X1] :
( ~ c_in(X0,v_x(v_y),t_a)
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,sF1)
| c_in(X0,X1,t_a) ) ),
introduced(definition,[new_symbols(definition,[spl4_44])],[avatar_definition]) ).
fof(f2254,plain,
( ! [X0,X1] :
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,sF1)
| ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,X1,t_a) )
| ~ spl4_44 ),
inference(avatar_component_clause,[],[f2253]) ).
fof(f2255,plain,
( spl4_18
| spl4_44
| ~ spl4_3
| spl4_25 ),
inference(avatar_split_clause,[],[f2251,f1895,f1676,f2253,f1827]) ).
fof(f2256,plain,
( ! [X0] :
( ~ c_in(X0,v_x(v_y),t_a)
| c_in(X0,v_y,t_a) )
| spl4_25
| ~ spl4_44 ),
inference(resolution,[],[f2254,f1897]) ).
fof(f2260,plain,
( spl4_18
| spl4_25
| ~ spl4_44 ),
inference(avatar_split_clause,[],[f2256,f2253,f1895,f1827]) ).
fof(f2267,plain,
( ~ c_in(v_y,v_S,sF1)
| ~ spl4_22 ),
inference(resolution,[],[f1874,f1637]) ).
fof(f2271,plain,
( $false
| ~ spl4_22 ),
inference(forward_subsumption_resolution,[],[f2267,f1458]) ).
fof(f2272,plain,
~ spl4_22,
inference(avatar_contradiction_clause,[],[f2271]) ).
cnf(s11,plain,
spl4_3,
inference(sat_conversion,[],[f1842]) ).
cnf(s12,plain,
( ~ spl4_3
| spl4_18
| spl4_21 ),
inference(sat_conversion,[],[f1849]) ).
cnf(s15,plain,
( ~ spl4_18
| spl4_22 ),
inference(sat_conversion,[],[f1882]) ).
cnf(s18,plain,
( ~ spl4_3
| spl4_18
| ~ spl4_21
| ~ spl4_25 ),
inference(sat_conversion,[],[f1899]) ).
cnf(s40,plain,
( ~ spl4_3
| spl4_18
| spl4_25
| spl4_44 ),
inference(sat_conversion,[],[f2255]) ).
cnf(s41,plain,
( spl4_18
| spl4_25
| ~ spl4_44 ),
inference(sat_conversion,[],[f2260]) ).
cnf(s42,plain,
~ spl4_22,
inference(sat_conversion,[],[f2272]) ).
cnf(s44,plain,
~ spl4_18,
inference(rat,[],[s15,s42]) ).
cnf(s46,plain,
( ~ spl4_3
| spl4_21 ),
inference(rat,[],[s12,s44]) ).
cnf(s48,plain,
spl4_21,
inference(rat,[],[s46,s11]) ).
cnf(s49,plain,
~ spl4_25,
inference(rat,[],[s18,s11,s44,s48]) ).
cnf(s50,plain,
~ spl4_44,
inference(rat,[],[s41,s44,s49]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s40,s11,s44,s50,s49]) ).
fof(f2275,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET862-1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.38 % Computer : n007.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Mon Sep 28 03:01:55 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 8.61/1.90 % (1985978)Input is clausal, will run a generic CNF schedule.
% 8.61/1.90 % (1985988)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=794400342:s2a=on:i=180:gtg=position_2999 on theBenchmark for (2999ds/180Mi)
% 8.61/1.90 % (1985986)lrs+10_1_sil=8000:sp=occurrence:random_seed=2033994380:i=107:sd=3:ss=axioms:sgt=8_2999 on theBenchmark for (2999ds/107Mi)
% 8.61/1.90 % (1985989)dis-21_1_sil=8000:lcm=predicate:random_seed=551627238: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)
% 8.61/1.90 % (1985984)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:urr=on:br=off:random_seed=1920232892:i=132376:av=off_2999 on theBenchmark for (2999ds/132376Mi)
% 8.61/1.90 % (1985987)dis-1002_1_to=lpo:sil=16000:fd=off:random_seed=574184333:st=1.5:i=114:aac=none:ins=7:ss=axioms:fsd=on_2999 on theBenchmark for (2999ds/114Mi)
% 8.61/1.90 % (1985983)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=863010976:i=140167_2999 on theBenchmark for (2999ds/140167Mi)
% 8.61/1.90 % (1985985)lrs+1002_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=ground:npcc=on:sp=reverse_frequency:spb=intro:random_seed=1995348669:i=137899:s2at=10:gtgl=3:kws=precedence:add=on:bd=preordered:gtg=position_2999 on theBenchmark for (2999ds/137899Mi)
% 8.61/1.90 % (1985986)Instruction limit reached!
