%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET790+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 : n007.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 0.44s 1.29s
% Output : CNFRefutation 0.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 3
% Syntax : Number of formulae : 47 ( 14 unt; 0 def)
% Number of atoms : 191 ( 35 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 230 ( 86 ~; 79 |; 39 &)
% ( 3 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 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 : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 118 ( 0 sgn 110 !; 8 ?; 39 :)
% 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(f11,conjecture,
! [X0,X1,X2] :
( ( least(X2,X0,X1)
& order(X0,X1) )
=> ! [X3] :
( least(X3,X0,X1)
=> X2 = X3 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thIV2) ).
fof(f12,negated_conjecture,
~ ! [X0,X1,X2] :
( ( least(X2,X0,X1)
& order(X0,X1) )
=> ! [X3] :
( least(X3,X0,X1)
=> X2 = X3 ) ),
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] :
( least(X2,X0,X1)
=> ( ! [X3] :
( member(X3,X1)
=> apply(X0,X2,X3) )
& member(X2,X1) ) ),
inference(unused_predicate_definition_removal,[],[f6]) ).
fof(f15,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(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(ennf_transformation,[],[f15]) ).
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(flattening,[],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ least(X2,X0,X1)
| ( ! [X3] :
( ~ member(X3,X1)
| apply(X0,X2,X3) )
& member(X2,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f19,plain,
? [X0,X1,X2] :
( least(X2,X0,X1)
& order(X0,X1)
& ? [X3] :
( least(X3,X0,X1)
& X2 != X3 ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f20,plain,
? [X0,X1,X2] :
( least(X2,X0,X1)
& order(X0,X1)
& ? [X3] :
( least(X3,X0,X1)
& X2 != X3 ) ),
inference(flattening,[],[f19]) ).
fof(f21,plain,
( least(sK2,sK0,sK1)
& order(sK0,sK1)
& least(sK3,sK0,sK1)
& sK2 != sK3 ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f20]) ).
fof(f23,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,[],[f17]) ).
fof(f25,plain,
! [X2,X3,X0,X1] :
( ~ least(X2,X0,X1)
| ~ member(X3,X1)
| apply(X0,X2,X3) ),
inference(cnf_transformation,[],[f18]) ).
fof(f26,plain,
! [X2,X0,X1] :
( ~ least(X2,X0,X1)
| member(X2,X1) ),
inference(cnf_transformation,[],[f18]) ).
fof(f27,plain,
least(sK2,sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f28,plain,
order(sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f29,plain,
least(sK3,sK0,sK1),
inference(cnf_transformation,[],[f21]) ).
fof(f30,plain,
sK2 != sK3,
inference(cnf_transformation,[],[f21]) ).
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,[],[f23]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ~ least(X0,X1,X2) ),
inference(cnf_transformation,[],[f26]) ).
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,[],[f25]) ).
tcf(c_54,negated_conjecture,
sK2 != sK3,
inference(cnf_transformation,[],[f30]) ).
tcf(c_55,negated_conjecture,
least(sK3,sK0,sK1),
inference(cnf_transformation,[],[f29]) ).
tcf(c_56,negated_conjecture,
order(sK0,sK1),
inference(cnf_transformation,[],[f28]) ).
tcf(c_57,negated_conjecture,
least(sK2,sK0,sK1),
inference(cnf_transformation,[],[f27]) ).
tcf(c_157,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_55]) ).
tcf(c_158,plain,
! [X0: $i] :
( apply(sK0,sK3,X0)
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_157]) ).
tcf(c_166,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_55]) ).
tcf(c_167,plain,
member(sK3,sK1),
inference(unflattening,[status(thm)],[c_166]) ).
tcf(c_171,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( apply(X1,X0,X3)
| ~ member(X3,X2)
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_53,c_57]) ).
tcf(c_172,plain,
! [X0: $i] :
( apply(sK0,sK2,X0)
| ~ member(X0,sK1) ),
inference(unflattening,[status(thm)],[c_171]) ).
tcf(c_180,plain,
! [X0: $i,X1: $i,X2: $i] :
( member(X0,X2)
| ( X2 != sK1 )
| ( X1 != sK0 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_57]) ).
tcf(c_181,plain,
member(sK2,sK1),
inference(unflattening,[status(thm)],[c_180]) ).
