%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET865-2 : 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 : n026.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 05:08:52 PM UTC 2026
% Result : Unsatisfiable 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 32
% Syntax : Number of clauses : 52 ( 13 unt; 0 nHn; 40 RR)
% Number of literals : 112 ( 42 equ; 64 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 120 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Zorn_Omaxchain__Zorn_0,axiom,
( c_Union(X4,X3) = X1
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Zorn_Omaxchain(X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Union(X4,X3),X1,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__Zorn_0) ).
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_0,negated_conjecture,
( c_in(c_Union(X1,t_a),v_S,tc_set(t_a))
| ~ c_in(X1,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_2,negated_conjecture,
( c_lessequals(X1,v_x(X1),tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
cnf(cls_conjecture_1,negated_conjecture,
( c_in(v_x(X1),v_S,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(cls_Zorn_Omaxchain__subset__chain_0,axiom,
c_lessequals(c_Zorn_Omaxchain(X1,X2),c_Zorn_Ochain(X1,X2),tc_set(tc_set(tc_set(X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__subset__chain_0) ).
cnf(cls_Zorn_OHausdorff_0,axiom,
c_in(c_Zorn_OHausdorff__1(X1,X2),c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OHausdorff_0) ).
cnf(cls_conjecture_3,negated_conjecture,
( X1 != v_x(X1)
| ~ c_in(X1,v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
cnf(i_0_8,axiom,
( c_Union(X4,X3) = X1
| ~ c_in(X1,X2,tc_set(X3))
| ~ c_in(X4,c_Zorn_Omaxchain(X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(c_Union(X4,X3),X1,tc_set(X3)) ),
cls_Zorn_Omaxchain__Zorn_0,
[final] ).
cnf(i_0_9,axiom,
( c_in(X1,X4,X3)
| ~ c_in(X1,X2,X3)
| ~ c_lessequals(X2,X4,tc_set(X3)) ),
cls_Set_OsubsetD_0,
[final] ).
cnf(i_0_10,negated_conjecture,
( c_in(c_Union(X1,t_a),v_S,tc_set(t_a))
| ~ c_in(X1,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
cls_conjecture_0,
[final] ).
cnf(i_0_11,negated_conjecture,
( c_lessequals(X1,v_x(X1),tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
cls_conjecture_2,
[final] ).
cnf(i_0_12,negated_conjecture,
( c_in(v_x(X1),v_S,tc_set(t_a))
| ~ c_in(X1,v_S,tc_set(t_a)) ),
cls_conjecture_1,
[final] ).
cnf(i_0_13,axiom,
c_lessequals(c_Zorn_Omaxchain(X1,X2),c_Zorn_Ochain(X1,X2),tc_set(tc_set(tc_set(X2)))),
cls_Zorn_Omaxchain__subset__chain_0,
[final] ).
cnf(i_0_14,axiom,
c_in(c_Zorn_OHausdorff__1(X1,X2),c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2))),
cls_Zorn_OHausdorff_0,
[final] ).
cnf(i_0_15,negated_conjecture,
( X1 != v_x(X1)
| ~ c_in(X1,v_S,tc_set(t_a)) ),
cls_conjecture_3,
[final] ).
cnf(i_0_16,axiom,
X1 = X1 ).
cnf(i_0_17,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_18,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_19,axiom,
( X1 != X2
| c_Union(X1,X3) = c_Union(X2,X3) ) ).
cnf(i_0_20,axiom,
( X1 != X2
| c_Union(X3,X1) = c_Union(X3,X2) ) ).
cnf(i_0_21,axiom,
( X1 != X2
| v_x(X1) = v_x(X2) ) ).
cnf(i_0_22,axiom,
( X1 != X2
| ~ c_in(X1,X3,X4)
| c_in(X2,X3,X4) ) ).
cnf(i_0_23,axiom,
( X1 != X2
| ~ c_in(X3,X1,X4)
| c_in(X3,X2,X4) ) ).
