%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET848-2 : 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 : n006.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 02:48:47 PM UTC 2026
% Result : Unsatisfiable 1.82s 1.27s
% Output : CNFRefutation 1.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 37 ( 24 unt; 6 def)
% Number of atoms : 95 ( 17 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 41 ( 24 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-3 aty)
% Number of variables : 42 ( 0 sgn 42 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X3,X0,X1] :
( c_in(X0,c_minus(X1,X3,tc_set(X2)),X2)
| c_in(X0,X3,X2)
| ~ c_in(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_ODiffI_0) ).
fof(f2,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f3,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/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__UnionI_0) ).
fof(f4,axiom,
! [X2,X0,X1] :
( c_in(X0,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_OTFin__chain__lemma4_0) ).
fof(f5,axiom,
! [X2,X0,X1] :
( c_Zorn_Osucc(X1,X0,X2) != X0
| ~ c_in(X0,c_minus(c_Zorn_Ochain(X1,X2),c_Zorn_Omaxchain(X1,X2),tc_set(tc_set(tc_set(X2)))),tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zorn_Osucc__not__equals_0) ).
fof(f6,negated_conjecture,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f7,negated_conjecture,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f8,plain,
c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)) = c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a),
inference(reorient_equations,[],[f7]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_in(X0,X3,X2)
| c_in(X0,c_minus(X1,X3,tc_set(X2)),X2)
| ~ c_in(X0,X1,X2) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] : c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[],[f2]) ).
tcf(c_58,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,[],[f3]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(X0,c_Zorn_Ochain(X1,X2),tc_set(tc_set(X2)))
| ~ c_in(X0,c_Zorn_OTFin(X1,X2),tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ c_in(X1,c_minus(c_Zorn_Ochain(X0,X2),c_Zorn_Omaxchain(X0,X2),tc_set(tc_set(tc_set(X2)))),tc_set(tc_set(X2)))
| ( c_Zorn_Osucc(X0,X1,X2) != X1 ) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_61,negated_conjecture,
~ c_in(c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f6]) ).
tcf(c_62,negated_conjecture,
c_Zorn_Osucc(v_S,c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),t_a) = c_Union(c_Zorn_OTFin(v_S,t_a),tc_set(t_a)),
inference(cnf_transformation,[],[f8]) ).
tcf(c_118,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( c_in(c_Union(X4,tc_set(X0)),c_Zorn_OTFin(X2,X0),tc_set(tc_set(X0)))
| ( X3 != X4 )
| ( c_Zorn_OTFin(X2,X0) != X3 )
| ( tc_set(tc_set(tc_set(X0))) != tc_set(X1) ) ),
inference(resolution_lifted,[status(thm)],[c_57,c_58]) ).
tcf(c_119,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_in(c_Union(c_Zorn_OTFin(X2,X0),tc_set(X0)),c_Zorn_OTFin(X2,X0),tc_set(tc_set(X0)))
| ( tc_set(tc_set(tc_set(X0))) != tc_set(X1) ) ),
inference(unflattening,[status(thm)],[c_118]) ).
tcf(c_177,definition,
iPr_def_10 = c_Zorn_OTFin(v_S,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_178,definition,
iPr_def_11 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_179,definition,
iPr_def_12 = c_Union(iPr_def_10,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_180,definition,
iPr_def_13 = c_Zorn_Osucc(v_S,iPr_def_12,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_181,definition,
iPr_def_14 = c_Zorn_Omaxchain(v_S,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_182,definition,
iPr_def_15 = tc_set(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_183,negated_conjecture,
iPr_def_13 = iPr_def_12,
inference(demodulation,[status(thm)],[c_62,c_178,c_177,c_179,c_180]) ).
tcf(c_184,negated_conjecture,
~ c_in(iPr_def_12,iPr_def_14,iPr_def_15),
inference(demodulation,[status(thm)],[c_61,c_182,c_181]) ).
tcf(c_385,plain,
c_Zorn_Osucc(v_S,iPr_def_12,t_a) = iPr_def_12,
inference(light_normalisation,[status(thm)],[c_180,c_183]) ).
tcf(c_390,plain,
! [X0: $i,X1: $i] : c_in(c_Union(c_Zorn_OTFin(X0,X1),tc_set(X1)),c_Zorn_OTFin(X0,X1),tc_set(tc_set(X1))),
inference(equality_resolution,[status(thm)],[c_119]) ).
