%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET863-2 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n009.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 : Tue May 5 05:08:51 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 14
% Syntax : Number of clauses : 46 ( 16 unt; 14 nHn; 38 RR)
% Number of literals : 108 ( 0 equ; 49 neg)
% Maximal clause size : 5 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% 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 : 80 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_3,negated_conjecture,
c_in(v_x,v_S,tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
cnf(cls_conjecture_5,negated_conjecture,
c_in(v_xa,v_x,t_a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
cnf(cls_conjecture_6,negated_conjecture,
~ c_in(v_xa,v_y,t_a),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_0) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Ochain__extend_1) ).
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/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetI_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,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_17,negated_conjecture,
c_in(v_x,v_S,tc_set(t_a)),
cls_conjecture_3 ).
cnf(c_0_18,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_19,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(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_16,c_0_17]) ).
cnf(c_0_20,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_21,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_22,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| 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(spm,[status(thm)],[c_0_18,c_0_19]),c_0_20])]) ).
cnf(c_0_23,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_24,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| 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(spm,[status(thm)],[c_0_21,c_0_19]),c_0_20])]) ).
cnf(c_0_25,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_26,negated_conjecture,
( c_in(c_Zorn_Ochain__extend__1(v_c,v_x,t_a),v_c,tc_set(t_a))
| c_in(X1,v_y,t_a)
| ~ c_in(X1,v_x,t_a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_27,negated_conjecture,
c_in(v_xa,v_x,t_a),
cls_conjecture_5 ).
cnf(c_0_28,negated_conjecture,
~ c_in(v_xa,v_y,t_a),
cls_conjecture_6 ).
cnf(c_0_29,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_25,c_0_23]) ).
cnf(c_0_30,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(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]) ).
cnf(c_0_31,negated_conjecture,
c_lessequals(v_y,v_x,tc_set(t_a)),
cls_conjecture_4 ).
cnf(c_0_32,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_29,c_0_30]) ).
cnf(c_0_33,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_34,negated_conjecture,
( c_in(X1,v_x,t_a)
| ~ c_in(X1,v_y,t_a) ),
inference(spm,[status(thm)],[c_0_25,c_0_31]) ).
cnf(c_0_35,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_32,c_0_33]) ).
cnf(c_0_36,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_37,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_38,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_34,c_0_35]) ).
cnf(c_0_39,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_lessequals(c_Zorn_Ochain__extend__1(v_c,X1,t_a),X1,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
inference(spm,[status(thm)],[c_0_36,c_0_15]) ).
cnf(c_0_40,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_37,c_0_38]) ).
cnf(c_0_41,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(v_S,t_a),tc_set(tc_set(t_a))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_17])]) ).
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(spm,[status(thm)],[c_0_18,c_0_41]),c_0_20])]) ).
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(spm,[status(thm)],[c_0_21,c_0_41]),c_0_20])]) ).
cnf(c_0_44,negated_conjecture,
( c_in(X1,v_y,t_a)
| ~ c_in(X1,v_x,t_a) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_23]),c_0_43]) ).
cnf(c_0_45,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_44]),c_0_27])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET863-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.32 % Computer : n009.cluster.edu
% 0.16/0.32 % Model : x86_64 x86_64
% 0.16/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.32 % Memory : 8042.1875MB
% 0.16/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.32 % CPULimit : 300
% 0.16/0.32 % WCLimit : 300
% 0.16/0.32 % DateTime : Tue May 5 02:37:56 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.26/1.71 % Version : CSE_E---1.7
% 1.26/1.71 % Problem : theBenchmark.p
% 1.26/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.26/1.71 % SZS output start CNFRefutation
% See solution above
% 1.26/1.71 % Total time : 1.370s
%------------------------------------------------------------------------------