%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET865-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/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 02:48:51 PM UTC 2026
% Result : Unsatisfiable 1.46s 1.15s
% Output : CNFRefutation 1.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 11
% Syntax : Number of formulae : 38 ( 15 unt; 3 def)
% Number of atoms : 103 ( 13 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 73 ( 40 ~; 33 |; 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 : 7 ( 5 usr; 4 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 49 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
! [X0] :
( ~ c_in(X0,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| c_in(c_Union(X0,t_a),v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f2,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| c_in(v_x(X0),v_S,tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f3,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| c_lessequals(X0,v_x(X0),tc_set(t_a)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f4,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| X0 != v_x(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f5,plain,
! [X0] :
( ~ c_in(X0,v_S,tc_set(t_a))
| v_x(X0) != X0 ),
inference(reorient_equations,[],[f4]) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,X3,X2)
| ~ c_lessequals(X1,X3,tc_set(X2))
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OsubsetD_0) ).
fof(f7,axiom,
! [X0,X1] : c_in(c_Zorn_OHausdorff__1(X0,X1),c_Zorn_Omaxchain(X0,X1),tc_set(tc_set(X1))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OHausdorff_0) ).
fof(f8,axiom,
! [X2,X3,X0,X1] :
( c_Union(X3,X2) = X0
| ~ c_lessequals(c_Union(X3,X2),X0,tc_set(X2))
| ~ c_in(X3,c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,X1,tc_set(X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__Zorn_0) ).
fof(f9,axiom,
! [X0,X1] : c_lessequals(c_Zorn_Omaxchain(X0,X1),c_Zorn_Ochain(X0,X1),tc_set(tc_set(tc_set(X1)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Omaxchain__subset__chain_0) ).
tcf(c_57,negated_conjecture,
! [X0: $i] :
( c_in(c_Union(X0,t_a),v_S,tc_set(t_a))
| ~ c_in(X0,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] :
( c_in(v_x(X0),v_S,tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_59,negated_conjecture,
! [X0: $i] :
( c_lessequals(X0,v_x(X0),tc_set(t_a))
| ~ c_in(X0,v_S,tc_set(t_a)) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_60,negated_conjecture,
! [X0: $i] :
( ~ c_in(X0,v_S,tc_set(t_a))
| ( v_x(X0) != X0 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X3,X1,X2)
| ~ c_in(X3,X0,X2)
| ~ c_lessequals(X0,X1,tc_set(X2)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] : c_in(c_Zorn_OHausdorff__1(X0,X1),c_Zorn_Omaxchain(X0,X1),tc_set(tc_set(X1))),
inference(cnf_transformation,[],[f7]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( c_Union(X0,X2) = X3 )
| ~ c_in(X3,X1,tc_set(X2))
| ~ c_lessequals(c_Union(X0,X2),X3,tc_set(X2))
| ~ c_in(X0,c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i] : c_lessequals(c_Zorn_Omaxchain(X0,X1),c_Zorn_Ochain(X0,X1),tc_set(tc_set(tc_set(X1)))),
inference(cnf_transformation,[],[f9]) ).
tcf(c_222,definition,
iPr_def_10 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_223,definition,
iPr_def_11 = c_Zorn_Ochain(v_S,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_224,definition,
iPr_def_12 = tc_set(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_225,negated_conjecture,
! [X0: $i] :
( ~ c_in(X0,v_S,iPr_def_10)
| ( v_x(X0) != X0 ) ),
inference(demodulation,[status(thm)],[c_60,c_222]) ).
tcf(c_226,negated_conjecture,
! [X0: $i] :
( c_lessequals(X0,v_x(X0),iPr_def_10)
| ~ c_in(X0,v_S,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_227,negated_conjecture,
! [X0: $i] :
( c_in(v_x(X0),v_S,iPr_def_10)
| ~ c_in(X0,v_S,iPr_def_10) ),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_228,negated_conjecture,
! [X0: $i] :
( c_in(c_Union(X0,t_a),v_S,iPr_def_10)
| ~ c_in(X0,iPr_def_11,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_57,c_224,c_223]) ).
tcf(c_426,plain,
! [X0: $i] : c_in(c_Zorn_OHausdorff__1(X0,t_a),c_Zorn_Omaxchain(X0,t_a),tc_set(iPr_def_10)),
inference(superposition,[status(thm)],[c_222,c_62]) ).
tcf(c_428,plain,
! [X0: $i] : c_in(c_Zorn_OHausdorff__1(X0,t_a),c_Zorn_Omaxchain(X0,t_a),iPr_def_12),
inference(light_normalisation,[status(thm)],[c_426,c_224]) ).
tcf(c_431,plain,
c_lessequals(c_Zorn_Omaxchain(v_S,t_a),iPr_def_11,tc_set(tc_set(tc_set(t_a)))),
inference(superposition,[status(thm)],[c_223,c_64]) ).
tcf(c_434,plain,
c_lessequals(c_Zorn_Omaxchain(v_S,t_a),iPr_def_11,tc_set(iPr_def_12)),
inference(light_normalisation,[status(thm)],[c_431,c_222,c_224]) ).
tcf(c_464,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_Union(c_Zorn_OHausdorff__1(X0,X1),X1) = X2 )
| ~ c_in(X2,X0,tc_set(X1))
| ~ c_lessequals(c_Union(c_Zorn_OHausdorff__1(X0,X1),X1),X2,tc_set(X1)) ),
inference(superposition,[status(thm)],[c_62,c_63]) ).
