%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:48:49 PM UTC 2026
% Result : Unsatisfiable 1.48s 0.96s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 11
% Syntax : Number of formulae : 44 ( 15 unt; 0 def)
% Number of atoms : 151 ( 10 equ)
% Maximal formula atoms : 5 ( 3 avg)
% Number of connectives : 187 ( 80 ~; 107 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-3 aty)
% Number of variables : 93 ( 0 sgn 93 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,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) ).
fof(f2,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) ).
fof(f3,negated_conjecture,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f4,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X3,X1,tc_set(X2))
| ~ c_lessequals(X3,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__trans_0) ).
fof(f6,axiom,
! [X2,X0,X1] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OAbrial__axiom1_0) ).
fof(f7,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_1) ).
fof(f9,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2) != X0
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_2) ).
fof(f10,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_lessequals(X3,X0,tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Osucc(X1,c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X2),X0,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma1_3) ).
fof(f11,axiom,
! [X2,X3,X0,X1] :
( X0 = X3
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| ~ c_lessequals(X0,X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__linear__lemma2_0) ).
tcf(c_60,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f1]) ).
tcf(c_61,negated_conjecture,
c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f2]) ).
tcf(c_62,negated_conjecture,
~ c_lessequals(v_n,v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f3]) ).
tcf(c_63,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f4]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X1,tc_set(X2))
| ~ c_lessequals(X3,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[],[f6]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X1,X0,X2),X0,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X1,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ( c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X1,tc_set(tc_set(X2)))
| c_lessequals(c_Zorn_Osucc(X0,X1,X2),X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_in(X1,c_Zorn_OTFin(X0,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(c_Zorn_Osucc(X0,c_Zorn_OTFin__linear__lemma1__1(X0,X1,X2),X2),X1,tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f10]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(c_Zorn_Osucc(X1,X0,X2),X3,tc_set(tc_set(X2)))
| ( X0 = X3 )
| ~ c_lessequals(X0,X3,tc_set(tc_set(X2)))
| ~ c_in(X3,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_151,plain,
! [X0_iProver_c_lessequals_2: iProver_c_lessequals_2,X0_iProver_c_in_3: iProver_c_in_3,X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1,X1_iProver_c_lessequals_2: iProver_c_lessequals_2] :
( c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,X0_iProver_c_in_3),X1_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3)))
| ( X0_iProver_c_lessequals_2 = X1_iProver_c_lessequals_2 )
| ~ c_lessequals(X0_iProver_c_lessequals_2,X1_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3)))
| ~ c_in(X1_iProver_c_lessequals_2,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3)))
| ~ c_in(X0_iProver_c_lessequals_2,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3))) ),
inference(subtyping,[status(esa)],[c_70]) ).
tcf(c_152,plain,
! [X0_iProver_c_lessequals_2: iProver_c_lessequals_2,X0_iProver_c_in_3: iProver_c_in_3,X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1,X1_iProver_c_lessequals_2: iProver_c_lessequals_2] :
( c_lessequals(X1_iProver_c_lessequals_2,X0_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3)))
| c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,X0_iProver_c_in_3),X1_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3)))
| ~ c_in(X1_iProver_c_lessequals_2,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3)))
| ~ c_in(X0_iProver_c_lessequals_2,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3)))
| ~ c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,X0_iProver_c_in_3),X0_iProver_c_in_3),X0_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3))) ),
inference(subtyping,[status(esa)],[c_69]) ).
tcf(c_153,plain,
! [X0_iProver_c_lessequals_2: iProver_c_lessequals_2,X0_iProver_c_in_3: iProver_c_in_3,X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1,X1_iProver_c_lessequals_2: iProver_c_lessequals_2] :
( c_lessequals(X1_iProver_c_lessequals_2,X0_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3)))
| c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,X0_iProver_c_in_3),X1_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3)))
| ~ c_in(X1_iProver_c_lessequals_2,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3)))
| ~ c_in(X0_iProver_c_lessequals_2,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3)))
| ( c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,X0_iProver_c_in_3) != X0_iProver_c_lessequals_2 ) ),
inference(subtyping,[status(esa)],[c_68]) ).
tcf(c_154,plain,
! [X0_iProver_c_lessequals_2: iProver_c_lessequals_2,X0_iProver_c_in_3: iProver_c_in_3,X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1,X1_iProver_c_lessequals_2: iProver_c_lessequals_2] :
( c_lessequals(X0_iProver_c_lessequals_2,X1_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,X1_iProver_c_lessequals_2,X0_iProver_c_in_3),X1_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3)))
| c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,X1_iProver_c_lessequals_2,X0_iProver_c_in_3),X0_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3)))
| ~ c_in(X1_iProver_c_lessequals_2,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3)))
| ~ c_in(X0_iProver_c_lessequals_2,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3))) ),
inference(subtyping,[status(esa)],[c_67]) ).
