%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET843-2 : 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 : n016.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 02:48:45 PM UTC 2026
% Result : Unsatisfiable 2.40s 6.31s
% Output : CNFRefutation 2.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 15
% Syntax : Number of formulae : 58 ( 23 unt; 5 def)
% Number of atoms : 207 ( 36 equ)
% Maximal formula atoms : 4 ( 3 avg)
% Number of connectives : 105 ( 53 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 61 ( 0 sgn 61 !; 0 ?; 33 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( c_lessequals(X0,c_Union(X1,X2),tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_OUnion__upper_0) ).
fof(f2,axiom,
! [X2,X0,X1] :
( X1 = X0
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__antisym_0) ).
fof(f3,plain,
! [X2,X0,X1] :
( X0 = X1
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(reorient_equations,[],[f2]) ).
fof(f4,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f5,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(f6,axiom,
! [X2,X0,X1] :
( c_in(c_Zorn_Osucc(X1,X0,X2),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_OsuccI_0) ).
fof(f7,axiom,
! [X2,X0,X1] :
( c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2)))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| X0 != c_Zorn_Osucc(X1,X0,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_Oeq__succ__upper_0) ).
fof(f9,plain,
! [X2,X3,X0,X1] :
( c_lessequals(X3,X0,tc_set(tc_set(X2)))
| c_Zorn_Osucc(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))) ),
inference(reorient_equations,[],[f8]) ).
fof(f10,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(f11,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f12,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/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,c_Union(X1,X2),tc_set(X2))
| ~ c_in(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,tc_set(X2))
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] : c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[],[f4]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : c_lessequals(X0,c_Zorn_Osucc(X1,X0,X2),tc_set(tc_set(X2))),
inference(cnf_transformation,[],[f5]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Zorn_Osucc(X1,X0,X2),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,[],[f6]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Union(X0,tc_set(X2)),c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(tc_set(X2)))) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X3,X1,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_Osucc(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f9]) ).
tcf(c_66,negated_conjecture,
c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f10]) ).
tcf(c_67,negated_conjecture,
( ( c_Zorn_Osucc(v_S,v_m,t_a) != v_m )
| ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) != v_m ) ),
inference(cnf_transformation,[],[f11]) ).
tcf(c_68,negated_conjecture,
( ( c_Zorn_Osucc(v_S,v_m,t_a) = v_m )
| ( c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = v_m ) ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_195,definition,
iPr_def_10 = c_Zorn_OTFin(v_S,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_196,definition,
iPr_def_11 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_197,definition,
iPr_def_12 = c_Union(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_198,definition,
iPr_def_13 = c_Zorn_Osucc(v_S,v_m,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_199,definition,
iPr_def_14 = tc_set(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_200,negated_conjecture,
( ( iPr_def_13 = v_m )
| ( iPr_def_12 = v_m ) ),
inference(demodulation,[status(thm)],[c_68,c_198,c_196,c_195,c_197]) ).
tcf(c_201,negated_conjecture,
( ( iPr_def_13 != v_m )
| ( iPr_def_12 != v_m ) ),
inference(demodulation,[status(thm)],[c_67]) ).
tcf(c_202,negated_conjecture,
c_in(v_m,iPr_def_10,iPr_def_14),
inference(demodulation,[status(thm)],[c_66,c_199]) ).
tcf(c_573,plain,
c_lessequals(v_m,iPr_def_13,tc_set(tc_set(t_a))),
inference(superposition,[status(thm)],[c_198,c_62]) ).
tcf(c_576,plain,
c_lessequals(v_m,iPr_def_13,iPr_def_14),
inference(light_normalisation,[status(thm)],[c_573,c_196,c_199]) ).
tcf(c_593,plain,
! [X0: $i] :
( c_lessequals(X0,iPr_def_12,tc_set(iPr_def_11))
| ~ c_in(X0,iPr_def_10,tc_set(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_197,c_59]) ).
