%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SET776+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n016.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 02:48:33 PM UTC 2026
% Result : Theorem 1.76s 1.29s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 2
% Syntax : Number of formulae : 62 ( 30 unt; 0 def)
% Number of atoms : 283 ( 2 equ)
% Maximal formula atoms : 17 ( 4 avg)
% Number of connectives : 334 ( 113 ~; 103 |; 94 &)
% ( 6 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 7 con; 0-0 aty)
% Number of variables : 132 ( 0 sgn 97 !; 35 ?; 28 :)
% Comments :
%------------------------------------------------------------------------------
fof(f16,axiom,
! [X0,X1] :
( pre_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] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET006+2.ax',pre_order) ).
fof(f17,conjecture,
! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( member(X4,X0)
& member(X3,X0) )
=> ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) ) )
& pre_order(X1,X0) )
=> ! [X5,X6,X7,X8] :
( ( member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7) )
=> apply(X1,X7,X8) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',thIII12) ).
fof(f18,negated_conjecture,
~ ! [X0,X1,X2] :
( ( ! [X3,X4] :
( ( member(X4,X0)
& member(X3,X0) )
=> ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) ) )
& pre_order(X1,X0) )
=> ! [X5,X6,X7,X8] :
( ( member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0) )
=> ( ( apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7) )
=> apply(X1,X7,X8) ) ) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f21,plain,
! [X0,X1] :
( pre_order(X0,X1)
<=> ( ! [X3,X4,X5] :
( ( member(X5,X1)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X4) )
=> apply(X0,X3,X5) ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
inference(rectify,[],[f16]) ).
fof(f22,plain,
! [X0,X1] :
( pre_order(X0,X1)
=> ( ! [X3,X4,X5] :
( ( member(X5,X1)
& member(X4,X1)
& member(X3,X1) )
=> ( ( apply(X0,X4,X5)
& apply(X0,X3,X4) )
=> apply(X0,X3,X5) ) )
& ! [X2] :
( member(X2,X1)
=> apply(X0,X2,X2) ) ) ),
inference(unused_predicate_definition_removal,[],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ pre_order(X0,X1)
| ( ! [X3,X4,X5] :
( ~ member(X5,X1)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X4)
| apply(X0,X3,X5) )
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f26,plain,
! [X0,X1] :
( ~ pre_order(X0,X1)
| ( ! [X3,X4,X5] :
( ~ member(X5,X1)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X4)
| apply(X0,X3,X5) )
& ! [X2] :
( ~ member(X2,X1)
| apply(X0,X2,X2) ) ) ),
inference(flattening,[],[f25]) ).
fof(f27,plain,
? [X0,X1,X2] :
( ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) ) )
& pre_order(X1,X0)
& ? [X5,X6,X7,X8] :
( member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& ~ apply(X1,X7,X8) ) ),
inference(ennf_transformation,[],[f18]) ).
fof(f28,plain,
? [X0,X1,X2] :
( ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ( apply(X2,X3,X4)
<=> ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) ) )
& pre_order(X1,X0)
& ? [X5,X6,X7,X8] :
( member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& ~ apply(X1,X7,X8) ) ),
inference(flattening,[],[f27]) ).
fof(f50,plain,
? [X0,X1,X2] :
( ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ( ( ~ apply(X2,X3,X4)
| ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) )
& ( ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| apply(X2,X3,X4) ) ) )
& pre_order(X1,X0)
& ? [X5,X6,X7,X8] :
( member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& ~ apply(X1,X7,X8) ) ),
inference(nnf_transformation,[],[f28]) ).
fof(f51,plain,
? [X0,X1,X2] :
( ! [X3,X4] :
( ~ member(X4,X0)
| ~ member(X3,X0)
| ( ( ~ apply(X2,X3,X4)
| ( apply(X1,X4,X3)
& apply(X1,X3,X4) ) )
& ( ~ apply(X1,X4,X3)
| ~ apply(X1,X3,X4)
| apply(X2,X3,X4) ) ) )
& pre_order(X1,X0)
& ? [X5,X6,X7,X8] :
( member(X8,X0)
& member(X7,X0)
& member(X6,X0)
& member(X5,X0)
& apply(X1,X5,X6)
& apply(X2,X6,X8)
& apply(X2,X5,X7)
& ~ apply(X1,X7,X8) ) ),
inference(flattening,[],[f50]) ).
