TSTP Solution File: SET854-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET854-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 14:35:59 EDT 2023
% Result : Unsatisfiable 13.33s 13.44s
% Output : CNFRefutation 13.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 31
% Syntax : Number of formulae : 85 ( 18 unt; 13 typ; 0 def)
% Number of atoms : 244 ( 25 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 271 ( 99 ~; 172 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 24 ( 9 >; 15 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 4 con; 0-4 aty)
% Number of variables : 155 ( 3 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
tc_set: $i > $i ).
tff(decl_23,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_24,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
c_Zorn_Osucc: ( $i * $i * $i ) > $i ).
tff(decl_27,type,
c_Zorn_OTFin: ( $i * $i ) > $i ).
tff(decl_28,type,
c_Zorn_OTFin__linear__lemma1__1: ( $i * $i * $i ) > $i ).
tff(decl_29,type,
c_Zorn_OUnion__lemma0__1: ( $i * $i * $i * $i ) > $i ).
tff(decl_30,type,
c_Union: ( $i * $i ) > $i ).
tff(decl_31,type,
v_Y: $i ).
tff(decl_32,type,
v_S: $i ).
tff(decl_33,type,
t_a: $i ).
tff(decl_34,type,
v_x: $i ).
cnf(cls_Set_OsubsetD_0,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Zorn_OTFin__linear__lemma1_3,axiom,
( c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Zorn_Osucc(X2,c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X3),X1,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
cnf(cls_conjecture_5,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a)))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,v_Y,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_Zorn_OTFin__linear__lemma1_1,axiom,
( c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X1,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
cnf(cls_Zorn_OTFin__linear__lemma1_0,axiom,
( c_in(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Zorn_OTFin__linear__lemma1_2,axiom,
( c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
cnf(cls_Zorn_OAbrial__axiom1_0,axiom,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
cnf(cls_Zorn_OUnion__lemma0_2,axiom,
( c_lessequals(X1,c_Union(X3,X4),tc_set(X4))
| c_lessequals(c_Union(X3,X4),X2,tc_set(X4))
| ~ c_lessequals(X1,c_Zorn_OUnion__lemma0__1(X2,X1,X3,X4),tc_set(X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_2) ).
cnf(cls_Zorn_OUnion__lemma0_0,axiom,
( c_in(c_Zorn_OUnion__lemma0__1(X1,X2,X3,X4),X3,tc_set(X4))
| c_lessequals(X2,c_Union(X3,X4),tc_set(X4))
| c_lessequals(c_Union(X3,X4),X1,tc_set(X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_0) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_Set_Osubset__antisym_0,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(v_x,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
v_x != c_Union(v_Y,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_Zorn_OUnion__lemma0_1,axiom,
( c_lessequals(X2,c_Union(X3,X4),tc_set(X4))
| c_lessequals(c_Union(X3,X4),X1,tc_set(X4))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X2,X3,X4),X1,tc_set(X4)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_1) ).
cnf(cls_Set_OsubsetI_0,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
cnf(cls_Set_OsubsetI_1,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OsubsetI_1) ).
cnf(c_0_18,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
cls_Set_OsubsetD_0 ).
cnf(c_0_19,negated_conjecture,
c_lessequals(v_Y,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),
cls_conjecture_0 ).
cnf(c_0_20,axiom,
( c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Zorn_Osucc(X2,c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X3),X1,tc_set(tc_set(X3))) ),
cls_Zorn_OTFin__linear__lemma1_3 ).
cnf(c_0_21,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a)))
| X1 = X2
| ~ c_lessequals(X1,X2,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,v_Y,tc_set(tc_set(t_a))) ),
cls_conjecture_5 ).
cnf(c_0_22,axiom,
( c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),X1,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
cls_Zorn_OTFin__linear__lemma1_1 ).
cnf(c_0_23,negated_conjecture,
( c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_24,axiom,
( c_in(c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
cls_Zorn_OTFin__linear__lemma1_0 ).
cnf(c_0_25,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_1 ).
cnf(c_0_26,axiom,
( c_lessequals(X4,X1,tc_set(tc_set(X3)))
| c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| c_Zorn_OTFin__linear__lemma1__1(X2,X1,X3) != X1 ),
cls_Zorn_OTFin__linear__lemma1_2 ).
cnf(c_0_27,negated_conjecture,
( c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) = X1
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a)))
| c_lessequals(X2,X1,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X1,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_24,c_0_25]) ).
cnf(c_0_29,plain,
( c_in(X1,X2,tc_set(X3))
| c_lessequals(X2,X4,tc_set(tc_set(X3)))
| c_Zorn_OTFin__linear__lemma1__1(X5,X4,X3) != X4
| ~ c_in(X2,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(X4,c_Zorn_OTFin(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_Osucc(X5,X4,X3),tc_set(X3)) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_30,axiom,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
cls_Zorn_OAbrial__axiom1_0 ).
