%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET858-2 : TPTP v9.2.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n015.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 05:08:49 PM UTC 2026
% Result : Unsatisfiable 1.27s 1.70s
% Output : CNFRefutation 1.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 11
% Syntax : Number of clauses : 35 ( 13 unt; 18 nHn; 33 RR)
% Number of literals : 99 ( 8 equ; 44 neg)
% Maximal clause size : 5 ( 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 : 63 ( 3 sgn)
% Comments :
%------------------------------------------------------------------------------
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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
cnf(cls_conjecture_1,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
cnf(cls_Set_Osubset__trans_0,axiom,
( c_lessequals(X4,X2,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X4,X1,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_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/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
cnf(cls_Zorn_OTFin__linear__lemma2_0,axiom,
( c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| X1 = X4
| ~ 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(X1,X4,tc_set(tc_set(X3))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma2_0) ).
cnf(cls_conjecture_3,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
cnf(c_0_11,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_12,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_1 ).
cnf(c_0_13,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_14,axiom,
( c_lessequals(X4,X2,tc_set(X3))
| ~ c_lessequals(X1,X2,tc_set(X3))
| ~ c_lessequals(X4,X1,tc_set(X3)) ),
cls_Set_Osubset__trans_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(c_Zorn_Osucc(v_S,X1,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,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_11,c_0_12]) ).
cnf(c_0_17,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_18,negated_conjecture,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
cls_conjecture_2 ).
cnf(c_0_19,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_20,axiom,
( c_lessequals(c_Zorn_Osucc(X2,X1,X3),X4,tc_set(tc_set(X3)))
| X1 = X4
| ~ 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(X1,X4,tc_set(tc_set(X3))) ),
cls_Zorn_OTFin__linear__lemma2_0 ).
cnf(c_0_21,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(v_n,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_13,c_0_12]) ).
cnf(c_0_22,plain,
( c_lessequals(X1,X2,tc_set(tc_set(X3)))
| ~ c_lessequals(c_Zorn_Osucc(X4,X1,X3),X2,tc_set(tc_set(X3))) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_23,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) != v_m ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_24,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
cls_conjecture_3 ).
cnf(c_0_25,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_n,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_n,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_19,c_0_12]) ).
cnf(c_0_26,negated_conjecture,
( X1 = v_m
| c_lessequals(c_Zorn_Osucc(v_S,X1,t_a),v_m,tc_set(tc_set(t_a)))
| ~ 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_20,c_0_17]) ).
cnf(c_0_27,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_17]),c_0_18]) ).
cnf(c_0_28,negated_conjecture,
c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) != v_m,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_29,negated_conjecture,
( c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_17]),c_0_18]) ).
cnf(c_0_30,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_31,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28]),c_0_29]) ).
cnf(c_0_32,negated_conjecture,
( c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X1,tc_set(tc_set(t_a)))
| 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(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_17])]) ).
cnf(c_0_33,negated_conjecture,
c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_12]),c_0_18]) ).
cnf(c_0_34,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_33]),c_0_24]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET858-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.13/0.31 % Computer : n015.cluster.edu
% 0.13/0.31 % Model : x86_64 x86_64
% 0.13/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.31 % Memory : 8042.1875MB
% 0.13/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.31 % CPULimit : 300
% 0.13/0.31 % WCLimit : 300
% 0.13/0.31 % DateTime : Tue May 5 02:38:32 EDT 2026
% 0.13/0.31 % CPUTime :
% 0.13/0.32 % start to proof: theBenchmark
% 1.27/1.70 % Version : CSE_E---1.7
% 1.27/1.70 % Problem : theBenchmark.p
% 1.27/1.70 % SZS status Unsatisfiable for theBenchmark.p
% 1.27/1.70 % SZS output start CNFRefutation
% See solution above
% 1.27/1.70 % Total time : 1.370s
%------------------------------------------------------------------------------