TSTP Solution File: SET863-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET863-2 : 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 : n023.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 14:36:03 EDT 2023
% Result : Unsatisfiable 0.46s 0.59s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 31
% Syntax : Number of formulae : 65 ( 15 unt; 17 typ; 0 def)
% Number of atoms : 125 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 140 ( 63 ~; 77 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 26 ( 10 >; 16 *; 0 +; 0 <<)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 7 con; 0-3 aty)
% Number of variables : 91 ( 0 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_23,type,
tc_set: $i > $i ).
tff(decl_24,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_25,type,
c_Main_OsubsetI__1: ( $i * $i * $i ) > $i ).
tff(decl_26,type,
c_Zorn_Ochain: ( $i * $i ) > $i ).
tff(decl_27,type,
c_Zorn_Ochain__extend__1: ( $i * $i * $i ) > $i ).
tff(decl_28,type,
c_emptyset: $i ).
tff(decl_29,type,
c_insert: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
c_union: ( $i * $i * $i ) > $i ).
tff(decl_31,type,
c_Zorn_Omaxchain: ( $i * $i ) > $i ).
tff(decl_32,type,
c_Zorn_Omaxchain__super__lemma__1: ( $i * $i * $i ) > $i ).
tff(decl_33,type,
v_c: $i ).
tff(decl_34,type,
v_S: $i ).
tff(decl_35,type,
t_a: $i ).
tff(decl_36,type,
v_x: $i ).
tff(decl_37,type,
v_y: $i ).
tff(decl_38,type,
v_xa: $i ).
cnf(cls_Zorn_Ochain__extend_0,axiom,
( c_in(c_Zorn_Ochain__extend__1(X4,X1,X3),X4,tc_set(X3))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Zorn_Omaxchain__super__lemma_1,axiom,
( c_in(X1,X6,X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X6,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_1) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_Zorn_Omaxchain__super__lemma_0,axiom,
( c_in(X1,X6,X3)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__super__lemma_0) ).
cnf(cls_conjecture_7,negated_conjecture,
( c_lessequals(X1,v_y,tc_set(t_a))
| ~ c_in(X1,v_c,tc_set(t_a)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
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_5,negated_conjecture,
c_in(v_xa,v_x,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_3,negated_conjecture,
c_in(v_x,v_S,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_6,negated_conjecture,
~ c_in(v_xa,v_y,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
cnf(cls_conjecture_4,negated_conjecture,
c_lessequals(v_y,v_x,tc_set(t_a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
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(cls_Zorn_Ochain__extend_1,axiom,
( c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X4,X1,X3),X1,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
cnf(c_0_14,axiom,
( c_in(c_Zorn_Ochain__extend__1(X4,X1,X3),X4,tc_set(X3))
| c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3))) ),
cls_Zorn_Ochain__extend_0 ).
cnf(c_0_15,negated_conjecture,
c_in(v_c,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_1 ).
cnf(c_0_16,axiom,
( c_in(X1,X6,X3)
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X6,tc_set(X3)) ),
cls_Zorn_Omaxchain__super__lemma_1 ).
cnf(c_0_17,negated_conjecture,
( c_in(c_union(c_insert(X1,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,negated_conjecture,
c_in(v_c,c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_0 ).
cnf(c_0_19,axiom,
( c_in(X1,X6,X3)
| c_in(c_Zorn_Omaxchain__super__lemma__1(X4,X6,X3),X4,tc_set(X3))
| ~ c_in(X1,X2,X3)
| ~ c_in(X4,c_Zorn_Omaxchain(X5,X3),tc_set(tc_set(X3)))
| ~ c_in(c_union(c_insert(X2,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X5,X3),tc_set(tc_set(X3))) ),
cls_Zorn_Omaxchain__super__lemma_0 ).
cnf(c_0_20,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(X2,X3,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X3,t_a),X3,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_in(X2,X1,t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18])]) ).
cnf(c_0_21,negated_conjecture,
( c_lessequals(X1,v_y,tc_set(t_a))
| ~ c_in(X1,v_c,tc_set(t_a)) ),
cls_conjecture_7 ).
cnf(c_0_22,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),v_c,tc_set(t_a))
| c_in(X3,X2,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_in(X3,X1,t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_18])]) ).
cnf(c_0_23,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_24,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(X2,v_y,t_a)
| ~ c_in(X1,v_S,tc_set(t_a))
| ~ c_in(X2,X1,t_a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]) ).
cnf(c_0_25,negated_conjecture,
c_in(v_xa,v_x,t_a),
cls_conjecture_5 ).
cnf(c_0_26,negated_conjecture,
c_in(v_x,v_S,tc_set(t_a)),
cls_conjecture_3 ).
cnf(c_0_27,negated_conjecture,
~ c_in(v_xa,v_y,t_a),
cls_conjecture_6 ).
