%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : NUM143-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n014.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 02:23:24 PM UTC 2026
% Result : Unsatisfiable 21.81s 4.25s
% Output : CNFRefutation 21.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 20
% Syntax : Number of formulae : 61 ( 23 unt; 6 def)
% Number of atoms : 162 ( 19 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 98 ( 47 ~; 51 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-2 aty)
% Number of variables : 72 ( 0 sgn 72 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_members) ).
fof(f2,axiom,
! [X0,X1] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members1) ).
fof(f3,axiom,
! [X0,X1] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',not_subclass_members2) ).
fof(f4,axiom,
! [X0] : subclass(X0,universal_class),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',class_elements_are_sets) ).
fof(f7,axiom,
! [X0,X1] :
( X0 = X1
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',subclass_implies_equal) ).
fof(f12,axiom,
! [X0] : unordered_pair(X0,X0) = singleton(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',singleton_set) ).
fof(f21,axiom,
! [X2,X0,X1] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection1) ).
fof(f22,axiom,
! [X2,X0,X1] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection2) ).
fof(f23,axiom,
! [X2,X0,X1] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',intersection3) ).
fof(f24,axiom,
! [X0,X1] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement1) ).
fof(f25,axiom,
! [X0,X1] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',complement2) ).
fof(f26,axiom,
! [X0,X1] : complement(intersection(complement(X0),complement(X1))) = union(X0,X1),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',union) ).
fof(f44,axiom,
! [X0] : union(X0,singleton(X0)) = successor(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SET004-0.ax',successor) ).
fof(f176,negated_conjecture,
intersection(successor(x),x) != x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_corollary_to_successor_of_set_is_set_1) ).
fof(f177,plain,
x != intersection(successor(x),x),
inference(reorient_equations,[],[f176]) ).
fof(f183,plain,
! [X0] : successor(X0) = complement(intersection(complement(X0),complement(unordered_pair(X0,X0)))),
inference(definition_unfolding,[],[f44,f26,f12]) ).
fof(f268,plain,
x != intersection(complement(intersection(complement(x),complement(unordered_pair(x,x)))),x),
inference(definition_unfolding,[],[f177,f183]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_209,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),X0) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_210,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| ~ member(not_subclass_element(X0,X1),X1) ),
inference(cnf_transformation,[],[f3]) ).
tcf(c_211,plain,
! [X0: $i] : subclass(X0,universal_class),
inference(cnf_transformation,[],[f4]) ).
tcf(c_214,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ subclass(X1,X0)
| ~ subclass(X0,X1) ),
inference(cnf_transformation,[],[f7]) ).
tcf(c_226,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f21]) ).
tcf(c_227,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[],[f22]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X2)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f23]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] :
( ~ member(X0,X1)
| ~ member(X0,complement(X1)) ),
inference(cnf_transformation,[],[f24]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i] :
( member(X0,X1)
| member(X0,complement(X1))
| ~ member(X0,universal_class) ),
inference(cnf_transformation,[],[f25]) ).
tcf(c_343,negated_conjecture,
intersection(complement(intersection(complement(x),complement(unordered_pair(x,x)))),x) != x,
inference(cnf_transformation,[],[f268]) ).
tcf(c_4621,definition,
iPr_def_10 = complement(x),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_4622,definition,
iPr_def_11 = unordered_pair(x,x),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_4623,definition,
iPr_def_12 = complement(iPr_def_11),
introduced(definition,[new_symbols(definition,[iPr_def_12])],[]) ).
tcf(c_4624,definition,
iPr_def_13 = intersection(iPr_def_10,iPr_def_12),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_4625,definition,
iPr_def_14 = complement(iPr_def_13),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_4626,definition,
iPr_def_15 = intersection(iPr_def_14,x),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_4627,negated_conjecture,
iPr_def_15 != x,
inference(demodulation,[status(thm)],[c_343,c_4622,c_4623,c_4621,c_4624,c_4625,c_4626]) ).
tcf(c_6040,plain,
! [X0: $i] :
( member(X0,x)
| ~ member(X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_4626,c_227]) ).
tcf(c_6137,plain,
! [X0: $i] :
( subclass(iPr_def_15,X0)
| member(not_subclass_element(iPr_def_15,X0),x) ),
inference(superposition,[status(thm)],[c_209,c_6040]) ).
tcf(c_6439,plain,
subclass(iPr_def_15,x),
inference(superposition,[status(thm)],[c_6137,c_210]) ).
tcf(c_6558,plain,
( ( iPr_def_15 = x )
| ~ subclass(iPr_def_15,x)
| ~ subclass(x,iPr_def_15) ),
inference(instantiation,[status(thm)],[c_214]) ).
tcf(c_6755,plain,
! [X0: $i] :
( member(X0,iPr_def_15)
| ~ member(X0,iPr_def_14)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_4626,c_228]) ).
tcf(c_62338,plain,
! [X0: $i] :
( member(X0,iPr_def_10)
| ~ member(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_4624,c_226]) ).
tcf(c_62361,plain,
! [X0: $i] :
( member(X0,x)
| ~ member(X0,iPr_def_15) ),
inference(superposition,[status(thm)],[c_4626,c_227]) ).
tcf(c_62381,plain,
! [X0: $i] :
( ~ member(X0,iPr_def_10)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_4621,c_229]) ).
tcf(c_62468,plain,
! [X0: $i] :
( subclass(iPr_def_15,X0)
| member(not_subclass_element(iPr_def_15,X0),x) ),
inference(superposition,[status(thm)],[c_209,c_62361]) ).