% 8.61/1.90 % (1985986)------------------------------
% 8.61/1.90 % (1985986)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1985986)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1985986)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1985986)Termination reason: Instruction limit
% 8.61/1.90 % (1985986)Termination phase: Saturation
% 8.61/1.90 % (1985986)Time elapsed: 0.060 s
% 8.61/1.90 % (1985986)Peak memory usage: 89 MB
% 8.61/1.90 % (1985986)Instructions burned: 109 (million)
% 8.61/1.90 % (1985987)Instruction limit reached!
% 8.61/1.90 % (1985987)------------------------------
% 8.61/1.90 % (1985987)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1985987)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1985987)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1985987)Termination reason: Instruction limit
% 8.61/1.90 % (1985987)Termination phase: Saturation
% 8.61/1.90 % (1985987)Time elapsed: 0.064 s
% 8.61/1.90 % (1985987)Peak memory usage: 88 MB
% 8.61/1.90 % (1985987)Instructions burned: 114 (million)
% 8.61/1.90 % (1985989)Instruction limit reached!
% 8.61/1.90 % (1985989)------------------------------
% 8.61/1.90 % (1985989)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1985989)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1985989)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1985989)Termination reason: Instruction limit
% 8.61/1.90 % (1985989)Termination phase: Saturation
% 8.61/1.90 % (1985989)Time elapsed: 0.068 s
% 8.61/1.90 % (1985989)Peak memory usage: 89 MB
% 8.61/1.90 % (1985989)Instructions burned: 118 (million)
% 8.61/1.90 % (1985988)Instruction limit reached!
% 8.61/1.90 % (1985988)------------------------------
% 8.61/1.90 % (1985988)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1985988)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1985988)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1985988)Termination reason: Instruction limit
% 8.61/1.90 % (1985988)Termination phase: Saturation
% 8.61/1.90 % (1985988)Time elapsed: 0.130 s
% 8.61/1.90 % (1985988)Peak memory usage: 90 MB
% 8.61/1.90 % (1985988)Instructions burned: 181 (million)
% 8.61/1.90 % (1985998)ott-1010_1_to=lpo:sil=16000:sos=on:spb=units:urr=on:bce=on:br=off:random_seed=691375157: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)
% 8.61/1.90 % (1985997)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=3486615420:i=143:sd=2:aac=none:ss=axioms:sgt=16_2997 on theBenchmark for (2997ds/143Mi)
% 8.61/1.90 % (1985999)lrs-1002_1_to=lpo:sil=8000:fde=none:sos=on:random_seed=1604464201:st=4:i=219:sd=3:ss=axioms_2997 on theBenchmark for (2997ds/219Mi)
% 8.61/1.90 % (1985997)Refutation not found, incomplete strategy
% 8.61/1.90 % (1985997)------------------------------
% 8.61/1.90 % (1985997)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1985997)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1985997)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1985997)Termination reason: Refutation not found, incomplete strategy
% 8.61/1.90 % (1985997)Time elapsed: 0.005 s
% 8.61/1.90 % (1985997)Peak memory usage: 88 MB
% 8.61/1.90 % (1985997)Instructions burned: 5 (million)
% 8.61/1.90 % (1985999)Refutation not found, incomplete strategy
% 8.61/1.90 % (1985999)------------------------------
% 8.61/1.90 % (1985999)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1985999)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1985999)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1985999)Termination reason: Refutation not found, incomplete strategy
% 8.61/1.90 % (1985999)Time elapsed: 0.009 s
% 8.61/1.90 % (1985999)Peak memory usage: 88 MB
% 8.61/1.90 % (1985999)Instructions burned: 12 (million)
% 8.61/1.90 % (1986000)lrs+10_64_to=lpo:sil=8000:random_seed=2063951346:i=126:bd=preordered_2996 on theBenchmark for (2996ds/126Mi)
% 8.61/1.90 % (1986000)Instruction limit reached!