cnf(i_0_24,axiom,
( X1 != X2
| ~ c_in(X3,X4,X1)
| c_in(X3,X4,X2) ) ).
cnf(i_0_25,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_26,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_27,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_16_001,axiom,
X1 = X1 ).
cnf(i_0_17_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_18_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_19_004,axiom,
( X1 != X2
| c_Union(X1,X3) = c_Union(X2,X3) ) ).
cnf(i_0_20_005,axiom,
( X1 != X2
| c_Union(X3,X1) = c_Union(X3,X2) ) ).
cnf(i_0_21_006,axiom,
( X1 != X2
| v_x(X1) = v_x(X2) ) ).
cnf(i_0_22_007,axiom,
( X1 != X2
| ~ c_in(X1,X3,X4)
| c_in(X2,X3,X4) ) ).
cnf(i_0_23_008,axiom,
( X1 != X2
| ~ c_in(X3,X1,X4)
| c_in(X3,X2,X4) ) ).
cnf(i_0_24_009,axiom,
( X1 != X2
| ~ c_in(X3,X4,X1)
| c_in(X3,X4,X2) ) ).
cnf(i_0_25_010,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_26_011,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_27_012,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_28,plain,
c_in(c_Zorn_OHausdorff__1(X1,X2),c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2))),
inference(scs_inference,[],[i_0_13,i_0_14,i_0_9]) ).
cnf(i_0_29,plain,
c_lessequals(c_Zorn_Omaxchain(X1,X2),c_Zorn_Ochain(X1,X2),tc_set(tc_set(tc_set(X2)))),
inference(rename_variables,[],[i_0_13]) ).
cnf(i_0_30,plain,
( ~ c_lessequals(X1,X2,tc_set(X3))
| c_in(X4,X2,X3)
| ~ c_in(X4,X1,X3) ),
inference(rename_variables,[],[i_0_9]) ).
cnf(i_0_31,plain,
c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,tc_set(t_a)),
inference(scs_inference,[],[i_0_13,i_0_14,i_0_9,i_0_10]) ).
cnf(i_0_32,plain,
( ~ c_in(X1,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(X1,t_a),v_S,tc_set(t_a)) ),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_33,plain,
c_lessequals(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),tc_set(t_a)),
inference(scs_inference,[],[i_0_13,i_0_14,i_0_9,i_0_10,i_0_11]) ).
cnf(i_0_34,plain,
( ~ c_in(X1,v_S,tc_set(t_a))
| c_lessequals(X1,v_x(X1),tc_set(t_a)) ),
inference(rename_variables,[],[i_0_11]) ).
cnf(i_0_35,plain,
c_in(v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),v_S,tc_set(t_a)),
inference(scs_inference,[],[i_0_13,i_0_14,i_0_9,i_0_10,i_0_11,i_0_12]) ).
cnf(i_0_36,plain,
( ~ c_in(X1,v_S,tc_set(t_a))
| c_in(v_x(X1),v_S,tc_set(t_a)) ),
inference(rename_variables,[],[i_0_12]) ).
cnf(i_0_37,plain,
c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a) != v_x(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a)),
inference(scs_inference,[],[i_0_13,i_0_14,i_0_9,i_0_10,i_0_11,i_0_12,i_0_15]) ).
cnf(i_0_38,plain,
( ~ c_in(X1,v_S,tc_set(t_a))
| X1 != v_x(X1) ),
inference(rename_variables,[],[i_0_15]) ).
cnf(i_0_39,plain,
$false,
inference(scs_inference,[],[i_0_13,i_0_14,i_0_9,i_0_10,i_0_11,i_0_12,i_0_15,i_0_8]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET865-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.15/0.33 % Computer : n026.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue May 5 02:38:23 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 0.25/1.61 % Version : CSE_E---1.7
% 0.25/1.61 % Problem : theBenchmark.p
% 0.25/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.25/1.61 % SZS output start CNFRefutation
% See solution above
% 0.25/1.64 % Total time : 1.269s
%------------------------------------------------------------------------------