%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET804+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 : 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 02:48:37 PM UTC 2026
% Result : Theorem 1.73s 1.28s
% Output : CNFRefutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 3
% Syntax : Number of formulae : 52 ( 17 unt; 0 def)
% Number of atoms : 149 ( 41 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 168 ( 71 ~; 60 |; 25 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 5 con; 0-0 aty)
% Number of variables : 104 ( 0 sgn 92 !; 12 ?; 42 :)
% Comments :
%------------------------------------------------------------------------------
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] :
( order(X0,X1)
=> ! [X2,X3] :
( ( X2 != X3
& min(X3,X0,X1)
& min(X2,X0,X1) )
=> ~ ? [X4] : least(X4,X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV16) ).
fof(f12,negated_conjecture,
~ ! [X0,X1] :
( order(X0,X1)
=> ! [X2,X3] :
( ( X2 != X3
& min(X3,X0,X1)
& min(X2,X0,X1) )
=> ~ ? [X4] : least(X4,X0,X1) ) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f14,plain,
! [X0,X1,X2] :
( min(X2,X0,X1)
=> ( ! [X3] :
( ( apply(X0,X3,X2)
& member(X3,X1) )
=> X2 = X3 )
& member(X2,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(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] :
( ~ min(X2,X0,X1)
| ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| X2 = X3 )
& member(X2,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ min(X2,X0,X1)
| ( ! [X3] :
( ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| X2 = X3 )
& member(X2,X1) ) ),
inference(flattening,[],[f20]) ).
fof(f22,plain,
? [X0,X1] :
( order(X0,X1)
& ? [X2,X3] :
( X2 != X3
& min(X3,X0,X1)
& min(X2,X0,X1)
& ? [X4] : least(X4,X0,X1) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f23,plain,
? [X0,X1] :
( order(X0,X1)
& ? [X2,X3] :
( X2 != X3
& min(X3,X0,X1)
& min(X2,X0,X1)
& ? [X4] : least(X4,X0,X1) ) ),
inference(flattening,[],[f22]) ).
fof(f24,plain,
( order(sK0,sK1)
& sK2 != sK3
& min(sK3,sK0,sK1)
& min(sK2,sK0,sK1)
& least(sK4,sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4)],[f23]) ).
fof(f28,plain,
! [X2,X3,X0,X1] :
( ~ least(X2,X0,X1)
| ~ member(X3,X1)
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X2,X0,X1] :
( ~ least(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f19]) ).
fof(f30,plain,
! [X2,X3,X0,X1] :
( ~ min(X2,X0,X1)
| ~ apply(X0,X3,X2)
| ~ member(X3,X1)
| X2 = X3 ),
inference(cnf_transformation,[],[f21]) ).
fof(f31,plain,
! [X2,X0,X1] :
( ~ min(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f21]) ).
fof(f33,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f24]) ).
fof(f34,plain,
min(sK3,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f35,plain,
min(sK2,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
fof(f36,plain,
least(sK4,sK0,sK1),
inference(cnf_transformation,[],[f24]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ least(X0,X1,X2) ),
inference(cnf_transformation,[],[f29]) ).
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,[],[f28]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ min(X0,X1,X2) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X2 )
| ~ member(X1,X3)
| ~ min(X2,X0,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_56,negated_conjecture,
least(sK4,sK0,sK1),
inference(cnf_transformation,[],[f36]) ).
tcf(c_57,negated_conjecture,
min(sK2,sK0,sK1),
inference(cnf_transformation,[],[f35]) ).
tcf(c_58,negated_conjecture,
min(sK3,sK0,sK1),
inference(cnf_transformation,[],[f34]) ).
tcf(c_59,negated_conjecture,
sK2 != sK3,
inference(cnf_transformation,[],[f33]) ).
tcf(c_189,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_56]) ).
tcf(c_190,plain,
! [X0: $i] :
( apply(sK0,sK4,X0)
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_189]) ).
tcf(c_198,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_56]) ).
tcf(c_199,plain,
member(sK4,sK1),
inference(unflattening,[status(thm)],[c_198]) ).
tcf(c_206,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_57]) ).
tcf(c_207,plain,
member(sK2,sK1),
inference(unflattening,[status(thm)],[c_206]) ).
tcf(c_211,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_58]) ).
tcf(c_212,plain,
member(sK3,sK1),
inference(unflattening,[status(thm)],[c_211]) ).
tcf(c_216,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ member(X3,X2)
| ~ apply(X0,X3,X1)
| ( X2 != sK1 )
| ( X1 != sK2 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_57]) ).
tcf(c_217,plain,
! [X0: $i] :
( ( sK2 = X0 )
| ~ member(X0,sK1)
| ~ apply(sK0,X0,sK2) ),
inference(unflattening,[status(thm)],[c_216]) ).