tcf(c_596,plain,
! [X0: $i] :
( c_lessequals(X0,iPr_def_12,iPr_def_14)
| ~ c_in(X0,iPr_def_10,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_593,c_199]) ).
tcf(c_612,plain,
c_lessequals(v_m,iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_202,c_596]) ).
tcf(c_641,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,iPr_def_14)
| ~ c_lessequals(X0,X1,tc_set(iPr_def_11)) ),
inference(superposition,[status(thm)],[c_199,c_60]) ).
tcf(c_642,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ c_lessequals(X1,X0,iPr_def_14)
| ~ c_lessequals(X0,X1,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_641,c_199]) ).
tcf(c_664,plain,
( c_in(iPr_def_13,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(superposition,[status(thm)],[c_198,c_63]) ).
tcf(c_669,plain,
( c_in(iPr_def_13,iPr_def_10,iPr_def_14)
| ~ c_in(v_m,iPr_def_10,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_664,c_195,c_196,c_199]) ).
tcf(c_670,plain,
c_in(iPr_def_13,iPr_def_10,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_669,c_202]) ).
tcf(c_689,plain,
! [X0: $i] :
( c_in(c_Union(X0,tc_set(t_a)),iPr_def_10,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(tc_set(t_a)))) ),
inference(superposition,[status(thm)],[c_195,c_64]) ).
tcf(c_698,plain,
! [X0: $i] :
( c_in(c_Union(X0,iPr_def_11),iPr_def_10,iPr_def_14)
| ~ c_lessequals(X0,iPr_def_10,tc_set(iPr_def_14)) ),
inference(light_normalisation,[status(thm)],[c_689,c_195,c_196,c_199]) ).
tcf(c_712,plain,
! [X0: $i] :
( c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(v_m,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ( v_m != iPr_def_13 ) ),
inference(superposition,[status(thm)],[c_198,c_65]) ).
tcf(c_719,plain,
! [X0: $i] :
( c_lessequals(X0,v_m,iPr_def_14)
| ~ c_in(v_m,iPr_def_10,iPr_def_14)
| ~ c_in(X0,iPr_def_10,iPr_def_14)
| ( v_m != iPr_def_13 ) ),
inference(light_normalisation,[status(thm)],[c_712,c_195,c_196,c_199]) ).
tcf(c_720,plain,
! [X0: $i] :
( c_lessequals(X0,v_m,iPr_def_14)
| ~ c_in(X0,iPr_def_10,iPr_def_14)
| ( v_m != iPr_def_13 ) ),
inference(forward_subsumption_resolution,[status(thm)],[c_719,c_202]) ).
tcf(c_730,plain,
c_lessequals(iPr_def_13,iPr_def_12,iPr_def_14),
inference(superposition,[status(thm)],[c_670,c_596]) ).
tcf(c_749,plain,
( c_in(iPr_def_12,iPr_def_10,iPr_def_14)
| ~ c_lessequals(iPr_def_10,iPr_def_10,tc_set(iPr_def_14)) ),
inference(superposition,[status(thm)],[c_197,c_698]) ).
tcf(c_751,plain,
c_in(iPr_def_12,iPr_def_10,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_749,c_61]) ).
tcf(c_772,plain,
! [X0: $i] :
( c_lessequals(X0,v_m,iPr_def_14)
| ( v_m = iPr_def_12 )
| ~ c_in(X0,iPr_def_10,iPr_def_14) ),
inference(superposition,[status(thm)],[c_200,c_720]) ).
tcf(c_787,plain,
( c_lessequals(iPr_def_12,v_m,iPr_def_14)
| ( v_m = iPr_def_12 ) ),
inference(superposition,[status(thm)],[c_751,c_772]) ).
tcf(c_872,plain,
( ( iPr_def_12 = iPr_def_13 )
| ~ c_lessequals(iPr_def_12,iPr_def_13,iPr_def_14) ),
inference(superposition,[status(thm)],[c_730,c_642]) ).
tcf(c_877,plain,
( ( v_m = iPr_def_12 )
| ~ c_lessequals(v_m,iPr_def_12,iPr_def_14) ),
inference(superposition,[status(thm)],[c_787,c_642]) ).
