%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET852-2 : 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 02:48:48 PM UTC 2026
% Result : Unsatisfiable 0.98s 6.07s
% Output : CNFRefutation 0.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 30 ( 11 unt; 4 def)
% Number of atoms : 150 ( 4 equ)
% Maximal formula atoms : 5 ( 5 avg)
% Number of connectives : 56 ( 16 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 45 ( 0 sgn 45 !; 0 ?; 32 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f2,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f3,negated_conjecture,
! [X0] :
( ~ c_in(X0,v_Y,tc_set(tc_set(t_a)))
| c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f4,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| c_in(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X2,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_0) ).
fof(f5,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X0,tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_1) ).
fof(f6,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(c_Union(X2,X3),X1,tc_set(X3))
| c_lessequals(X0,c_Union(X2,X3),tc_set(X3))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(X1,X0,X2,X3),tc_set(X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_OUnion__lemma0_2) ).
tcf(c_55,negated_conjecture,
~ c_lessequals(c_Union(v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f2]) ).
tcf(c_57,negated_conjecture,
! [X0: $i] :
( c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),X0,tc_set(tc_set(t_a)))
| ~ c_in(X0,v_Y,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| c_in(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X2,tc_set(X3)) ),
inference(cnf_transformation,[],[f4]) ).
tcf(c_59,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X1,c_Union(X2,X3),tc_set(X3))
| c_lessequals(c_Union(X2,X3),X0,tc_set(X3))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,X2,X3),X0,tc_set(X3)) ),
inference(cnf_transformation,[],[f5]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_Union(X2,X3),tc_set(X3))
| c_lessequals(c_Union(X2,X3),X1,tc_set(X3))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(X1,X0,X2,X3),tc_set(X3)) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_93,plain,
! [X0: $i,X1: $i] :
( c_lessequals(X1,c_Union(v_Y,tc_set(t_a)),tc_set(tc_set(t_a)))
| c_lessequals(c_Union(v_Y,tc_set(t_a)),X0,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,v_Y,tc_set(t_a)),v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_OUnion__lemma0__1(X0,X1,v_Y,tc_set(t_a)),tc_set(tc_set(t_a))) ),
inference(resolution,[status(thm)],[c_57,c_58]) ).
tcf(c_135,definition,
iPr_def_10 = c_Zorn_Osucc(v_S,v_m,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_136,definition,
iPr_def_11 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_137,definition,
iPr_def_12 = tc_set(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_138,definition,
iPr_def_13 = c_Union(v_Y,iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_139,plain,
! [X0: $i,X1: $i] :
( c_lessequals(iPr_def_13,X0,iPr_def_12)
| c_lessequals(X1,iPr_def_13,iPr_def_12)
| c_lessequals(iPr_def_10,c_Zorn_OUnion__lemma0__1(X0,X1,v_Y,iPr_def_11),iPr_def_12)
| c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,v_Y,iPr_def_11),v_m,iPr_def_12) ),
inference(demodulation,[status(thm)],[c_93,c_138,c_137,c_136,c_135]) ).
tcf(c_140,negated_conjecture,
~ c_lessequals(iPr_def_10,iPr_def_13,iPr_def_12),
inference(demodulation,[status(thm)],[c_56]) ).
tcf(c_141,negated_conjecture,
~ c_lessequals(iPr_def_13,v_m,iPr_def_12),
inference(demodulation,[status(thm)],[c_55]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,c_Union(X2,iPr_def_11),tc_set(iPr_def_11))
| c_lessequals(c_Union(X2,iPr_def_11),X0,tc_set(iPr_def_11))
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,X2,iPr_def_11),X0,iPr_def_12) ),
inference(superposition,[status(thm)],[c_137,c_59]) ).
tcf(c_319,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X1,c_Union(X2,iPr_def_11),iPr_def_12)
| c_lessequals(c_Union(X2,iPr_def_11),X0,iPr_def_12)
| ~ c_lessequals(c_Zorn_OUnion__lemma0__1(X0,X1,X2,iPr_def_11),X0,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_318,c_137]) ).
tcf(c_335,plain,
! [X0: $i] :
( c_lessequals(iPr_def_13,v_m,iPr_def_12)
| c_lessequals(X0,iPr_def_13,iPr_def_12)
| c_lessequals(c_Union(v_Y,iPr_def_11),v_m,iPr_def_12)
| c_lessequals(X0,c_Union(v_Y,iPr_def_11),iPr_def_12)
| c_lessequals(iPr_def_10,c_Zorn_OUnion__lemma0__1(v_m,X0,v_Y,iPr_def_11),iPr_def_12) ),
inference(superposition,[status(thm)],[c_139,c_319]) ).
tcf(c_336,plain,
! [X0: $i] :
( c_lessequals(iPr_def_13,v_m,iPr_def_12)
| c_lessequals(X0,iPr_def_13,iPr_def_12)
| c_lessequals(iPr_def_10,c_Zorn_OUnion__lemma0__1(v_m,X0,v_Y,iPr_def_11),iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_335,c_138]) ).
