%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET792+4 : 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 : n008.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 02:48:35 PM UTC 2026
% Result : Theorem 0.42s 1.25s
% Output : CNFRefutation 0.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of formulae : 64 ( 18 unt; 1 def)
% Number of atoms : 253 ( 44 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 283 ( 108 ~; 101 |; 46 &)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 2 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-3 aty)
% Number of variables : 149 ( 0 sgn 141 !; 8 ?; 46 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X2,X3,X4] :
( ( member(X4,X1)
& member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X4)
& apply(X0,X2,X3) )
=> apply(X0,X2,X4) ) )
& ! [X2,X3] :
( ( member(X3,X1)
& member(X2,X1) )
=> ( ( apply(X0,X3,X2)
& apply(X0,X2,X3) )
=> X2 = X3 ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',order) ).
fof(f6,axiom,
! [X0,X1,X2] :
( least(X2,X0,X1)
<=> ( ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) )
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',least) ).
fof(f8,axiom,
! [X0,X1,X2] :
( min(X2,X0,X1)
<=> ( ! [X3] :
( ( apply(X0,X3,X2)
& member(X3,X1) )
=> X2 = X3 )
& member(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET006+3.ax',min) ).
fof(f11,conjecture,
! [X0,X1,X2] :
( ( least(X2,X0,X1)
& order(X0,X1) )
=> min(X2,X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV4) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
( ( least(X2,X0,X1)
& order(X0,X1) )
=> min(X2,X0,X1) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,plain,
! [X0,X1] :
( order(X0,X1)
<=> ( ! [X5,X6,X7] :
( ( member(X7,X1)
& member(X6,X1)
& member(X5,X1) )
=> ( ( apply(X0,X6,X7)
& apply(X0,X5,X6) )
=> apply(X0,X5,X7) ) )
& ! [X3,X4] :
( ( member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X3)
& apply(X0,X3,X4) )
=> X3 = X4 ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
inference(rectify,[],[f1]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ( ! [X3] :
( ( apply(X0,X3,X2)
& member(X3,X1) )
=> X2 = X3 )
& member(X2,X1) )
=> min(X2,X0,X1) ),
inference(unused_predicate_definition_removal,[],[f8]) ).
fof(f15,plain,
! [X0,X1,X2] :
( least(X2,X0,X1)
=> ( ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) )
& member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f16,plain,
! [X0,X1] :
( order(X0,X1)
=> ( ! [X5,X6,X7] :
( ( member(X7,X1)
& member(X6,X1)
& member(X5,X1) )
=> ( ( apply(X0,X6,X7)
& apply(X0,X5,X6) )
=> apply(X0,X5,X7) ) )
& ! [X3,X4] :
( ( member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X3)
& apply(X0,X3,X4) )
=> X3 = X4 ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
inference(unused_predicate_definition_removal,[],[f13]) ).
fof(f17,plain,
! [X0,X1] :
( ~ order(X0,X1)
| ( ! [X5,X6,X7] :
( ~ member(X7,X1)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| apply(X0,X5,X7) )
& ! [X3,X4] :
( ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X3)
| ~ apply(X0,X3,X4)
| X3 = X4 )
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ) ),
inference(ennf_transformation,[],[f16]) ).
fof(f18,plain,
! [X0,X1] :
( ~ order(X0,X1)
| ( ! [X5,X6,X7] :
( ~ member(X7,X1)
| ~ member(X6,X1)
| ~ member(X5,X1)
| ~ apply(X0,X6,X7)
| ~ apply(X0,X5,X6)
| apply(X0,X5,X7) )
& ! [X3,X4] :
( ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X3)
| ~ apply(X0,X3,X4)
| X3 = X4 )
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ) ),
inference(flattening,[],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ least(X2,X0,X1)
| ( ! [X3] :
( ~ member(X3,X1)
| apply(X0,X2,X3) )
& member(X2,X1) ) ),
inference(ennf_transformation,[],[f15]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1)
& X2 != X3 )
| ~ member(X2,X1)
| min(X2,X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ? [X3] :
( apply(X0,X3,X2)
& member(X3,X1)
& X2 != X3 )
| ~ member(X2,X1)
| min(X2,X0,X1) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
? [X0,X1,X2] :
( least(X2,X0,X1)
& order(X0,X1)
& ~ min(X2,X0,X1) ),
inference(ennf_transformation,[],[f12]) ).
fof(f23,plain,
? [X0,X1,X2] :
( least(X2,X0,X1)
& order(X0,X1)
& ~ min(X2,X0,X1) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ( apply(X0,sK0(X0,X1,X2),X2)
& member(sK0(X0,X1,X2),X1)
& sK0(X0,X1,X2) != X2 )
| ~ member(X2,X1)
| min(X2,X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f21]) ).