cnf(c_0_28,negated_conjecture,
( c_in(X1,v_y,t_a)
| ~ c_in(X2,v_c,tc_set(t_a))
| ~ c_in(X1,X2,t_a) ),
inference(spm,[status(thm)],[c_0_23,c_0_21]) ).
cnf(c_0_29,negated_conjecture,
c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26])]),c_0_27]) ).
cnf(c_0_30,negated_conjecture,
c_lessequals(v_y,v_x,tc_set(t_a)),
cls_conjecture_4 ).
cnf(c_0_31,negated_conjecture,
( c_in(X1,v_y,t_a)
| ~ c_in(X1,c_Zorn_Ochain__extend__1(v_c,v_x,t_a),t_a) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_32,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_33,negated_conjecture,
( c_in(X1,v_x,t_a)
| ~ c_in(X1,v_y,t_a) ),
inference(spm,[status(thm)],[c_0_23,c_0_30]) ).
cnf(c_0_34,negated_conjecture,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X1,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X1,t_a),v_y,t_a) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_35,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_36,negated_conjecture,
( c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X1,tc_set(t_a))
| c_in(c_Main_OsubsetI__1(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),X1,t_a),v_x,t_a) ),
inference(spm,[status(thm)],[c_0_33,c_0_34]) ).
cnf(c_0_37,axiom,
( c_in(c_union(c_insert(X1,c_emptyset,tc_set(X3)),X4,tc_set(X3)),c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Zorn_Ochain(X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Zorn_Ochain__extend__1(X4,X1,X3),X1,tc_set(X3)) ),
cls_Zorn_Ochain__extend_1 ).
cnf(c_0_38,negated_conjecture,
c_lessequals(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_x,tc_set(t_a)),
inference(spm,[status(thm)],[c_0_35,c_0_36]) ).
cnf(c_0_39,negated_conjecture,
( c_in(c_union(c_insert(v_x,c_emptyset,tc_set(t_a)),v_c,tc_set(t_a)),c_Zorn_Ochain(X1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_c,c_Zorn_Ochain(X1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,X1,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_40,negated_conjecture,
( c_in(X1,X2,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),X2,tc_set(t_a))
| ~ c_in(v_c,c_Zorn_Omaxchain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_c,c_Zorn_Ochain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,X3,tc_set(t_a))
| ~ c_in(X1,v_x,t_a) ),
inference(spm,[status(thm)],[c_0_16,c_0_39]) ).
cnf(c_0_41,negated_conjecture,
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(X2,X1,t_a)
| ~ c_in(v_c,c_Zorn_Omaxchain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_c,c_Zorn_Ochain(X3,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_x,X3,tc_set(t_a))
| ~ c_in(X2,v_x,t_a) ),
inference(spm,[status(thm)],[c_0_19,c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( c_in(X1,X2,t_a)
| ~ c_lessequals(c_Zorn_Omaxchain__super__lemma__1(v_c,X2,t_a),X2,tc_set(t_a))
| ~ c_in(X1,v_x,t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_18]),c_0_15]),c_0_26])]) ).
cnf(c_0_43,negated_conjecture,
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(X2,X1,t_a)
| ~ c_in(X2,v_x,t_a) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_18]),c_0_15]),c_0_26])]) ).
cnf(c_0_44,negated_conjecture,
( c_in(X1,v_y,t_a)
| ~ c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,v_y,t_a),v_c,tc_set(t_a))
| ~ c_in(X1,v_x,t_a) ),
inference(spm,[status(thm)],[c_0_42,c_0_21]) ).
cnf(c_0_45,negated_conjecture,
( c_in(c_Zorn_Omaxchain__super__lemma__1(v_c,X1,t_a),v_c,tc_set(t_a))
| c_in(v_xa,X1,t_a) ),
inference(spm,[status(thm)],[c_0_43,c_0_25]) ).
cnf(c_0_46,negated_conjecture,
( c_in(X1,v_y,t_a)
| ~ c_in(X1,v_x,t_a) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_27]) ).
cnf(c_0_47,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_46]),c_0_25])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET863-2 : TPTP v8.1.2. Released v3.2.0.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Sat Aug 26 16:13:56 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.46/0.57 start to proof: theBenchmark
% 0.46/0.59 % Version : CSE_E---1.5
% 0.46/0.59 % Problem : theBenchmark.p
% 0.46/0.59 % Proof found
% 0.46/0.59 % SZS status Theorem for theBenchmark.p
% 0.46/0.59 % SZS output start Proof
% See solution above
% 0.46/0.59 % Total time : 0.010000 s
% 0.46/0.59 % SZS output end Proof
% 0.46/0.59 % Total time : 0.013000 s
%------------------------------------------------------------------------------