% 8.61/1.90 % (1986000)------------------------------
% 8.61/1.90 % (1986000)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1986000)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1986000)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1986000)Termination reason: Instruction limit
% 8.61/1.90 % (1986000)Termination phase: Saturation
% 8.61/1.90 % (1986000)Time elapsed: 0.042 s
% 8.61/1.90 % (1986000)Peak memory usage: 89 MB
% 8.61/1.90 % (1986000)Instructions burned: 128 (million)
% 8.61/1.90 % (1985998)Instruction limit reached!
% 8.61/1.90 % (1985998)------------------------------
% 8.61/1.90 % (1985998)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1985998)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1985998)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1985998)Termination reason: Instruction limit
% 8.61/1.90 % (1985998)Termination phase: Saturation
% 8.61/1.90 % (1985998)Time elapsed: 0.117 s
% 8.61/1.90 % (1985998)Peak memory usage: 90 MB
% 8.61/1.90 % (1985998)Instructions burned: 190 (million)
% 8.61/1.90 % (1986005)lrs+1011_16_to=lpo:sil=8000:drc=off:sp=reverse_frequency:spb=goal_then_units:random_seed=1684605615:avsq=on:i=194:fgj=on:bd=preordered_2995 on theBenchmark for (2995ds/194Mi)
% 8.61/1.90 % (1985997)------------------------------
% 8.61/1.90 % (1985997)------------------------------
% 8.61/1.90 % (1985999)------------------------------
% 8.61/1.90 % (1985999)------------------------------
% 8.61/1.90 % (1986005)Instruction limit reached!
% 8.61/1.90 % (1986005)------------------------------
% 8.61/1.90 % (1986005)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1986005)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1986005)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1986005)Termination reason: Instruction limit
% 8.61/1.90 % (1986005)Termination phase: Saturation
% 8.61/1.90 % (1986005)Time elapsed: 0.052 s
% 8.61/1.90 % (1986005)Peak memory usage: 89 MB
% 8.61/1.90 % (1986005)Instructions burned: 197 (million)
% 8.61/1.90 % (1986006)lrs+10_1_sil=8000:tgt=full:acc=on:random_seed=1472574638:i=157:gtg=all_2994 on theBenchmark for (2994ds/157Mi)
% 8.61/1.90 % (1986006)Instruction limit reached!
% 8.61/1.90 % (1986006)------------------------------
% 8.61/1.90 % (1986006)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1986006)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1986006)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1986006)Termination reason: Instruction limit
% 8.61/1.90 % (1986006)Termination phase: Saturation
% 8.61/1.90 % (1986006)Time elapsed: 0.096 s
% 8.61/1.90 % (1986006)Peak memory usage: 91 MB
% 8.61/1.90 % (1986006)Instructions burned: 158 (million)
% 8.61/1.90 % (1986010)lrs+2_4096_sil=8000:plsq=on:plsqr=12672147,131072:sos=on:spb=goal:lcm=predicate:random_seed=4207193985:i=107_2993 on theBenchmark for (2993ds/107Mi)
% 8.61/1.90 % (1986009)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=928671945:cts=off:s2a=on:i=106:fsr=off:gsp=on:ss=axioms:sgt=16:rawr=on_2993 on theBenchmark for (2993ds/106Mi)
% 8.61/1.90 % (1986008)lrs+10_1_ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:random_seed=1598008682:i=3394:sd=4:ss=included:sgt=64_2993 on theBenchmark for (2993ds/3394Mi)
% 8.61/1.90 % (1986010)Instruction limit reached!
% 8.61/1.90 % (1986010)------------------------------
% 8.61/1.90 % (1986010)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1986010)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1986010)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1986010)Termination reason: Instruction limit
% 8.61/1.90 % (1986010)Termination phase: Saturation
% 8.61/1.90 % (1986010)Time elapsed: 0.038 s
% 8.61/1.90 % (1986010)Peak memory usage: 89 MB
% 8.61/1.90 % (1986010)Instructions burned: 109 (million)
% 8.61/1.90 % (1986009)Instruction limit reached!