fof(f25,plain,
( least(sK3,sK1,sK2)
& order(sK1,sK2)
& ~ min(sK3,sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3)],[f23]) ).
fof(f27,plain,
! [X3,X0,X1,X4] :
( ~ order(X0,X1)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X3)
| ~ apply(X0,X3,X4)
| X3 = X4 ),
inference(cnf_transformation,[],[f18]) ).
fof(f29,plain,
! [X2,X3,X0,X1] :
( ~ least(X2,X0,X1)
| ~ member(X3,X1)
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X2,X0,X1] :
( ~ least(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f31,plain,
! [X2,X0,X1] :
( apply(X0,sK0(X0,X1,X2),X2)
| ~ member(X2,X1)
| min(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f32,plain,
! [X2,X0,X1] :
( member(sK0(X0,X1,X2),X1)
| ~ member(X2,X1)
| min(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f33,plain,
! [X2,X0,X1] :
( sK0(X0,X1,X2) != X2
| ~ member(X2,X1)
| min(X2,X0,X1) ),
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
least(sK3,sK1,sK2),
inference(cnf_transformation,[],[f25]) ).
fof(f35,plain,
order(sK1,sK2),
inference(cnf_transformation,[],[f25]) ).
fof(f36,plain,
~ min(sK3,sK1,sK2),
inference(cnf_transformation,[],[f25]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ~ order(X0,X3)
| ~ member(X2,X3)
| ~ member(X1,X3)
| ~ apply(X0,X2,X1)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f27]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ least(X0,X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_53,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ~ least(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( min(X2,X0,X1)
| ~ member(X2,X1)
| ( sK0(X0,X1,X2) != X2 ) ),
inference(cnf_transformation,[],[f33]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( min(X0,X2,X1)
| member(sK0(X2,X1,X0),X1)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f32]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i,X2: $i] :
( min(X0,X2,X1)
| apply(X2,sK0(X2,X1,X0),X0)
| ~ member(X0,X1) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_57,negated_conjecture,
~ min(sK3,sK1,sK2),
inference(cnf_transformation,[],[f36]) ).
tcf(c_58,negated_conjecture,
order(sK1,sK2),
inference(cnf_transformation,[],[f35]) ).
tcf(c_59,negated_conjecture,
least(sK3,sK1,sK2),
inference(cnf_transformation,[],[f34]) ).
tcf(c_199,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_59]) ).
tcf(c_200,plain,
! [X0: $i] :
( apply(sK1,sK3,X0)
| ~ member(X0,sK2) ),
inference(unflattening,[status(thm)],[c_199]) ).
tcf(c_208,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ( X2 != sK2 )
| ( X1 != sK1 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_59]) ).
tcf(c_209,plain,
member(sK3,sK2),
inference(unflattening,[status(thm)],[c_208]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i] :
( ~ member(X2,X1)
| ( X2 != sK3 )
| ( X1 != sK2 )
| ( X0 != sK1 )
| ( sK0(X0,X1,X2) != X2 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_57]) ).
tcf(c_217,plain,
( ~ member(sK3,sK2)
| ( sK0(sK1,sK2,sK3) != sK3 ) ),
inference(unflattening,[status(thm)],[c_216]) ).
tcf(c_218,plain,
sK0(sK1,sK2,sK3) != sK3,
inference(global_subsumption_just,[status(thm)],[c_217,c_209,c_217]) ).
tcf(c_223,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(X2,sK0(X2,X1,X0),X0)
| ~ member(X0,X1)
| ( X2 != sK1 )
| ( X1 != sK2 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_56,c_57]) ).
tcf(c_224,plain,
( apply(sK1,sK0(sK1,sK2,sK3),sK3)
| ~ member(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_223]) ).
tcf(c_225,plain,
apply(sK1,sK0(sK1,sK2,sK3),sK3),
inference(global_subsumption_just,[status(thm)],[c_224,c_209,c_224]) ).
tcf(c_230,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(sK0(X2,X1,X0),X1)
| ~ member(X0,X1)
| ( X2 != sK1 )
| ( X1 != sK2 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_57]) ).
tcf(c_231,plain,
( member(sK0(sK1,sK2,sK3),sK2)
| ~ member(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_230]) ).
tcf(c_232,plain,
member(sK0(sK1,sK2,sK3),sK2),
inference(global_subsumption_just,[status(thm)],[c_231,c_209,c_231]) ).
tcf(c_249,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X2 = X3 )
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ apply(X0,X3,X2)
| ~ apply(X0,X2,X3)
| ( X1 != sK2 )
| ( X0 != sK1 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_58]) ).
tcf(c_250,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X1,sK2)
| ~ member(X0,sK2)
| ~ apply(sK1,X1,X0)
| ~ apply(sK1,X0,X1) ),
inference(unflattening,[status(thm)],[c_249]) ).