tcf(c_155,plain,
! [X0_iProver_c_lessequals_2: iProver_c_lessequals_2,X0_iProver_c_in_3: iProver_c_in_3,X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1,X1_iProver_c_lessequals_2: iProver_c_lessequals_2] :
( c_lessequals(X0_iProver_c_lessequals_2,X1_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3)))
| c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,X1_iProver_c_lessequals_2,X0_iProver_c_in_3),X0_iProver_c_lessequals_2,tc_set(tc_set(X0_iProver_c_in_3)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,X1_iProver_c_lessequals_2,X0_iProver_c_in_3),c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3)))
| ~ c_in(X1_iProver_c_lessequals_2,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3)))
| ~ c_in(X0_iProver_c_lessequals_2,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3))) ),
inference(subtyping,[status(esa)],[c_66]) ).
tcf(c_156,plain,
! [X0_iProver_c_lessequals_2: iProver_c_lessequals_2,X0_iProver_c_in_3: iProver_c_in_3,X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1] : c_lessequals(X0_iProver_c_lessequals_2,c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,X0_iProver_c_in_3),tc_set(tc_set(X0_iProver_c_in_3))),
inference(subtyping,[status(esa)],[c_65]) ).
tcf(c_157,plain,
! [X0_iProver_c_lessequals_2: iProver_c_lessequals_2,X0_iProver_c_in_3: iProver_c_in_3,X1_iProver_c_lessequals_2: iProver_c_lessequals_2,X2_iProver_c_lessequals_2: iProver_c_lessequals_2] :
( c_lessequals(X2_iProver_c_lessequals_2,X1_iProver_c_lessequals_2,tc_set(X0_iProver_c_in_3))
| ~ c_lessequals(X2_iProver_c_lessequals_2,X0_iProver_c_lessequals_2,tc_set(X0_iProver_c_in_3))
| ~ c_lessequals(X0_iProver_c_lessequals_2,X1_iProver_c_lessequals_2,tc_set(X0_iProver_c_in_3)) ),
inference(subtyping,[status(esa)],[c_64]) ).
tcf(c_158,negated_conjecture,
~ c_lessequals(v_m,v_n,tc_set(tc_set(t_a))),
inference(subtyping,[status(esa)],[c_63]) ).
tcf(c_374,plain,
! [X0_iProver_c_lessequals_2: iProver_c_lessequals_2] :
( ~ c_lessequals(v_m,X0_iProver_c_lessequals_2,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0_iProver_c_lessequals_2,v_n,tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_157,c_158]) ).
tcf(c_385,plain,
! [X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1] : ~ c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,v_m,t_a),v_n,tc_set(tc_set(t_a))),
inference(resolution,[status(thm)],[c_374,c_156]) ).
tcf(c_386,plain,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_n,tc_set(tc_set(t_a))),
inference(instantiation,[status(thm)],[c_385]) ).
tcf(c_414,plain,
! [X0_iProver_c_lessequals_2: iProver_c_lessequals_2,X0_iProver_c_in_3: iProver_c_in_3,X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1,X1_iProver_c_in_3: iProver_c_in_3,X1_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1] :
( c_lessequals(c_Zorn_Osucc(X1_iProver_c_Zorn_Osucc_1,c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,X0_iProver_c_in_3),X1_iProver_c_in_3),X0_iProver_c_lessequals_2,tc_set(tc_set(X1_iProver_c_in_3)))
| ( c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,X0_iProver_c_in_3) = X0_iProver_c_lessequals_2 )
| ~ c_in(X0_iProver_c_lessequals_2,c_Zorn_OTFin(X1_iProver_c_Zorn_Osucc_1,X1_iProver_c_in_3),tc_set(tc_set(X1_iProver_c_in_3)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,X0_iProver_c_in_3),X0_iProver_c_lessequals_2,tc_set(tc_set(X1_iProver_c_in_3)))
| ~ c_in(c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,X0_iProver_c_in_3),c_Zorn_OTFin(X1_iProver_c_Zorn_Osucc_1,X1_iProver_c_in_3),tc_set(tc_set(X1_iProver_c_in_3))) ),
inference(instantiation,[status(thm)],[c_151]) ).
