%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET853-2 : 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 : n020.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 05:08:48 PM UTC 2026
% Result : Unsatisfiable 1.26s 1.71s
% Output : CNFRefutation 1.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 13
% Syntax : Number of clauses : 39 ( 17 unt; 17 nHn; 35 RR)
% Number of literals : 108 ( 15 equ; 47 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 3 ( 2 avg)
% 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)
% Comments :
%------------------------------------------------------------------------------
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(rw,[status(thm)],[c_0_27,c_0_36]),c_0_37])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET853-2 : 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
% 0.16/0.33 % Computer : n020.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 02:37:50 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
%------------------------------------------------------------------------------