% 8.61/1.90 % (1986009)------------------------------
% 8.61/1.90 % (1986009)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1986009)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1986009)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1986009)Termination reason: Instruction limit
% 8.61/1.90 % (1986009)Termination phase: Saturation
% 8.61/1.90 % (1986009)Time elapsed: 0.062 s
% 8.61/1.90 % (1986009)Peak memory usage: 89 MB
% 8.61/1.90 % (1986009)Instructions burned: 106 (million)
% 8.61/1.90 % (1986013)lrs+1011_20_sil=64000:tgt=ground:plsq=on:fde=unused:plsqc=1:plsqr=14,1:plsql=on:nwc=0.6:random_seed=1600043007:st=6:i=242:gtgl=5:kws=arity_squared:av=off:gtg=exists_sym:ss=included_2992 on theBenchmark for (2992ds/242Mi)
% 8.61/1.90 % (1986016)lrs+1010_1_ncem=casc2026/models/all5champsBiggishL14.pt:sil=16000:tgt=ground:npcc=on:sims=off:random_seed=531283900:cond=fast:i=5208:av=off_2991 on theBenchmark for (2991ds/5208Mi)
% 8.61/1.90 % (1985985)First to succeed.
% 8.61/1.90 % (1985985)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-1985978"
% 8.61/1.90 % (1986017)lrs+1011_16_sil=32000:erd=off:bce=on:random_seed=2230988422:i=134:sd=2:doe=on:ss=axioms:sgt=14_2991 on theBenchmark for (2991ds/134Mi)
% 8.61/1.90 % (1986017)Refutation not found, incomplete strategy
% 8.61/1.90 % (1986017)------------------------------
% 8.61/1.90 % (1986017)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1986017)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1986017)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1986017)Termination reason: Refutation not found, incomplete strategy
% 8.61/1.90 % (1986017)Time elapsed: 0.010 s
% 8.61/1.90 % (1986017)Peak memory usage: 89 MB
% 8.61/1.90 % (1986017)Instructions burned: 12 (million)
% 8.61/1.90 % (1986013)Instruction limit reached!
% 8.61/1.90 % (1986013)------------------------------
% 8.61/1.90 % (1986013)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/1.90 % (1986013)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/1.90 % (1986013)CaDiCaL version: 2.1.3
% 8.61/1.90 % (1986013)Termination reason: Instruction limit
% 8.61/1.90 % (1986013)Termination phase: Saturation
% 8.61/1.90 % (1986013)Time elapsed: 0.130 s
% 8.61/1.90 % (1986013)Peak memory usage: 89 MB
% 8.61/1.90 % (1986013)Instructions burned: 243 (million)
% 8.61/1.90 % (1986021)ott+10_5:4_to=lpo:sil=8000:prc=on:fde=unused:sp=unary_frequency:spb=goal:urr=on:random_seed=352605366:i=499:bd=all_2989 on theBenchmark for (2989ds/499Mi)
% 8.61/1.90 % (1985983)Also succeeded, but the first one will report.
% 8.61/1.90 % (1985985)Refutation found. Thanks to Tanya!
% 8.61/1.90 % SZS status Unsatisfiable for theBenchmark
% 8.61/1.90 % SZS output start Proof for theBenchmark
% See solution above
% 8.61/2.00 % (1985985)------------------------------
% 8.61/2.00 % (1985985)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 8.61/2.00 % (1985985)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 8.61/2.00 % (1985985)CaDiCaL version: 2.1.3
% 8.61/2.00 % (1985985)Termination reason: Refutation
% 8.61/2.00 % (1985985)Time elapsed: 0.847 s
% 8.61/2.00 % (1985985)Peak memory usage: 136 MB
% 8.61/2.00 % (1985985)Instructions burned: 1294 (million)
% 8.61/2.00 % (1985985)------------------------------
% 8.61/2.00 % (1985985)------------------------------
% 8.61/2.00 % (1985978)Success in time 1.287 s
% 8.61/2.00 % Vampire exiting
%------------------------------------------------------------------------------