cnf(c_0_31,negated_conjecture,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a)))
| c_lessequals(X2,X1,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X2,v_Y,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_32,axiom,
( c_lessequals(X1,c_Union(X3,X4),tc_set(X4))
| c_lessequals(c_Union(X3,X4),X2,tc_set(X4))
| ~ c_lessequals(X1,c_Zorn_OUnion__lemma0__1(X2,X1,X3,X4),tc_set(X4)) ),
cls_Zorn_OUnion__lemma0_2 ).
cnf(c_0_33,negated_conjecture,
( c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) = X1
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),X2,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X1,tc_set(tc_set(t_a)))
| c_lessequals(X2,X1,tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_23]) ).
cnf(c_0_34,negated_conjecture,
( c_in(X1,v_x,tc_set(t_a))
| c_lessequals(v_x,X2,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X2,t_a) != X2
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_Osucc(v_S,X2,t_a),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_29,c_0_25]) ).
cnf(c_0_35,plain,
( c_in(X1,c_Zorn_Osucc(X2,X3,X4),tc_set(X4))
| ~ c_in(X1,X3,tc_set(X4)) ),
inference(spm,[status(thm)],[c_0_18,c_0_30]) ).
cnf(c_0_36,negated_conjecture,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(X1,v_x,tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_31,c_0_25]) ).
cnf(c_0_37,axiom,
( c_in(c_Zorn_OUnion__lemma0__1(X1,X2,X3,X4),X3,tc_set(X4))
| c_lessequals(X2,c_Union(X3,X4),tc_set(X4))
| c_lessequals(c_Union(X3,X4),X1,tc_set(X4)) ),
cls_Zorn_OUnion__lemma0_0 ).
cnf(c_0_38,plain,
( c_lessequals(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(X2,X3,X4),X5,tc_set(X4)),X3,tc_set(tc_set(X4)))
| c_lessequals(c_Zorn_Osucc(X2,X3,X4),c_Union(X5,tc_set(X4)),tc_set(tc_set(X4)))
| c_lessequals(c_Union(X5,tc_set(X4)),X1,tc_set(tc_set(X4)))
| c_Zorn_OTFin__linear__lemma1__1(X2,X3,X4) != X3
| ~ c_in(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(X2,X3,X4),X5,tc_set(X4)),c_Zorn_OTFin(X2,X4),tc_set(tc_set(X4)))
| ~ c_in(X3,c_Zorn_OTFin(X2,X4),tc_set(tc_set(X4))) ),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_39,negated_conjecture,
( c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) = X1
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_x,tc_set(tc_set(t_a)))
| c_lessequals(v_x,X1,tc_set(tc_set(t_a)))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_33,c_0_25]) ).
cnf(c_0_40,negated_conjecture,
( c_in(X1,v_x,tc_set(t_a))
| c_lessequals(v_x,X2,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X2,t_a) != X2
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X1,X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_41,negated_conjecture,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(X2,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_42,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
cls_conjecture_4 ).
cnf(c_0_43,axiom,
( X2 = X1
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X2,X1,tc_set(X3)) ),
cls_Set_Osubset__antisym_0 ).
cnf(c_0_44,negated_conjecture,
c_lessequals(v_x,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
cls_conjecture_2 ).
cnf(c_0_45,negated_conjecture,
v_x != c_Union(v_Y,tc_set(t_a)),
cls_conjecture_3 ).
cnf(c_0_46,negated_conjecture,
( c_lessequals(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),X3,tc_set(t_a)),X2,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X2,t_a),c_Union(X3,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(X3,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X2,t_a) != X2
| ~ c_in(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),X3,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_38,c_0_23]) ).
cnf(c_0_47,negated_conjecture,
( c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) = X1
| c_in(X2,v_x,tc_set(t_a))
| c_lessequals(v_x,X1,tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_Osucc(v_S,X1,t_a),tc_set(t_a))
| ~ c_in(X1,v_Y,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_18,c_0_39]) ).
cnf(c_0_48,negated_conjecture,
( c_in(X1,v_x,tc_set(t_a))
| c_lessequals(v_x,X2,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X2,t_a) != X2
| ~ c_in(X2,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X1,X2,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_40,c_0_23]) ).
cnf(c_0_49,axiom,
( c_lessequals(X2,c_Union(X3,X4),tc_set(X4))
| c_lessequals(c_Union(X3,X4),X1,tc_set(X4))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X2,X3,X4),X1,tc_set(X4)) ),
cls_Zorn_OUnion__lemma0_1 ).
cnf(c_0_50,negated_conjecture,
( c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_41]),c_0_42]) ).
cnf(c_0_51,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).