tcf(c_372,definition,
iPr_def_10 = sK0(sK1,sK2,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_374,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X1,sK2)
| ~ member(X0,sK2)
| ~ apply(sK1,X1,X0)
| ~ apply(sK1,X0,X1) ),
inference(demodulation,[status(thm)],[c_250]) ).
tcf(c_376,plain,
member(iPr_def_10,sK2),
inference(demodulation,[status(thm)],[c_232,c_372]) ).
tcf(c_377,plain,
apply(sK1,iPr_def_10,sK3),
inference(demodulation,[status(thm)],[c_225]) ).
tcf(c_378,plain,
iPr_def_10 != sK3,
inference(demodulation,[status(thm)],[c_218]) ).
tcf(c_379,plain,
member(sK3,sK2),
inference(demodulation,[status(thm)],[c_209]) ).
tcf(c_380,plain,
! [X0: $i] :
( apply(sK1,sK3,X0)
| ~ member(X0,sK2) ),
inference(demodulation,[status(thm)],[c_200]) ).
tcf(c_558,plain,
( ( sK3 = iPr_def_10 )
| ~ member(iPr_def_10,sK2)
| ~ member(sK3,sK2)
| ~ apply(sK1,sK3,iPr_def_10) ),
inference(superposition,[status(thm)],[c_377,c_374]) ).
tcf(c_559,plain,
( ( sK3 = iPr_def_10 )
| ~ apply(sK1,sK3,iPr_def_10) ),
inference(forward_subsumption_resolution,[status(thm)],[c_558,c_376,c_379]) ).
tcf(c_596,plain,
( ( sK3 = iPr_def_10 )
| ~ member(iPr_def_10,sK2) ),
inference(superposition,[status(thm)],[c_380,c_559]) ).
tcf(c_597,plain,
sK3 = iPr_def_10,
inference(forward_subsumption_resolution,[status(thm)],[c_596,c_376]) ).
tcf(c_600,plain,
iPr_def_10 != iPr_def_10,
inference(demodulation,[status(thm)],[c_378,c_597]) ).
tcf(c_603,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_600]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET792+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.03 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.34 % Computer : n008.cluster.edu
% 0.10/0.34 % Model : x86_64 x86_64
% 0.10/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.34 % Memory : 8046.5625MB
% 0.10/0.34 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 11:59:09 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/0.38 Running first-order theorem proving
% 0.13/0.38 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
% 0.13/0.39
% 0.13/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.13/0.39
% 0.13/0.39 % Detected problem language: tptp
% 0.13/0.41 % Proving...
% 0.42/1.25 % SZS status Started for theBenchmark.p
% 0.42/1.25 % SZS status Theorem for theBenchmark.p
% 0.42/1.25
% 0.42/1.25 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.42/1.25
% 0.42/1.25 % ------ iProver source info
% 0.42/1.25
% 0.42/1.25 % git: date: 2026-07-19 20:42:38 +0200
% 0.42/1.25 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.42/1.25 % git: non_committed_changes: false
% 0.42/1.25
% 0.42/1.25 % ------ Parsing...
% 0.42/1.25 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.42/1.25
% 0.42/1.25 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 4 0s sf_e pe_s pe_e %
% 0.42/1.25
% 0.42/1.25 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.42/1.25
% 0.42/1.25 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.42/1.25 % ------ Proving...
% 0.42/1.25 % ------ Problem Properties
% 0.42/1.25
% 0.42/1.25 %
% 0.42/1.25 % clauses 9
% 0.42/1.25 % conjectures 0
% 0.42/1.25 % EPR 8
% 0.42/1.25 % Horn 9
% 0.42/1.25 % unary 5
% 0.42/1.25 % binary 2
% 0.42/1.25 % lits 20
% 0.42/1.25 % lits eq 3
% 0.42/1.25 % fd_pure 0
% 0.42/1.25 % fd_pseudo 0
% 0.42/1.25 % fd_cond 0
% 0.42/1.25 % fd_pseudo_cond 1
% 0.42/1.25 % AC symbols 0
% 0.42/1.25
% 0.42/1.25 % ------ Schedule dynamic 5 is on
% 0.42/1.25
% 0.42/1.25 % ------ no conjectures: strip conj schedule
% 0.42/1.25
% 0.42/1.25 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" stripped conjectures Time Limit: 10.
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% 0.42/1.25
% 0.42/1.25 % ------
% 0.42/1.25 % Current options:
% 0.42/1.25 % ------
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% 0.42/1.25 % ------ Proving...
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% 0.42/1.25 % SZS status Theorem for theBenchmark.p
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% 0.42/1.25 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
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