fof(f52,plain,
? [X0,X1,X2] :
( ! [X7,X8] :
( ~ member(X8,X0)
| ~ member(X7,X0)
| ( ( ~ apply(X2,X7,X8)
| ( apply(X1,X8,X7)
& apply(X1,X7,X8) ) )
& ( ~ apply(X1,X8,X7)
| ~ apply(X1,X7,X8)
| apply(X2,X7,X8) ) ) )
& pre_order(X1,X0)
& ? [X3,X4,X5,X6] :
( member(X6,X0)
& member(X5,X0)
& member(X4,X0)
& member(X3,X0)
& apply(X1,X3,X4)
& apply(X2,X4,X6)
& apply(X2,X3,X5)
& ~ apply(X1,X5,X6) ) ),
inference(rectify,[],[f51]) ).
fof(f53,plain,
( ! [X7,X8] :
( ~ member(X8,sK3)
| ~ member(X7,sK3)
| ( ( ~ apply(sK5,X7,X8)
| ( apply(sK4,X8,X7)
& apply(sK4,X7,X8) ) )
& ( ~ apply(sK4,X8,X7)
| ~ apply(sK4,X7,X8)
| apply(sK5,X7,X8) ) ) )
& pre_order(sK4,sK3)
& member(sK9,sK3)
& member(sK8,sK3)
& member(sK7,sK3)
& member(sK6,sK3)
& apply(sK4,sK6,sK7)
& apply(sK5,sK7,sK9)
& apply(sK5,sK6,sK8)
& ~ apply(sK4,sK8,sK9) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5,sK6,sK7,sK8,sK9]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5),skolemize(X3,sK6),skolemize(X4,sK7),skolemize(X5,sK8),skolemize(X6,sK9)],[f52]) ).
fof(f83,plain,
! [X3,X0,X1,X4,X5] :
( ~ pre_order(X0,X1)
| ~ member(X5,X1)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ apply(X0,X4,X5)
| ~ apply(X0,X3,X4)
| apply(X0,X3,X5) ),
inference(cnf_transformation,[],[f26]) ).
fof(f85,plain,
! [X8,X7] :
( ~ member(X8,sK3)
| ~ member(X7,sK3)
| ~ apply(sK5,X7,X8)
| apply(sK4,X8,X7) ),
inference(cnf_transformation,[],[f53]) ).
fof(f86,plain,
! [X8,X7] :
( ~ member(X8,sK3)
| ~ member(X7,sK3)
| ~ apply(sK5,X7,X8)
| apply(sK4,X7,X8) ),
inference(cnf_transformation,[],[f53]) ).
fof(f88,plain,
pre_order(sK4,sK3),
inference(cnf_transformation,[],[f53]) ).
fof(f89,plain,
member(sK9,sK3),
inference(cnf_transformation,[],[f53]) ).
fof(f90,plain,
member(sK8,sK3),
inference(cnf_transformation,[],[f53]) ).
fof(f91,plain,
member(sK7,sK3),
inference(cnf_transformation,[],[f53]) ).
fof(f92,plain,
member(sK6,sK3),
inference(cnf_transformation,[],[f53]) ).
fof(f93,plain,
apply(sK4,sK6,sK7),
inference(cnf_transformation,[],[f53]) ).
fof(f94,plain,
apply(sK5,sK7,sK9),
inference(cnf_transformation,[],[f53]) ).
fof(f95,plain,
apply(sK5,sK6,sK8),
inference(cnf_transformation,[],[f53]) ).
fof(f96,plain,
~ apply(sK4,sK8,sK9),
inference(cnf_transformation,[],[f53]) ).
tcf(c_79,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,X1,X3)
| ~ pre_order(X0,X4)
| ~ member(X3,X4)
| ~ member(X2,X4)
| ~ member(X1,X4)
| ~ apply(X0,X2,X3)
| ~ apply(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_80,negated_conjecture,
~ apply(sK4,sK8,sK9),
inference(cnf_transformation,[],[f96]) ).
