%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET851-2 : 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 : n005.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 0.44s 1.27s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 11
% Syntax : Number of formulae : 36 ( 19 unt; 4 def)
% Number of atoms : 92 ( 20 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 52 ( 24 ~; 28 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 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 : 7 ( 7 usr; 4 con; 0-3 aty)
% Number of variables : 19 ( 0 sgn 19 !; 0 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : c_lessequals(X0,X0,tc_set(X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Set_Osubset__refl_0) ).
fof(f2,axiom,
! [X2,X3,X0,X1] :
( c_lessequals(X0,c_Zorn_Osucc(X3,X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(X2))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zorn_Osucc__trans_0) ).
fof(f3,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f4,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
fof(f5,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
fof(f6,negated_conjecture,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
fof(f7,negated_conjecture,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| X0 = v_m
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
fof(f8,plain,
! [X0] :
( ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| v_m = X0
| c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a))) ),
inference(reorient_equations,[],[f7]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] : c_lessequals(X0,X0,tc_set(X1)),
inference(cnf_transformation,[],[f1]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( c_lessequals(X0,c_Zorn_Osucc(X3,X1,X2),tc_set(tc_set(X2)))
| ~ c_lessequals(X0,X1,tc_set(tc_set(X2))) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_58,negated_conjecture,
c_in(v_x,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f3]) ).
tcf(c_59,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f4]) ).
tcf(c_60,negated_conjecture,
~ c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),c_Zorn_Osucc(v_S,v_x,t_a),tc_set(tc_set(t_a))),
inference(cnf_transformation,[],[f5]) ).
tcf(c_61,negated_conjecture,
( c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| c_lessequals(c_Zorn_Osucc(v_S,v_m,t_a),v_x,tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[],[f6]) ).
tcf(c_62,negated_conjecture,
! [X0: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a)))
| ( X0 = v_m )
| ~ c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ~ c_in(X0,c_Zorn_OTFin(v_S,t_a),tc_set(tc_set(t_a))) ),
inference(cnf_transformation,[],[f8]) ).
tcf(c_112,plain,
! [X0: $i] :
( c_lessequals(c_Zorn_Osucc(v_S,X0,t_a),v_m,tc_set(tc_set(t_a)))
| ( X0 = v_m )
| ~ c_lessequals(X0,v_m,tc_set(tc_set(t_a)))
| ( X0 != v_x )
| ( c_Zorn_OTFin(v_S,t_a) != c_Zorn_OTFin(v_S,t_a) )
| ( tc_set(tc_set(t_a)) != tc_set(tc_set(t_a)) ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_62]) ).
tcf(c_113,plain,
( c_lessequals(c_Zorn_Osucc(v_S,v_x,t_a),v_m,tc_set(tc_set(t_a)))
| ( v_x = v_m )
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(unflattening,[status(thm)],[c_112]) ).
tcf(c_114,plain,
( ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a)))
| ( v_x = v_m ) ),
inference(global_subsumption_just,[status(thm)],[c_113,c_59,c_113]) ).
tcf(c_115,plain,
( ( v_x = v_m )
| ~ c_lessequals(v_x,v_m,tc_set(tc_set(t_a))) ),
inference(renaming,[status(thm)],[c_114]) ).
tcf(c_158,definition,
iPr_def_10 = tc_set(t_a),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_159,definition,
iPr_def_11 = tc_set(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_160,definition,
iPr_def_12 = c_Zorn_Osucc(v_S,v_m,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_161,definition,
iPr_def_13 = c_Zorn_Osucc(v_S,v_x,t_a),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_162,plain,
( ( v_x = v_m )
| ~ c_lessequals(v_x,v_m,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_115,c_158,c_159]) ).
tcf(c_163,negated_conjecture,
( c_lessequals(iPr_def_12,v_x,iPr_def_11)
| c_lessequals(v_x,v_m,iPr_def_11) ),
inference(demodulation,[status(thm)],[c_61,c_160]) ).
tcf(c_164,negated_conjecture,
~ c_lessequals(iPr_def_12,iPr_def_13,iPr_def_11),
inference(demodulation,[status(thm)],[c_60,c_161]) ).