cnf(c_0_52,negated_conjecture,
( c_lessequals(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),v_Y,tc_set(t_a)),X2,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,X2,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X2,t_a) != X2
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_46,c_0_37]) ).
cnf(c_0_53,negated_conjecture,
( c_in(X1,v_x,tc_set(t_a))
| c_lessequals(v_x,X2,tc_set(tc_set(t_a)))
| ~ c_in(X2,v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X1,X2,tc_set(t_a)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_35]),c_0_48]) ).
cnf(c_0_54,negated_conjecture,
c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_50]),c_0_42]),c_0_51]) ).
cnf(c_0_55,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a) != X1
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_49,c_0_52]) ).
cnf(c_0_56,negated_conjecture,
( c_in(X1,v_x,tc_set(t_a))
| c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(X2,X3,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X2,tc_set(tc_set(t_a)))
| c_lessequals(X3,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OUnion__lemma0__1(X2,X3,v_Y,tc_set(t_a)),tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_53,c_0_37]) ).
cnf(c_0_57,axiom,
( c_in(c_Main_OsubsetI__1(X1,X2,X3),X1,X3)
| c_lessequals(X1,X2,tc_set(X3)) ),
cls_Set_OsubsetI_0 ).
cnf(c_0_58,negated_conjecture,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(X1,v_x,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,v_Y,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_27,c_0_54]) ).
cnf(c_0_59,negated_conjecture,
c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) != v_x,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_55]),c_0_25])]),c_0_51]) ).
cnf(c_0_60,axiom,
( c_lessequals(X1,X2,tc_set(X3))
| ~ c_in(c_Main_OsubsetI__1(X1,X2,X3),X2,X3) ),
cls_Set_OsubsetI_1 ).
cnf(c_0_61,negated_conjecture,
( c_in(c_Main_OsubsetI__1(c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),X3,tc_set(t_a)),v_x,tc_set(t_a))
| c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),X3,tc_set(tc_set(t_a)))
| c_lessequals(X2,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_56,c_0_57]) ).
cnf(c_0_62,negated_conjecture,
( c_lessequals(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),X2,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(X2,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(X2,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),X2,tc_set(t_a)),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,v_Y,tc_set(tc_set(t_a))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_58]),c_0_59]) ).
cnf(c_0_63,negated_conjecture,
( c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),X3,tc_set(t_a)) = X2
| c_lessequals(c_Zorn_Osucc(v_S,X2,t_a),c_Union(X3,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(X3,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),X3,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X2,c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),X3,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_32,c_0_21]) ).
cnf(c_0_64,negated_conjecture,
( c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X1,X2,v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| c_lessequals(X2,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_65,negated_conjecture,
( c_lessequals(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),X2,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),c_Union(X2,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(X2,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| ~ c_in(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),X2,tc_set(t_a)),v_Y,tc_set(tc_set(t_a)))
| ~ c_in(v_x,v_Y,tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_62,c_0_23]) ).
cnf(c_0_66,negated_conjecture,
( c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),v_Y,tc_set(t_a)) = X2
| c_lessequals(c_Zorn_Osucc(v_S,X2,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| ~ c_in(X2,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X2,c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,X2,t_a),v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_63,c_0_37]) ).
cnf(c_0_67,negated_conjecture,
( c_lessequals(v_x,c_Zorn_OUnion__lemma0__1(v_x,X1,v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(X1,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_64]),c_0_51]) ).
cnf(c_0_68,negated_conjecture,
( c_lessequals(c_Zorn_OUnion__lemma0__1(X1,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)),v_x,tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X1,tc_set(tc_set(t_a)))
| ~ c_in(v_x,v_Y,tc_set(tc_set(t_a))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_37]),c_0_42]) ).
cnf(c_0_69,negated_conjecture,
c_Zorn_OUnion__lemma0__1(v_x,c_Zorn_Osucc(v_S,v_x,t_a),v_Y,tc_set(t_a)) = v_x,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_25])]),c_0_42]),c_0_51]) ).
cnf(c_0_70,negated_conjecture,
~ c_in(v_x,v_Y,tc_set(tc_set(t_a))),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_68]),c_0_42]),c_0_51]) ).
cnf(c_0_71,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_69]),c_0_70]),c_0_42]),c_0_51]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13 % Problem : SET854-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35 % Computer : n004.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Aug 26 13:09:22 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.20/0.56 start to proof: theBenchmark
% 13.33/13.44 % Version : CSE_E---1.5
% 13.33/13.44 % Problem : theBenchmark.p
% 13.33/13.44 % Proof found
% 13.33/13.44 % SZS status Theorem for theBenchmark.p
% 13.33/13.44 % SZS output start Proof
% See solution above
% 13.33/13.45 % Total time : 12.870000 s
% 13.33/13.45 % SZS output end Proof
% 13.33/13.45 % Total time : 12.874000 s
%------------------------------------------------------------------------------