tcf(c_228,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ( X1 = X3 )
| ~ member(X3,X2)
| ~ apply(X0,X3,X1)
| ( X2 != sK1 )
| ( X1 != sK3 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_58]) ).
tcf(c_229,plain,
! [X0: $i] :
( ( sK3 = X0 )
| ~ member(X0,sK1)
| ~ apply(sK0,X0,sK3) ),
inference(unflattening,[status(thm)],[c_228]) ).
tcf(c_406,plain,
! [X0: $i] :
( ( sK3 = X0 )
| ~ member(X0,sK1)
| ~ apply(sK0,X0,sK3) ),
inference(demodulation,[status(thm)],[c_229]) ).
tcf(c_407,plain,
! [X0: $i] :
( ( sK2 = X0 )
| ~ member(X0,sK1)
| ~ apply(sK0,X0,sK2) ),
inference(demodulation,[status(thm)],[c_217]) ).
tcf(c_408,plain,
member(sK3,sK1),
inference(demodulation,[status(thm)],[c_212]) ).
tcf(c_409,plain,
member(sK2,sK1),
inference(demodulation,[status(thm)],[c_207]) ).
tcf(c_410,plain,
member(sK4,sK1),
inference(demodulation,[status(thm)],[c_199]) ).
tcf(c_411,plain,
! [X0: $i] :
( apply(sK0,sK4,X0)
| ~ member(X0,sK1) ),
inference(demodulation,[status(thm)],[c_190]) ).
tcf(c_412,negated_conjecture,
sK2 != sK3,
inference(demodulation,[status(thm)],[c_59]) ).
tcf(c_586,plain,
( ( sK4 = sK3 )
| ~ member(sK3,sK1)
| ~ member(sK4,sK1) ),
inference(superposition,[status(thm)],[c_411,c_406]) ).
tcf(c_588,plain,
sK4 = sK3,
inference(forward_subsumption_resolution,[status(thm)],[c_586,c_408,c_410]) ).
tcf(c_589,plain,
! [X0: $i] :
( apply(sK0,sK3,X0)
| ~ member(X0,sK1) ),
inference(demodulation,[status(thm)],[c_411,c_588]) ).
tcf(c_629,plain,
( ( sK2 = sK3 )
| ~ member(sK3,sK1)
| ~ member(sK2,sK1) ),
inference(superposition,[status(thm)],[c_589,c_407]) ).
tcf(c_633,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_629,c_412,c_408,c_409]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET804+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 12:00:04 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 1.73/1.28 % SZS status Started for theBenchmark.p
% 1.73/1.28 % SZS status Theorem for theBenchmark.p
% 1.73/1.28
% 1.73/1.28 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.73/1.28
% 1.73/1.28 % ------ iProver source info
% 1.73/1.28
% 1.73/1.28 % git: date: 2026-07-19 20:42:38 +0200
% 1.73/1.28 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.73/1.28 % git: non_committed_changes: false
% 1.73/1.28
% 1.73/1.28 % ------ Parsing...
% 1.73/1.28 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.73/1.28
% 1.73/1.28 % ------ 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 %
% 1.73/1.28
% 1.73/1.28 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.73/1.28
% 1.73/1.28 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.73/1.28 % ------ Proving...
% 1.73/1.28 % ------ Problem Properties
% 1.73/1.28
% 1.73/1.28 %
% 1.73/1.28 % clauses 10
% 1.73/1.28 % conjectures 1
% 1.73/1.28 % EPR 10
% 1.73/1.28 % Horn 10
% 1.73/1.28 % unary 4
% 1.73/1.28 % binary 2
% 1.73/1.28 % lits 25
% 1.73/1.28 % lits eq 4
% 1.73/1.28 % fd_pure 0
% 1.73/1.28 % fd_pseudo 0
% 1.73/1.28 % fd_cond 2
% 1.73/1.28 % fd_pseudo_cond 1
% 1.73/1.28 % AC symbols 0
% 1.73/1.28
% 1.73/1.28 % ------ Schedule dynamic 5 is on
% 1.73/1.28
% 1.73/1.28 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.73/1.28
% 1.73/1.28
% 1.73/1.28 % ------
% 1.73/1.28 % Current options:
% 1.73/1.28 % ------
% 1.73/1.28
% 1.73/1.28
% 1.73/1.28 %
% 1.73/1.28
% 1.73/1.28 % ------ Proving...
% 1.73/1.28 %
% 1.73/1.28
% 1.73/1.28 % SZS status Theorem for theBenchmark.p
% 1.73/1.28
% 1.73/1.28 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.73/1.28
% 1.73/1.28
%------------------------------------------------------------------------------