tcf(c_200,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 != sK1 )
| ( X0 != sK0 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_56]) ).
tcf(c_201,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X1,sK1)
| ~ member(X0,sK1)
| ~ apply(sK0,X1,X0)
| ~ apply(sK0,X0,X1) ),
inference(unflattening,[status(thm)],[c_200]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i] :
( ( X0 = X1 )
| ~ member(X1,sK1)
| ~ member(X0,sK1)
| ~ apply(sK0,X1,X0)
| ~ apply(sK0,X0,X1) ),
inference(demodulation,[status(thm)],[c_201]) ).
tcf(c_331,plain,
member(sK2,sK1),
inference(demodulation,[status(thm)],[c_181]) ).
tcf(c_332,plain,
! [X0: $i] :
( apply(sK0,sK2,X0)
| ~ member(X0,sK1) ),
inference(demodulation,[status(thm)],[c_172]) ).
tcf(c_333,plain,
member(sK3,sK1),
inference(demodulation,[status(thm)],[c_167]) ).
tcf(c_334,plain,
! [X0: $i] :
( apply(sK0,sK3,X0)
| ~ member(X0,sK1) ),
inference(demodulation,[status(thm)],[c_158]) ).
tcf(c_335,negated_conjecture,
sK2 != sK3,
inference(demodulation,[status(thm)],[c_54]) ).
tcf(c_494,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ member(sK2,sK1)
| ~ member(X0,sK1)
| ~ apply(sK0,X0,sK2) ),
inference(superposition,[status(thm)],[c_332,c_329]) ).
tcf(c_496,plain,
! [X0: $i] :
( ( X0 = sK2 )
| ~ member(X0,sK1)
| ~ apply(sK0,X0,sK2) ),
inference(forward_subsumption_resolution,[status(thm)],[c_494,c_331]) ).
tcf(c_537,plain,
( ( sK2 = sK3 )
| ~ member(sK3,sK1)
| ~ member(sK2,sK1) ),
inference(superposition,[status(thm)],[c_334,c_496]) ).
tcf(c_540,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_537,c_335,c_333,c_331]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET790+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n007.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 11:56:07 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 0.44/1.29 % SZS status Started for theBenchmark.p
% 0.44/1.29 % SZS status Theorem for theBenchmark.p
% 0.44/1.29
% 0.44/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.44/1.29
% 0.44/1.29 % ------ iProver source info
% 0.44/1.29
% 0.44/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 0.44/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.44/1.29 % git: non_committed_changes: false
% 0.44/1.29
% 0.44/1.29 % ------ Parsing...
% 0.44/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.44/1.29
% 0.44/1.29 % ------ 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: 3 0s sf_e pe_s pe_e %
% 0.44/1.29
% 0.44/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.44/1.29
% 0.44/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.44/1.29 % ------ Proving...
% 0.44/1.29 % ------ Problem Properties
% 0.44/1.29
% 0.44/1.29 %
% 0.44/1.29 % clauses 8
% 0.44/1.29 % conjectures 1
% 0.44/1.29 % EPR 8
% 0.44/1.29 % Horn 8
% 0.44/1.29 % unary 3
% 0.44/1.29 % binary 3
% 0.44/1.29 % lits 20
% 0.44/1.29 % lits eq 2
% 0.44/1.29 % fd_pure 0
% 0.44/1.29 % fd_pseudo 0
% 0.44/1.29 % fd_cond 0
% 0.44/1.29 % fd_pseudo_cond 1
% 0.44/1.29 % AC symbols 0
% 0.44/1.29
% 0.44/1.29 % ------ Schedule dynamic 5 is on
% 0.44/1.29
% 0.44/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.44/1.29
% 0.44/1.29
% 0.44/1.29 % ------
% 0.44/1.29 % Current options:
% 0.44/1.29 % ------
% 0.44/1.29
% 0.44/1.29
% 0.44/1.29 %
% 0.44/1.29
% 0.44/1.29 % ------ Proving...
% 0.44/1.29 %
% 0.44/1.29
% 0.44/1.29 % SZS status Theorem for theBenchmark.p
% 0.44/1.29
% 0.44/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.44/1.29
% 0.44/1.29
%------------------------------------------------------------------------------