tcf(c_407,plain,
! [X0: $i] :
( c_in(X0,c_Zorn_Ochain(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_in(X0,iPr_def_10,tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm)],[c_177,c_59]) ).
tcf(c_410,plain,
! [X0: $i] :
( c_in(X0,c_Zorn_Ochain(v_S,t_a),iPr_def_15)
| ~ c_in(X0,iPr_def_10,iPr_def_15) ),
inference(light_normalisation,[status(thm)],[c_407,c_178,c_182]) ).
tcf(c_426,plain,
~ c_in(iPr_def_12,c_minus(c_Zorn_Ochain(v_S,t_a),c_Zorn_Omaxchain(v_S,t_a),tc_set(tc_set(tc_set(t_a)))),tc_set(tc_set(t_a))),
inference(superposition,[status(thm)],[c_385,c_60]) ).
tcf(c_427,plain,
~ c_in(iPr_def_12,c_minus(c_Zorn_Ochain(v_S,t_a),iPr_def_14,tc_set(iPr_def_15)),iPr_def_15),
inference(light_normalisation,[status(thm)],[c_426,c_178,c_181,c_182]) ).
tcf(c_432,plain,
( c_in(iPr_def_12,iPr_def_14,iPr_def_15)
| ~ c_in(iPr_def_12,c_Zorn_Ochain(v_S,t_a),iPr_def_15) ),
inference(superposition,[status(thm)],[c_56,c_427]) ).
tcf(c_433,plain,
~ c_in(iPr_def_12,c_Zorn_Ochain(v_S,t_a),iPr_def_15),
inference(forward_subsumption_resolution,[status(thm)],[c_432,c_184]) ).
tcf(c_434,plain,
~ c_in(iPr_def_12,iPr_def_10,iPr_def_15),
inference(superposition,[status(thm)],[c_410,c_433]) ).
tcf(c_438,plain,
c_in(c_Union(iPr_def_10,tc_set(t_a)),iPr_def_10,tc_set(tc_set(t_a))),
inference(superposition,[status(thm)],[c_177,c_390]) ).
tcf(c_442,plain,
c_in(iPr_def_12,iPr_def_10,iPr_def_15),
inference(light_normalisation,[status(thm)],[c_438,c_178,c_179,c_182]) ).
tcf(c_443,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_442,c_434]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET848-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n006.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % 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 12:12:11 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.13/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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
% 0.13/0.41
% 0.13/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.41
% 0.13/0.41 % Detected problem language: tptp
% 0.13/0.42 % Proving...
% 1.82/1.27 % SZS status Started for theBenchmark.p
% 1.82/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.82/1.27
% 1.82/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.82/1.27
% 1.82/1.27 % ------ iProver source info
% 1.82/1.27
% 1.82/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.82/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.82/1.27 % git: non_committed_changes: false
% 1.82/1.27
% 1.82/1.27 % ------ Parsing...% successful
% 1.82/1.27
% 1.82/1.27
% 1.82/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.82/1.27
% 1.82/1.27 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 1.82/1.27
% 1.82/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.82/1.27
% 1.82/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.82/1.27 % ------ Proving...
% 1.82/1.27 % ------ Problem Properties
% 1.82/1.27
% 1.82/1.27 %
% 1.82/1.27 % clauses 12
% 1.82/1.27 % conjectures 2
% 1.82/1.27 % EPR 2
% 1.82/1.27 % Horn 11
% 1.82/1.27 % unary 8
% 1.82/1.27 % binary 3
% 1.82/1.27 % lits 17
% 1.82/1.27 % lits eq 9
% 1.82/1.27 % fd_pure 0
% 1.82/1.27 % fd_pseudo 0
% 1.82/1.27 % fd_cond 0
% 1.82/1.27 % fd_pseudo_cond 0
% 1.82/1.27 % AC symbols 0
% 1.82/1.27
% 1.82/1.27 % ------ Schedule dynamic 5 is on
% 1.82/1.27
% 1.82/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.82/1.27
% 1.82/1.27
% 1.82/1.27 % ------
% 1.82/1.27 % Current options:
% 1.82/1.27 % ------
% 1.82/1.27
% 1.82/1.27
% 1.82/1.27 %
% 1.82/1.27
% 1.82/1.27 % ------ Proving...
% 1.82/1.27 %
% 1.82/1.27
% 1.82/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 1.82/1.27
% 1.82/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.82/1.28
% 1.82/1.28
%------------------------------------------------------------------------------