tcf(c_81,negated_conjecture,
apply(sK5,sK6,sK8),
inference(cnf_transformation,[],[f95]) ).
tcf(c_82,negated_conjecture,
apply(sK5,sK7,sK9),
inference(cnf_transformation,[],[f94]) ).
tcf(c_83,negated_conjecture,
apply(sK4,sK6,sK7),
inference(cnf_transformation,[],[f93]) ).
tcf(c_84,negated_conjecture,
member(sK6,sK3),
inference(cnf_transformation,[],[f92]) ).
tcf(c_85,negated_conjecture,
member(sK7,sK3),
inference(cnf_transformation,[],[f91]) ).
tcf(c_86,negated_conjecture,
member(sK8,sK3),
inference(cnf_transformation,[],[f90]) ).
tcf(c_87,negated_conjecture,
member(sK9,sK3),
inference(cnf_transformation,[],[f89]) ).
tcf(c_88,negated_conjecture,
pre_order(sK4,sK3),
inference(cnf_transformation,[],[f88]) ).
tcf(c_90,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK4,X0,X1)
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| ~ apply(sK5,X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_91,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK4,X1,X0)
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| ~ apply(sK5,X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_614,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( apply(X0,X2,X4)
| ~ member(X4,X1)
| ~ member(X3,X1)
| ~ member(X2,X1)
| ~ apply(X0,X3,X4)
| ~ apply(X0,X2,X3)
| ( X1 != sK3 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_79,c_88]) ).
tcf(c_615,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(sK4,X0,X2)
| ~ member(X2,sK3)
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| ~ apply(sK4,X1,X2)
| ~ apply(sK4,X0,X1) ),
inference(unflattening,[status(thm)],[c_614]) ).
tcf(c_1247,plain,
! [X0: $i,X1: $i,X2: $i] :
( apply(sK4,X0,X2)
| ~ member(X2,sK3)
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| ~ apply(sK4,X1,X2)
| ~ apply(sK4,X0,X1) ),
inference(demodulation,[status(thm)],[c_615]) ).
tcf(c_1248,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK4,X1,X0)
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| ~ apply(sK5,X0,X1) ),
inference(demodulation,[status(thm)],[c_91]) ).
tcf(c_1249,negated_conjecture,
! [X0: $i,X1: $i] :
( apply(sK4,X0,X1)
| ~ member(X1,sK3)
| ~ member(X0,sK3)
| ~ apply(sK5,X0,X1) ),
inference(demodulation,[status(thm)],[c_90]) ).
tcf(c_1251,negated_conjecture,
member(sK9,sK3),
inference(demodulation,[status(thm)],[c_87]) ).
tcf(c_1252,negated_conjecture,
member(sK8,sK3),
inference(demodulation,[status(thm)],[c_86]) ).
tcf(c_1253,negated_conjecture,
member(sK7,sK3),
inference(demodulation,[status(thm)],[c_85]) ).
tcf(c_1254,negated_conjecture,
member(sK6,sK3),
inference(demodulation,[status(thm)],[c_84]) ).
tcf(c_1255,negated_conjecture,
apply(sK4,sK6,sK7),
inference(demodulation,[status(thm)],[c_83]) ).
tcf(c_1256,negated_conjecture,
apply(sK5,sK7,sK9),
inference(demodulation,[status(thm)],[c_82]) ).
tcf(c_1257,negated_conjecture,
apply(sK5,sK6,sK8),
inference(demodulation,[status(thm)],[c_81]) ).
tcf(c_1258,negated_conjecture,
~ apply(sK4,sK8,sK9),
inference(demodulation,[status(thm)],[c_80]) ).
tcf(c_1996,plain,
( apply(sK4,sK8,sK6)
| ~ member(sK6,sK3)
| ~ member(sK8,sK3) ),
inference(superposition,[status(thm)],[c_1257,c_1248]) ).
tcf(c_1999,plain,
apply(sK4,sK8,sK6),
inference(forward_subsumption_resolution,[status(thm)],[c_1996,c_1254,c_1252]) ).
tcf(c_2009,plain,
( apply(sK4,sK7,sK9)
| ~ member(sK7,sK3)
| ~ member(sK9,sK3) ),
inference(superposition,[status(thm)],[c_1256,c_1249]) ).