tcf(c_296,plain,
( c_lessequals(iPr_def_12,v_x,iPr_def_11)
| ( v_x = v_m ) ),
inference(superposition,[status(thm)],[c_163,c_162]) ).
tcf(c_305,plain,
! [X0: $i] : c_lessequals(X0,X0,iPr_def_11),
inference(superposition,[status(thm)],[c_159,c_56]) ).
tcf(c_311,plain,
! [X0: $i] :
( c_lessequals(X0,iPr_def_13,tc_set(tc_set(t_a)))
| ~ c_lessequals(X0,v_x,tc_set(tc_set(t_a))) ),
inference(superposition,[status(thm)],[c_161,c_57]) ).
tcf(c_318,plain,
! [X0: $i] :
( c_lessequals(X0,iPr_def_13,iPr_def_11)
| ~ c_lessequals(X0,v_x,iPr_def_11) ),
inference(light_normalisation,[status(thm)],[c_311,c_158,c_159]) ).
tcf(c_347,plain,
( c_lessequals(iPr_def_12,iPr_def_13,iPr_def_11)
| ( v_x = v_m ) ),
inference(superposition,[status(thm)],[c_296,c_318]) ).
tcf(c_349,plain,
v_x = v_m,
inference(forward_subsumption_resolution,[status(thm)],[c_347,c_164]) ).
tcf(c_352,plain,
c_Zorn_Osucc(v_S,v_m,t_a) = iPr_def_13,
inference(demodulation,[status(thm)],[c_161,c_349]) ).
tcf(c_354,plain,
iPr_def_12 = iPr_def_13,
inference(light_normalisation,[status(thm)],[c_352,c_160]) ).
tcf(c_356,plain,
~ c_lessequals(iPr_def_12,iPr_def_12,iPr_def_11),
inference(demodulation,[status(thm)],[c_164,c_354]) ).
tcf(c_357,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_356,c_305]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET851-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.07/0.35 % Computer : n005.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Thu Sep 24 12:13:04 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.07/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.39 Running first-order theorem proving
% 0.13/0.39 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
% 0.13/0.41
% 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...
% 0.44/1.27 % SZS status Started for theBenchmark.p
% 0.44/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 0.44/1.27
% 0.44/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.44/1.27
% 0.44/1.27 % ------ iProver source info
% 0.44/1.27
% 0.44/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 0.44/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.44/1.27 % git: non_committed_changes: false
% 0.44/1.27
% 0.44/1.27 % ------ Parsing...% successful
% 0.44/1.27
% 0.44/1.27
% 0.44/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.44/1.27
% 0.44/1.27 % ------ 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 %
% 0.44/1.27
% 0.44/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.44/1.27
% 0.44/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.44/1.27 % ------ Proving...
% 0.44/1.27 % ------ Problem Properties
% 0.44/1.27
% 0.44/1.27 %
% 0.44/1.27 % clauses 10
% 0.44/1.27 % conjectures 3
% 0.44/1.27 % EPR 4
% 0.44/1.27 % Horn 9
% 0.44/1.27 % unary 7
% 0.44/1.27 % binary 3
% 0.44/1.27 % lits 13
% 0.44/1.27 % lits eq 5
% 0.44/1.27 % fd_pure 0
% 0.44/1.27 % fd_pseudo 0
% 0.44/1.27 % fd_cond 0
% 0.44/1.27 % fd_pseudo_cond 0
% 0.44/1.27 % AC symbols 0
% 0.44/1.27
% 0.44/1.27 % ------ Schedule dynamic 5 is on
% 0.44/1.27
% 0.44/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.44/1.27
% 0.44/1.27
% 0.44/1.27 % ------
% 0.44/1.27 % Current options:
% 0.44/1.27 % ------
% 0.44/1.27
% 0.44/1.27
% 0.44/1.27 %
% 0.44/1.27
% 0.44/1.27 % ------ Proving...
% 0.44/1.27 %
% 0.44/1.27
% 0.44/1.27 % SZS status Unsatisfiable for theBenchmark.p
% 0.44/1.27
% 0.44/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.44/1.27
% 0.44/1.27
%------------------------------------------------------------------------------