tcf(c_880,plain,
v_m = iPr_def_12,
inference(forward_subsumption_resolution,[status(thm)],[c_877,c_612]) ).
tcf(c_895,plain,
c_lessequals(iPr_def_12,iPr_def_13,iPr_def_14),
inference(demodulation,[status(thm)],[c_576,c_880]) ).
tcf(c_897,plain,
( ( iPr_def_12 != iPr_def_13 )
| ( iPr_def_12 != iPr_def_12 ) ),
inference(demodulation,[status(thm)],[c_201,c_880]) ).
tcf(c_900,plain,
iPr_def_12 != iPr_def_13,
inference(equality_resolution_simp,[status(thm)],[c_897]) ).
tcf(c_901,plain,
~ c_lessequals(iPr_def_12,iPr_def_13,iPr_def_14),
inference(backward_subsumption_resolution,[status(thm)],[c_872,c_900]) ).
tcf(c_902,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_895,c_901]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET843-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/5.38 % Computer : n016.cluster.edu
% 0.12/5.38 % Model : x86_64 x86_64
% 0.12/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/5.38 % Memory : 8046.5625MB
% 0.12/5.38 % OS : Linux 6.8.0-71-generic
% 0.12/5.38 % CPULimit : 300
% 0.12/5.38 % WCLimit : 300
% 0.12/5.38 % DateTime : Thu Sep 24 12:15:33 UTC 2026
% 0.12/5.39 % CPUTime :
% 0.12/5.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/5.43 Running first-order theorem proving
% 0.16/5.43 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
% 0.16/5.44
% 0.16/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.16/5.44
% 0.16/5.44 % Detected problem language: tptp
% 0.16/5.45 % Proving...
% 2.40/6.31 % SZS status Started for theBenchmark.p
% 2.40/6.31 % SZS status Unsatisfiable for theBenchmark.p
% 2.40/6.31
% 2.40/6.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.40/6.31
% 2.40/6.31 % ------ iProver source info
% 2.40/6.31
% 2.40/6.31 % git: date: 2026-07-19 20:42:38 +0200
% 2.40/6.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.40/6.31 % git: non_committed_changes: false
% 2.40/6.31
% 2.40/6.31 % ------ Parsing...% successful
% 2.40/6.31
% 2.40/6.31
% 2.40/6.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.40/6.31
% 2.40/6.31 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.40/6.31
% 2.40/6.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.40/6.31
% 2.40/6.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.40/6.31 % ------ Proving...
% 2.40/6.31 % ------ Problem Properties
% 2.40/6.31
% 2.40/6.31 %
% 2.40/6.31 % clauses 15
% 2.40/6.31 % conjectures 3
% 2.40/6.31 % EPR 3
% 2.40/6.31 % Horn 14
% 2.40/6.31 % unary 8
% 2.40/6.31 % binary 5
% 2.40/6.31 % lits 25
% 2.40/6.31 % lits eq 11
% 2.40/6.31 % fd_pure 0
% 2.40/6.31 % fd_pseudo 0
% 2.40/6.31 % fd_cond 0
% 2.40/6.31 % fd_pseudo_cond 1
% 2.40/6.31 % AC symbols 0
% 2.40/6.31
% 2.40/6.31 % ------ Schedule dynamic 5 is on
% 2.40/6.31
% 2.40/6.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.40/6.31
% 2.40/6.31
% 2.40/6.31 % ------
% 2.40/6.31 % Current options:
% 2.40/6.31 % ------
% 2.40/6.31
% 2.40/6.31
% 2.40/6.31 %
% 2.40/6.31
% 2.40/6.31 % ------ Proving...
% 2.40/6.31 %
% 2.40/6.31
% 2.40/6.31 % SZS status Unsatisfiable for theBenchmark.p
% 2.40/6.31
% 2.40/6.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.40/6.31
% 2.40/6.31
%------------------------------------------------------------------------------