tcf(c_2010,plain,
apply(sK4,sK7,sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_2009,c_1253,c_1251]) ).
tcf(c_2056,plain,
! [X0: $i] :
( apply(sK4,sK6,X0)
| ~ member(sK7,sK3)
| ~ member(sK6,sK3)
| ~ member(X0,sK3)
| ~ apply(sK4,sK7,X0) ),
inference(superposition,[status(thm)],[c_1255,c_1247]) ).
tcf(c_2058,plain,
! [X0: $i] :
( apply(sK4,sK8,X0)
| ~ member(sK6,sK3)
| ~ member(sK8,sK3)
| ~ member(X0,sK3)
| ~ apply(sK4,sK6,X0) ),
inference(superposition,[status(thm)],[c_1999,c_1247]) ).
tcf(c_2074,plain,
! [X0: $i] :
( apply(sK4,sK8,X0)
| ~ member(X0,sK3)
| ~ apply(sK4,sK6,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2058,c_1254,c_1252]) ).
tcf(c_2078,plain,
! [X0: $i] :
( apply(sK4,sK6,X0)
| ~ member(X0,sK3)
| ~ apply(sK4,sK7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[c_2056,c_1253,c_1254]) ).
tcf(c_2345,plain,
( apply(sK4,sK6,sK9)
| ~ member(sK9,sK3) ),
inference(superposition,[status(thm)],[c_2010,c_2078]) ).
tcf(c_2347,plain,
apply(sK4,sK6,sK9),
inference(forward_subsumption_resolution,[status(thm)],[c_2345,c_1251]) ).
tcf(c_2350,plain,
( apply(sK4,sK8,sK9)
| ~ member(sK9,sK3) ),
inference(superposition,[status(thm)],[c_2347,c_2074]) ).
tcf(c_2351,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2350,c_1258,c_1251]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET776+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.36 % Computer : n016.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Thu Sep 24 11:59:57 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.12/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.40 Running first-order theorem proving
% 0.12/0.40 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
% 0.12/0.42
% 0.12/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.42
% 0.12/0.42 % Detected problem language: tptp
% 0.12/0.43 % Proving...
% 1.76/1.29 % SZS status Started for theBenchmark.p
% 1.76/1.29 % SZS status Theorem for theBenchmark.p
% 1.76/1.29
% 1.76/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.76/1.29
% 1.76/1.29 % ------ iProver source info
% 1.76/1.29
% 1.76/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 1.76/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.76/1.29 % git: non_committed_changes: false
% 1.76/1.29
% 1.76/1.29 % ------ Parsing...
% 1.76/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.76/1.29
% 1.76/1.29 % ------ 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 %
% 1.76/1.29
% 1.76/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.76/1.29
% 1.76/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.76/1.29 % ------ Proving...
% 1.76/1.29 % ------ Problem Properties
% 1.76/1.29
% 1.76/1.29 %
% 1.76/1.29 % clauses 42
% 1.76/1.29 % conjectures 11
% 1.76/1.29 % EPR 15
% 1.76/1.29 % Horn 37
% 1.76/1.29 % unary 12
% 1.76/1.29 % binary 18
% 1.76/1.29 % lits 91
% 1.76/1.29 % lits eq 3
% 1.76/1.29 % fd_pure 0
% 1.76/1.29 % fd_pseudo 0
% 1.76/1.29 % fd_cond 0
% 1.76/1.29 % fd_pseudo_cond 2
% 1.76/1.29 % AC symbols 0
% 1.76/1.29
% 1.76/1.29 % ------ Schedule dynamic 5 is on
% 1.76/1.29
% 1.76/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.76/1.29
% 1.76/1.29
% 1.76/1.29 % ------
% 1.76/1.29 % Current options:
% 1.76/1.29 % ------
% 1.76/1.29
% 1.76/1.29
% 1.76/1.29 %
% 1.76/1.29
% 1.76/1.29 % ------ Proving...
% 1.76/1.29 %
% 1.76/1.29
% 1.76/1.29 % SZS status Theorem for theBenchmark.p
% 1.76/1.29
% 1.76/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.76/1.29
% 1.76/1.29
%------------------------------------------------------------------------------