TSTP Solution File: SET853-2 by CSE_E---1.5
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%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : SET853-2 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 14:35:58 EDT 2023
% Result : Unsatisfiable 0.13s 0.46s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 23
% Syntax : Number of formulae : 49 ( 17 unt; 10 typ; 0 def)
% Number of atoms : 108 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 116 ( 47 ~; 69 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 15 ( 6 >; 9 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 58 ( 4 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
v_x: $i ).
tff(decl_23,type,
v_S: $i ).
tff(decl_24,type,
t_a: $i ).
tff(decl_25,type,
c_Zorn_OTFin: ( $i * $i ) > $i ).
tff(decl_26,type,
tc_set: $i > $i ).
tff(decl_27,type,
c_in: ( $i * $i * $i ) > $o ).
tff(decl_28,type,
v_xa: $i ).
tff(decl_29,type,
c_Zorn_Osucc: ( $i * $i * $i ) > $i ).
tff(decl_30,type,
c_lessequals: ( $i * $i * $i ) > $o ).
tff(decl_31,type,
c_Zorn_OTFin__linear__lemma1__1: ( $i * $i * $i ) > $i ).
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/sandbox2/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),v_x,tc_set(tc_set(t_a)))
| X1 = v_x
| ~ 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))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
cnf(cls_conjecture_2,negated_conjecture,
c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_3,negated_conjecture,
v_xa != c_Zorn_Osucc(v_S,v_x,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
cnf(cls_conjecture_4,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
cnf(cls_Zorn_Osucc__trans_0,axiom,
( c_lessequals(X1,c_Zorn_Osucc(X4,X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(X1,X2,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
cnf(cls_Set_Osubset__refl_0,axiom,
c_lessequals(X1,X1,tc_set(X2)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
cnf(c_0_13,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_14,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_x,tc_set(tc_set(t_a)))
| X1 = v_x
| ~ 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))) ),
cls_conjecture_5 ).
cnf(c_0_15,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_0 ).
cnf(c_0_16,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_17,negated_conjecture,
c_in(v_xa,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_1 ).
cnf(c_0_18,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_19,negated_conjecture,
c_lessequals(v_xa,c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
cls_conjecture_2 ).
cnf(c_0_20,negated_conjecture,
v_xa != c_Zorn_Osucc(v_S,v_x,t_a),
cls_conjecture_3 ).
cnf(c_0_21,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_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| ~ 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_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_15])]) ).
cnf(c_0_22,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,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(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_23,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_xa,tc_set(tc_set(t_a))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20]) ).
cnf(c_0_24,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_25,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(v_xa,v_x,tc_set(tc_set(t_a)))
| c_lessequals(X1,v_x,tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a),v_x,tc_set(tc_set(t_a)))
| ~ c_in(X1,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_15])]),c_0_23]) ).
cnf(c_0_26,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,X1,t_a),X1,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,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_17]) ).
cnf(c_0_27,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
cls_conjecture_4 ).
cnf(c_0_28,axiom,
( c_lessequals(X1,c_Zorn_Osucc(X4,X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(X1,X2,tc_set(tc_set(X3))) ),
cls_Zorn_Osucc__trans_0 ).
cnf(c_0_29,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_30,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(v_xa,v_x,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))) ),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_15])]),c_0_23]) ).
cnf(c_0_31,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_xa,t_a),v_x,tc_set(tc_set(t_a))),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_xa,tc_set(tc_set(t_a)))
| c_lessequals(v_xa,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_29,c_0_17]) ).
cnf(c_0_33,negated_conjecture,
( c_Zorn_OTFin__linear__lemma1__1(v_S,v_x,t_a) = v_x
| c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_17]),c_0_23]) ).
cnf(c_0_34,negated_conjecture,
( v_xa = v_x
| ~ c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_14]),c_0_17])]) ).
cnf(c_0_35,negated_conjecture,
c_lessequals(v_xa,v_x,tc_set(tc_set(t_a))),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_15])]),c_0_23]) ).
cnf(c_0_36,negated_conjecture,
v_xa = v_x,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_34,c_0_35])]) ).
cnf(c_0_37,axiom,
c_lessequals(X1,X1,tc_set(X2)),
cls_Set_Osubset__refl_0 ).
cnf(c_0_38,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_36]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : SET853-2 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.09 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.27 % Computer : n032.cluster.edu
% 0.10/0.27 % Model : x86_64 x86_64
% 0.10/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.27 % Memory : 8042.1875MB
% 0.10/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.27 % CPULimit : 300
% 0.10/0.27 % WCLimit : 300
% 0.10/0.27 % DateTime : Sat Aug 26 08:40:44 EDT 2023
% 0.10/0.28 % CPUTime :
% 0.13/0.45 start to proof: theBenchmark
% 0.13/0.46 % Version : CSE_E---1.5
% 0.13/0.46 % Problem : theBenchmark.p
% 0.13/0.46 % Proof found
% 0.13/0.46 % SZS status Theorem for theBenchmark.p
% 0.13/0.46 % SZS output start Proof
% See solution above
% 0.13/0.46 % Total time : 0.005000 s
% 0.13/0.46 % SZS output end Proof
% 0.13/0.46 % Total time : 0.007000 s
%------------------------------------------------------------------------------