tcf(c_483,plain,
! [X0: $i] :
( c_in(X0,iPr_def_11,iPr_def_12)
| ~ c_in(X0,c_Zorn_Omaxchain(v_S,t_a),iPr_def_12) ),
inference(superposition,[status(thm)],[c_434,c_61]) ).
tcf(c_500,plain,
c_in(c_Zorn_OHausdorff__1(v_S,t_a),iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_428,c_483]) ).
tcf(c_595,plain,
! [X0: $i,X1: $i] :
( ( c_Union(c_Zorn_OHausdorff__1(X0,t_a),t_a) = X1 )
| ~ c_in(X1,X0,tc_set(t_a))
| ~ c_lessequals(c_Union(c_Zorn_OHausdorff__1(X0,t_a),t_a),X1,iPr_def_10) ),
inference(superposition,[status(thm)],[c_222,c_464]) ).
tcf(c_601,plain,
! [X0: $i,X1: $i] :
( ( c_Union(c_Zorn_OHausdorff__1(X0,t_a),t_a) = X1 )
| ~ c_in(X1,X0,iPr_def_10)
| ~ c_lessequals(c_Union(c_Zorn_OHausdorff__1(X0,t_a),t_a),X1,iPr_def_10) ),
inference(light_normalisation,[status(thm)],[c_595,c_222]) ).
tcf(c_629,plain,
! [X0: $i] :
( ( v_x(c_Union(c_Zorn_OHausdorff__1(X0,t_a),t_a)) = c_Union(c_Zorn_OHausdorff__1(X0,t_a),t_a) )
| ~ c_in(c_Union(c_Zorn_OHausdorff__1(X0,t_a),t_a),v_S,iPr_def_10)
| ~ c_in(v_x(c_Union(c_Zorn_OHausdorff__1(X0,t_a),t_a)),X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_226,c_601]) ).
tcf(c_651,plain,
! [X0: $i] :
( ~ c_in(c_Union(c_Zorn_OHausdorff__1(X0,t_a),t_a),v_S,iPr_def_10)
| ~ c_in(v_x(c_Union(c_Zorn_OHausdorff__1(X0,t_a),t_a)),X0,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_629,c_225]) ).
tcf(c_658,plain,
~ c_in(c_Union(c_Zorn_OHausdorff__1(v_S,t_a),t_a),v_S,iPr_def_10),
inference(superposition,[status(thm)],[c_227,c_651]) ).
tcf(c_663,plain,
~ c_in(c_Zorn_OHausdorff__1(v_S,t_a),iPr_def_11,iPr_def_12),
inference(superposition,[status(thm)],[c_228,c_658]) ).
tcf(c_665,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_663,c_500]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET865-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.35 % Computer : n012.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Thu Sep 24 12:17:36 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.39 Running first-order theorem proving
% 0.11/0.39 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.40
% 0.11/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.40
% 0.11/0.40 % Detected problem language: tptp
% 0.11/0.41 % Proving...
% 1.46/1.15 % SZS status Started for theBenchmark.p
% 1.46/1.15 % SZS status Unsatisfiable for theBenchmark.p
% 1.46/1.15
% 1.46/1.15 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.46/1.15
% 1.46/1.15 % ------ iProver source info
% 1.46/1.15
% 1.46/1.15 % git: date: 2026-07-19 20:42:38 +0200
% 1.46/1.15 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.46/1.15 % git: non_committed_changes: false
% 1.46/1.15
% 1.46/1.15 % ------ Parsing...% successful
% 1.46/1.15
% 1.46/1.15
% 1.46/1.15 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.46/1.15
% 1.46/1.15 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.46/1.15
% 1.46/1.15 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.46/1.15
% 1.46/1.15 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.46/1.15 % ------ Proving...
% 1.46/1.15 % ------ Problem Properties
% 1.46/1.15
% 1.46/1.15 %
% 1.46/1.15 % clauses 11
% 1.46/1.15 % conjectures 4
% 1.46/1.15 % EPR 0
% 1.46/1.15 % Horn 11
% 1.46/1.15 % unary 5
% 1.46/1.15 % binary 4
% 1.46/1.15 % lits 20
% 1.46/1.15 % lits eq 5
% 1.46/1.15 % fd_pure 0
% 1.46/1.15 % fd_pseudo 0
% 1.46/1.15 % fd_cond 0
% 1.46/1.15 % fd_pseudo_cond 1
% 1.46/1.15 % AC symbols 0
% 1.46/1.15
% 1.46/1.15 % ------ Schedule dynamic 5 is on
% 1.46/1.15
% 1.46/1.15 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.46/1.15
% 1.46/1.15
% 1.46/1.15 % ------
% 1.46/1.15 % Current options:
% 1.46/1.15 % ------
% 1.46/1.15
% 1.46/1.15
% 1.46/1.15 %
% 1.46/1.15
% 1.46/1.15 % ------ Proving...
% 1.46/1.15 %
% 1.46/1.15
% 1.46/1.15 % SZS status Unsatisfiable for theBenchmark.p
% 1.46/1.15
% 1.46/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.46/1.15
% 1.46/1.15
%------------------------------------------------------------------------------