%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SET844-2 : 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 : 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 0.25s 1.61s
% Output : CNFRefutation 0.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 30
% Syntax : Number of clauses : 44 ( 17 unt; 0 nHn; 31 RR)
% Number of literals : 89 ( 42 equ; 49 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 : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 111 ( 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/sandbox/benchmark/theBenchmark.p',cls_Zorn_Oeq__succ__upper_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/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
cnf(cls_conjecture_2,negated_conjecture,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
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_Set_Osubset__refl_0,axiom,
c_lessequals(X1,X1,tc_set(X2)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
cnf(cls_conjecture_1,negated_conjecture,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
cnf(i_0_6,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,
[final] ).
cnf(i_0_7,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,
[final] ).
cnf(i_0_8,negated_conjecture,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
cls_conjecture_2,
[final] ).
cnf(i_0_9,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
cls_conjecture_0,
[final] ).
cnf(i_0_10,axiom,
c_lessequals(X1,X1,tc_set(X2)),
cls_Set_Osubset__refl_0,
[final] ).
cnf(i_0_11,negated_conjecture,
v_m = c_Zorn_Osucc(v_S,v_m,t_a),
cls_conjecture_1,
[final] ).
cnf(i_0_12,axiom,
X1 = X1 ).
cnf(i_0_13,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_14,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_15,axiom,
( X1 != X2
| c_Zorn_Osucc(X1,X3,X4) = c_Zorn_Osucc(X2,X3,X4) ) ).
cnf(i_0_16,axiom,
( X1 != X2
| c_Zorn_Osucc(X3,X1,X4) = c_Zorn_Osucc(X3,X2,X4) ) ).
cnf(i_0_17,axiom,
( X1 != X2
| c_Zorn_Osucc(X3,X4,X1) = c_Zorn_Osucc(X3,X4,X2) ) ).
cnf(i_0_18,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_19,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_20,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_21,axiom,
( X1 != X2
| ~ c_in(X1,X3,X4)
| c_in(X2,X3,X4) ) ).
cnf(i_0_22,axiom,
( X1 != X2
| ~ c_in(X3,X1,X4)
| c_in(X3,X2,X4) ) ).
cnf(i_0_23,axiom,
( X1 != X2
| ~ c_in(X3,X4,X1)
| c_in(X3,X4,X2) ) ).
cnf(i_0_12_001,axiom,
X1 = X1 ).
cnf(i_0_13_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_14_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_15_004,axiom,
( X1 != X2
| c_Zorn_Osucc(X1,X3,X4) = c_Zorn_Osucc(X2,X3,X4) ) ).
cnf(i_0_16_005,axiom,
( X1 != X2
| c_Zorn_Osucc(X3,X1,X4) = c_Zorn_Osucc(X3,X2,X4) ) ).
cnf(i_0_17_006,axiom,
( X1 != X2
| c_Zorn_Osucc(X3,X4,X1) = c_Zorn_Osucc(X3,X4,X2) ) ).
cnf(i_0_18_007,axiom,
( X1 != X2
| ~ c_lessequals(X1,X3,X4)
| c_lessequals(X2,X3,X4) ) ).
cnf(i_0_19_008,axiom,
( X1 != X2
| ~ c_lessequals(X3,X1,X4)
| c_lessequals(X3,X2,X4) ) ).
cnf(i_0_20_009,axiom,
( X1 != X2
| ~ c_lessequals(X3,X4,X1)
| c_lessequals(X3,X4,X2) ) ).
cnf(i_0_21_010,axiom,
( X1 != X2
| ~ c_in(X1,X3,X4)
| c_in(X2,X3,X4) ) ).
cnf(i_0_22_011,axiom,
( X1 != X2
| ~ c_in(X3,X1,X4)
| c_in(X3,X2,X4) ) ).
cnf(i_0_23_012,axiom,
( X1 != X2
| ~ c_in(X3,X4,X1)
| c_in(X3,X4,X2) ) ).
cnf(i_0_24,plain,
c_in(c_Union(c_Zorn_OTFin(X1,X2),tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))),
inference(scs_inference,[],[i_0_10,i_0_7]) ).
cnf(i_0_25,plain,
c_lessequals(X1,X1,tc_set(X2)),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_26,plain,
( ~ c_lessequals(X1,c_Zorn_OTFin(X2,X3),tc_set(tc_set(tc_set(X3))))
| c_in(c_Union(X1,tc_set(X3)),c_Zorn_OTFin(X2,X3),tc_set(tc_set(X3))) ),
inference(rename_variables,[],[i_0_7]) ).
cnf(i_0_27,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = v_m,
inference(scs_inference,[],[i_0_11,i_0_10,i_0_7,i_0_13]) ).
cnf(i_0_28,plain,
v_m != c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(scs_inference,[],[i_0_8,i_0_11,i_0_10,i_0_25,i_0_7,i_0_13,i_0_18]) ).
cnf(i_0_29,plain,
c_lessequals(X1,X1,tc_set(X2)),
inference(rename_variables,[],[i_0_10]) ).
cnf(i_0_30,plain,
~ c_lessequals(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Osucc(v_S,v_m,t_a),tc_set(tc_set(t_a))),
inference(scs_inference,[],[i_0_8,i_0_11,i_0_10,i_0_25,i_0_7,i_0_13,i_0_18,i_0_19]) ).
cnf(i_0_31,plain,
$false,
inference(scs_inference,[],[i_0_8,i_0_9,i_0_11,i_0_10,i_0_25,i_0_7,i_0_13,i_0_18,i_0_19,i_0_6]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET844-2 : TPTP v9.2.1. Released v3.2.0.
% 0.00/0.12 % 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
% 0.15/0.32 % Computer : n028.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % 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 02:37:31 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
%------------------------------------------------------------------------------