tcf(c_337,plain,
! [X0: $i] :
( c_lessequals(X0,iPr_def_13,iPr_def_12)
| c_lessequals(iPr_def_10,c_Zorn_OUnion__lemma0__1(v_m,X0,v_Y,iPr_def_11),iPr_def_12) ),
inference(forward_subsumption_resolution,[status(thm)],[c_336,c_141]) ).
tcf(c_348,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,c_Union(X2,iPr_def_11),tc_set(iPr_def_11))
| c_lessequals(c_Union(X2,iPr_def_11),X1,tc_set(iPr_def_11))
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(X1,X0,X2,iPr_def_11),iPr_def_12) ),
inference(superposition,[status(thm)],[c_137,c_60]) ).
tcf(c_349,plain,
! [X0: $i,X1: $i,X2: $i] :
( c_lessequals(X0,c_Union(X2,iPr_def_11),iPr_def_12)
| c_lessequals(c_Union(X2,iPr_def_11),X1,iPr_def_12)
| ~ c_lessequals(X0,c_Zorn_OUnion__lemma0__1(X1,X0,X2,iPr_def_11),iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_348,c_137]) ).
tcf(c_381,plain,
( c_lessequals(iPr_def_10,iPr_def_13,iPr_def_12)
| c_lessequals(iPr_def_10,c_Union(v_Y,iPr_def_11),iPr_def_12)
| c_lessequals(c_Union(v_Y,iPr_def_11),v_m,iPr_def_12) ),
inference(superposition,[status(thm)],[c_337,c_349]) ).
tcf(c_382,plain,
( c_lessequals(iPr_def_13,v_m,iPr_def_12)
| c_lessequals(iPr_def_10,iPr_def_13,iPr_def_12) ),
inference(light_normalisation,[status(thm)],[c_381,c_138]) ).
tcf(c_383,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_382,c_141,c_140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SET852-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.06/5.31 % Computer : n012.cluster.edu
% 0.06/5.31 % Model : x86_64 x86_64
% 0.06/5.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/5.31 % Memory : 8046.5625MB
% 0.06/5.31 % OS : Linux 6.8.0-71-generic
% 0.06/5.31 % CPULimit : 300
% 0.06/5.31 % WCLimit : 300
% 0.06/5.31 % DateTime : Thu Sep 24 12:13:28 UTC 2026
% 0.06/5.32 % CPUTime :
% 0.06/5.32 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.06/5.34 Running first-order theorem proving
% 0.06/5.34 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
% 0.06/5.34
% 0.06/5.34 % ======== iProver multi-core TPTP/SMT =========
% 0.06/5.34
% 0.06/5.34 % Detected problem language: tptp
% 0.06/5.35 % Proving...
% 0.98/6.07 % SZS status Started for theBenchmark.p
% 0.98/6.07 % SZS status Unsatisfiable for theBenchmark.p
% 0.98/6.07
% 0.98/6.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.98/6.07
% 0.98/6.07 % ------ iProver source info
% 0.98/6.07
% 0.98/6.07 % git: date: 2026-07-19 20:42:38 +0200
% 0.98/6.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.98/6.07 % git: non_committed_changes: false
% 0.98/6.07
% 0.98/6.07 % ------ Parsing...% successful
% 0.98/6.07
% 0.98/6.07
% 0.98/6.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.98/6.07
% 0.98/6.07 % ------ Preprocessing... sf_s rm: 0 0s sf_e pe_s pe:1:0s pe_e sf_s rm: 0 0s sf_e pe_s pe_e %
% 0.98/6.07
% 0.98/6.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.98/6.07
% 0.98/6.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.98/6.07 % ------ Proving...
% 0.98/6.07 % ------ Problem Properties
% 0.98/6.07
% 0.98/6.07 %
% 0.98/6.07 % clauses 9
% 0.98/6.07 % conjectures 2
% 0.98/6.07 % EPR 2
% 0.98/6.07 % Horn 6
% 0.98/6.07 % unary 6
% 0.98/6.07 % binary 0
% 0.98/6.07 % lits 16
% 0.98/6.07 % lits eq 4
% 0.98/6.07 % fd_pure 0
% 0.98/6.07 % fd_pseudo 0
% 0.98/6.07 % fd_cond 0
% 0.98/6.07 % fd_pseudo_cond 0
% 0.98/6.07 % AC symbols 0
% 0.98/6.07
% 0.98/6.07 % ------ Schedule dynamic 5 is on
% 0.98/6.07
% 0.98/6.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.98/6.07
% 0.98/6.07
% 0.98/6.07 % ------
% 0.98/6.07 % Current options:
% 0.98/6.07 % ------
% 0.98/6.07
% 0.98/6.07
% 0.98/6.07 %
% 0.98/6.07
% 0.98/6.07 % ------ Proving...
% 0.98/6.07 %
% 0.98/6.07
% 0.98/6.07 % SZS status Unsatisfiable for theBenchmark.p
% 0.98/6.07
% 0.98/6.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.98/6.07
% 0.98/6.07
%------------------------------------------------------------------------------