tcf(c_62627,plain,
! [X0: $i,X1: $i] :
( member(X0,universal_class)
| ~ member(X0,X1) ),
inference(superposition,[status(thm)],[c_211,c_208]) ).
tcf(c_62683,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| member(X0,iPr_def_13)
| ~ member(X0,universal_class) ),
inference(superposition,[status(thm)],[c_4625,c_230]) ).
tcf(c_62798,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),universal_class) ),
inference(superposition,[status(thm)],[c_209,c_62627]) ).
tcf(c_62933,plain,
subclass(iPr_def_15,x),
inference(superposition,[status(thm)],[c_62468,c_210]) ).
tcf(c_62937,plain,
( ( x = iPr_def_15 )
| ~ subclass(x,iPr_def_15) ),
inference(superposition,[status(thm)],[c_62933,c_214]) ).
tcf(c_62978,plain,
~ subclass(x,iPr_def_15),
inference(global_subsumption_just,[status(thm)],[c_62937,c_4627,c_6439,c_6558]) ).
tcf(c_63016,plain,
! [X0: $i] :
( member(X0,iPr_def_15)
| ~ member(X0,iPr_def_14)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_4626,c_228]) ).
tcf(c_64127,plain,
! [X0: $i,X1: $i] :
( subclass(X0,X1)
| member(not_subclass_element(X0,X1),iPr_def_14)
| member(not_subclass_element(X0,X1),iPr_def_13) ),
inference(superposition,[status(thm)],[c_62798,c_62683]) ).
tcf(c_65825,plain,
! [X0: $i] :
( subclass(X0,iPr_def_14)
| member(not_subclass_element(X0,iPr_def_14),iPr_def_13) ),
inference(superposition,[status(thm)],[c_64127,c_210]) ).
tcf(c_65890,plain,
! [X0: $i] :
( subclass(X0,iPr_def_14)
| member(not_subclass_element(X0,iPr_def_14),iPr_def_10) ),
inference(superposition,[status(thm)],[c_65825,c_62338]) ).
tcf(c_66459,plain,
! [X0: $i] :
( subclass(X0,iPr_def_14)
| ~ member(not_subclass_element(X0,iPr_def_14),x) ),
inference(superposition,[status(thm)],[c_65890,c_62381]) ).
tcf(c_67462,plain,
subclass(x,iPr_def_14),
inference(superposition,[status(thm)],[c_209,c_66459]) ).
tcf(c_67467,plain,
! [X0: $i] :
( member(X0,iPr_def_14)
| ~ member(X0,x) ),
inference(superposition,[status(thm)],[c_67462,c_208]) ).
tcf(c_68077,plain,
! [X0: $i] :
( member(X0,iPr_def_15)
| ~ member(X0,x) ),
inference(global_subsumption_just,[status(thm)],[c_63016,c_6755,c_67467]) ).
tcf(c_68084,plain,
! [X0: $i] :
( subclass(x,X0)
| member(not_subclass_element(x,X0),iPr_def_15) ),
inference(superposition,[status(thm)],[c_209,c_68077]) ).
tcf(c_68134,plain,
subclass(x,iPr_def_15),
inference(superposition,[status(thm)],[c_68084,c_210]) ).
tcf(c_68139,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_68134,c_62978]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM143-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.36 % Computer : n014.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 03:01:48 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.13/0.40 Running first-order theorem proving
% 0.13/0.40 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...
% 21.81/4.25 % SZS status Started for theBenchmark.p
% 21.81/4.25 % SZS status Unsatisfiable for theBenchmark.p
% 21.81/4.25
% 21.81/4.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 21.81/4.25
% 21.81/4.25 % ------ iProver source info
% 21.81/4.25
% 21.81/4.25 % git: date: 2026-07-19 20:42:38 +0200
% 21.81/4.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 21.81/4.25 % git: non_committed_changes: false
% 21.81/4.25
% 21.81/4.25 % ------ Parsing...% successful
% 21.81/4.25
% 21.81/4.25
% 21.81/4.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 21.81/4.25
% 21.81/4.25 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 21.81/4.25
% 21.81/4.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 21.81/4.25
% 21.81/4.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 21.81/4.25 % ------ Proving...
% 21.81/4.25 % ------ Problem Properties
% 21.81/4.25
% 21.81/4.25 %
% 21.81/4.25 % clauses 121
% 21.81/4.25 % conjectures 1
% 21.81/4.25 % EPR 15
% 21.81/4.25 % Horn 109
% 21.81/4.25 % unary 32
% 21.81/4.25 % binary 58
% 21.81/4.25 % lits 255
% 21.81/4.25 % lits eq 46
% 21.81/4.25 % fd_pure 0
% 21.81/4.25 % fd_pseudo 0
% 21.81/4.25 % fd_cond 5
% 21.81/4.25 % fd_pseudo_cond 10
% 21.81/4.25 % AC symbols 0
% 21.81/4.25
% 21.81/4.25 % ------ Schedule dynamic 5 is on
% 21.81/4.25
% 21.81/4.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 21.81/4.25
% 21.81/4.25
% 21.81/4.25 % ------
% 21.81/4.25 % Current options:
% 21.81/4.25 % ------
% 21.81/4.25
% 21.81/4.25
% 21.81/4.25 %
% 21.81/4.25
% 21.81/4.25 % ------ Proving...
% 21.81/4.25 %
% 21.81/4.25
% 21.81/4.25 % SZS status Unsatisfiable for theBenchmark.p
% 21.81/4.25
% 21.81/4.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 21.81/4.25
% 21.81/4.25
%------------------------------------------------------------------------------