tcf(c_415,plain,
( 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_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) = v_m )
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a),v_m,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(instantiation,[status(thm)],[c_414]) ).
tcf(c_416,plain,
! [X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1] :
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,v_m,t_a),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_154]) ).
tcf(c_417,plain,
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| 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)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_416]) ).
tcf(c_444,plain,
! [X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1] :
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| c_in(c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,v_m,t_a),c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_155]) ).
tcf(c_445,plain,
( c_lessequals(v_n,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)))
| 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)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_444]) ).
tcf(c_463,plain,
! [X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1] :
( c_lessequals(v_n,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,v_m,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,v_m,t_a),t_a),v_m,tc_set(tc_set(t_a))) ),
inference(instantiation,[status(thm)],[c_152]) ).
tcf(c_464,plain,
( c_lessequals(v_n,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)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ 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))) ),
inference(instantiation,[status(thm)],[c_463]) ).
tcf(c_680,plain,
! [X0_iProver_c_lessequals_2: iProver_c_lessequals_2,X0_iProver_c_Zorn_Osucc_1: iProver_c_Zorn_Osucc_1] :
( c_lessequals(v_n,X0_iProver_c_lessequals_2,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,t_a),v_n,tc_set(tc_set(t_a)))
| ~ c_in(v_n,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0_iProver_c_lessequals_2,c_Zorn_OTFin(X0_iProver_c_Zorn_Osucc_1,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(X0_iProver_c_Zorn_Osucc_1,X0_iProver_c_lessequals_2,t_a) != X0_iProver_c_lessequals_2 ) ),
inference(instantiation,[status(thm)],[c_153]) ).
tcf(c_681,plain,
( c_lessequals(v_n,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)))
| ~ c_in(v_n,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ( c_Zorn_OTFin__linear__lemma1__1(v_S,v_m,t_a) != v_m ) ),
inference(instantiation,[status(thm)],[c_680]) ).
tcf(c_682,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_681,c_464,c_445,c_417,c_415,c_386,c_60,c_61,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET858-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Thu Sep 24 12:15:40 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.03/0.32 Running first-order theorem proving
% 0.03/0.32 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.32
% 0.03/0.32 % ======== iProver multi-core TPTP/SMT =========
% 0.03/0.32
% 0.03/0.32 % Detected problem language: tptp
% 0.07/0.33 % Proving...
% 1.48/0.96 % SZS status Started for theBenchmark.p
% 1.48/0.96 % SZS status Unsatisfiable for theBenchmark.p
% 1.48/0.96
% 1.48/0.96 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.48/0.96
% 1.48/0.96 % ------ iProver source info
% 1.48/0.96
% 1.48/0.96 % git: date: 2026-07-19 20:42:38 +0200
% 1.48/0.96 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.48/0.96 % git: non_committed_changes: false
% 1.48/0.96
% 1.48/0.96 % ------ Parsing...% successful
% 1.48/0.96
% 1.48/0.96
% 1.48/0.96 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.48/0.96
% 1.48/0.96 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.48/0.96
% 1.48/0.96 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.48/0.96
% 1.48/0.96 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.48/0.96 % ------ Proving...
% 1.48/0.96 % ------ Problem Properties
% 1.48/0.96
% 1.48/0.96 %
% 1.48/0.96 % clauses 11
% 1.48/0.96 % conjectures 4
% 1.48/0.96 % EPR 0
% 1.48/0.96 % Horn 6
% 1.48/0.96 % unary 5
% 1.48/0.96 % binary 0
% 1.48/0.96 % lits 33
% 1.48/0.96 % lits eq 2
% 1.48/0.96 % fd_pure 0
% 1.48/0.96 % fd_pseudo 0
% 1.48/0.96 % fd_cond 0
% 1.48/0.96 % fd_pseudo_cond 1
% 1.48/0.96 % AC symbols 0
% 1.48/0.96
% 1.48/0.96 % ------ Input Options Time Limit: Unbounded
% 1.48/0.96
% 1.48/0.96
% 1.48/0.96 % ------
% 1.48/0.96 % Current options:
% 1.48/0.96 % ------
% 1.48/0.96
% 1.48/0.96
% 1.48/0.96 %
% 1.48/0.96
% 1.48/0.96 % ------ Proving...
% 1.48/0.96 %
% 1.48/0.96
% 1.48/0.96 % SZS status Unsatisfiable for theBenchmark.p
% 1.48/0.96
% 1.48/0.96 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.48/0.96
% 1.48/0.96
%------------------------------------------------------------------------------