%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET843-2 : 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 : n028.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 05:08:42 PM UTC 2026
% Result : Unsatisfiable 1.25s 1.71s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 10
% Syntax : Number of clauses : 35 ( 11 unt; 4 nHn; 30 RR)
% Number of literals : 74 ( 27 equ; 39 neg)
% Maximal clause size : 4 ( 2 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 62 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_Zorn_Oeq__succ__upper_0,axiom,
( c_lessequals(X4,X1,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)))
| X1 != c_Zorn_Osucc(X2,X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Oeq__succ__upper_0) ).
cnf(cls_conjecture_0,negated_conjecture,
c_in(v_m,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_Set_OUnion__upper_0,axiom,
( c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| ~ c_in(X1,X2,tc_set(X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).
cnf(cls_conjecture_2,negated_conjecture,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
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_Zorn_OAbrial__axiom1_0,axiom,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
cnf(cls_Zorn_OTFin_OsuccI_0,axiom,
( c_in(c_Zorn_Osucc(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin_OsuccI_0) ).
cnf(cls_Zorn_OTFin__UnionI_0,axiom,
( c_in(c_Union(X1,tc_set(X3)),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(tc_set(X3)))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
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(cls_conjecture_1,negated_conjecture,
( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m != c_Zorn_Osucc(v_S,v_m,t_a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(c_0_10,axiom,
( c_lessequals(X4,X1,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)))
| X1 != c_Zorn_Osucc(X2,X1,X3) ),
cls_Zorn_Oeq__succ__upper_0 ).
cnf(c_0_11,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_0 ).
cnf(c_0_12,axiom,
( c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| ~ c_in(X1,X2,tc_set(X3)) ),
cls_Set_OUnion__upper_0 ).
cnf(c_0_13,negated_conjecture,
( v_m = c_Zorn_Osucc(v_S,v_m,t_a)
| v_m = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) ),
cls_conjecture_2 ).
cnf(c_0_14,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_15,axiom,
c_lessequals(X1,c_Zorn_Osucc(X2,X1,X3),tc_set(tc_set(X3))),
cls_Zorn_OAbrial__axiom1_0 ).
cnf(c_0_16,negated_conjecture,
( c_lessequals(v_m,X1,tc_set(tc_set(t_a)))
| c_Zorn_Osucc(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_10,c_0_11]) ).
cnf(c_0_17,axiom,
( c_in(c_Zorn_Osucc(X2,X1,X3),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_in(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
cls_Zorn_OTFin_OsuccI_0 ).
cnf(c_0_18,negated_conjecture,
( c_Zorn_Osucc(v_S,v_m,t_a) = v_m
| c_lessequals(X1,v_m,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_12,c_0_13]) ).
cnf(c_0_19,plain,
( c_Zorn_Osucc(X1,X2,X3) = X2
| ~ c_lessequals(c_Zorn_Osucc(X1,X2,X3),X2,tc_set(tc_set(X3))) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_20,negated_conjecture,
( c_lessequals(v_m,c_Zorn_Osucc(v_S,X1,t_a),tc_set(tc_set(t_a)))
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,X1,t_a),t_a) != c_Zorn_Osucc(v_S,X1,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_21,negated_conjecture,
( c_Zorn_Osucc(v_S,v_m,t_a) = v_m
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_m,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_18,c_0_17]) ).
cnf(c_0_22,plain,
( c_Zorn_Osucc(X1,c_Union(X2,tc_set(X3)),X3) = c_Union(X2,tc_set(X3))
| ~ c_in(c_Zorn_Osucc(X1,c_Union(X2,tc_set(X3)),X3),X2,tc_set(tc_set(X3))) ),
inference(spm,[status(thm)],[c_0_19,c_0_12]) ).
cnf(c_0_23,negated_conjecture,
( c_Zorn_Osucc(v_S,X1,t_a) = v_m
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,X1,t_a),t_a) != c_Zorn_Osucc(v_S,X1,t_a)
| ~ c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_m,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_14,c_0_20]) ).
cnf(c_0_24,plain,
( c_lessequals(c_Zorn_Osucc(X1,X2,X3),X4,tc_set(tc_set(X3)))
| c_Zorn_Osucc(X1,X4,X3) != X4
| ~ c_in(X4,c_Zorn_OTFin(X1,X3),tc_set(tc_set(X3)))
| ~ c_in(X2,c_Zorn_OTFin(X1,X3),tc_set(tc_set(X3))) ),
inference(spm,[status(thm)],[c_0_10,c_0_17]) ).
cnf(c_0_25,negated_conjecture,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_11]),c_0_19]) ).
cnf(c_0_26,plain,
( c_Zorn_Osucc(X1,c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),X2) = c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2))
| ~ c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(spm,[status(thm)],[c_0_22,c_0_17]) ).
cnf(c_0_27,axiom,
( c_in(c_Union(X1,tc_set(X3)),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3)))
| ~ c_lessequals(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(tc_set(X3)))) ),
cls_Zorn_OTFin__UnionI_0 ).
cnf(c_0_28,axiom,
c_lessequals(X1,X1,tc_set(X2)),
cls_Set_Osubset__refl_0 ).
cnf(c_0_29,negated_conjecture,
( v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a))
| v_m != c_Zorn_Osucc(v_S,v_m,t_a) ),
cls_conjecture_1 ).
cnf(c_0_30,negated_conjecture,
( c_Zorn_Osucc(v_S,X1,t_a) = v_m
| c_Zorn_Osucc(v_S,c_Zorn_Osucc(v_S,X1,t_a),t_a) != c_Zorn_Osucc(v_S,X1,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(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_25]),c_0_11])]) ).
cnf(c_0_31,plain,
c_Zorn_Osucc(X1,c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),X2) = c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]) ).
cnf(c_0_32,negated_conjecture,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != v_m,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_29,c_0_25])]) ).
cnf(c_0_33,negated_conjecture,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),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_30,c_0_31]),c_0_31])]),c_0_32]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_27]),c_0_28])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET843-2 : 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
% 0.14/0.32 % Computer : n028.cluster.edu
% 0.14/0.32 % Model : x86_64 x86_64
% 0.14/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.32 % Memory : 8042.1875MB
% 0.14/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 5 02:37:31 EDT 2026
% 0.14/0.33 % CPUTime :
% 0.14/0.34 % start to proof: theBenchmark
% 1.25/1.71 % Version : CSE_E---1.7
% 1.25/1.71 % Problem : theBenchmark.p
% 1.25/1.71 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.71 % SZS output start CNFRefutation
% See solution above
% 1.25/1.71 % Total time : 1.372s
%------------------------------------------------------------------------------