%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV406+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n002.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 03:17:33 PM UTC 2026
% Result : Theorem 3.70s 1.18s
% Output : CNFRefutation 3.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 6
% Syntax : Number of formulae : 96 ( 11 unt; 0 def)
% Number of atoms : 273 ( 31 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 299 ( 122 ~; 129 |; 26 &)
% ( 10 <=>; 11 =>; 0 <=; 1 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 3 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 9 con; 0-3 aty)
% Number of variables : 259 ( 0 sgn 236 !; 23 ?; 74 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',totality) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( ~ less_than(X1,X0)
& less_than(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
<=> ( ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax23) ).
fof(f25,axiom,
! [X0,X1,X2,X3,X4] :
( less_than(X4,X3)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> check_cpq(triple(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax37) ).
fof(f26,axiom,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax38) ).
fof(f42,conjecture,
! [X0] :
( ! [X1,X2] :
( check_cpq(triple(X1,X0,X2))
<=> ! [X3,X4] :
( pair_in_list(X0,X3,X4)
=> less_than(X4,X3) ) )
=> ! [X5,X6,X7,X8] :
( check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6))
<=> ! [X9,X10] :
( pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10)
=> less_than(X10,X9) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l42_co) ).
fof(f43,negated_conjecture,
~ ! [X0] :
( ! [X1,X2] :
( check_cpq(triple(X1,X0,X2))
<=> ! [X3,X4] :
( pair_in_list(X0,X3,X4)
=> less_than(X4,X3) ) )
=> ! [X5,X6,X7,X8] :
( check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6))
<=> ! [X9,X10] :
( pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10)
=> less_than(X10,X9) ) ) ),
inference(negated_conjecture,[status(cth)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(true_and_false_elimination,[],[f26]) ).
fof(f45,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(flattening,[],[f44]) ).
fof(f50,plain,
! [X0,X1] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f51,plain,
? [X0] :
( ! [X1,X2] :
( check_cpq(triple(X1,X0,X2))
<=> ! [X3,X4] :
( ~ pair_in_list(X0,X3,X4)
| less_than(X4,X3) ) )
& ? [X5,X6,X7,X8] :
( check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6))
<~> ! [X9,X10] :
( ~ pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10)
| less_than(X10,X9) ) ) ),
inference(ennf_transformation,[],[f43]) ).
fof(f54,plain,
! [X0,X1,X2,X3,X4] :
( ~ strictly_less_than(X3,X4)
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(ennf_transformation,[],[f45]) ).
fof(f55,plain,
! [X0,X1,X2,X3,X4] :
( ~ less_than(X4,X3)
| ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> check_cpq(triple(X0,X1,X2)) ) ),
inference(ennf_transformation,[],[f25]) ).
fof(f59,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(ennf_transformation,[],[f50]) ).
fof(f60,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(flattening,[],[f59]) ).
fof(f72,plain,
? [X0] :
( ! [X1,X2] :
( ( ~ check_cpq(triple(X1,X0,X2))
| ! [X3,X4] :
( ~ pair_in_list(X0,X3,X4)
| less_than(X4,X3) ) )
& ( ? [X3,X4] :
( pair_in_list(X0,X3,X4)
& ~ less_than(X4,X3) )
| check_cpq(triple(X1,X0,X2)) ) )
& ? [X5,X6,X7,X8] :
( ( check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6))
| ! [X9,X10] :
( ~ pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10)
| less_than(X10,X9) ) )
& ( ~ check_cpq(triple(X5,insert_slb(X0,pair(X7,X8)),X6))
| ? [X9,X10] :
( pair_in_list(insert_slb(X0,pair(X7,X8)),X9,X10)
& ~ less_than(X10,X9) ) ) ) ),
inference(nnf_transformation,[],[f51]) ).
fof(f73,plain,
? [X0] :
( ! [X9,X10] :
( ( ~ check_cpq(triple(X9,X0,X10))
| ! [X13,X14] :
( ~ pair_in_list(X0,X13,X14)
| less_than(X14,X13) ) )
& ( ? [X11,X12] :
( pair_in_list(X0,X11,X12)
& ~ less_than(X12,X11) )
| check_cpq(triple(X9,X0,X10)) ) )
& ? [X1,X2,X3,X4] :
( ( check_cpq(triple(X1,insert_slb(X0,pair(X3,X4)),X2))
| ! [X7,X8] :
( ~ pair_in_list(insert_slb(X0,pair(X3,X4)),X7,X8)
| less_than(X8,X7) ) )
& ( ~ check_cpq(triple(X1,insert_slb(X0,pair(X3,X4)),X2))
| ? [X5,X6] :
( pair_in_list(insert_slb(X0,pair(X3,X4)),X5,X6)
& ~ less_than(X6,X5) ) ) ) ),
inference(rectify,[],[f72]) ).
fof(f74,plain,
( ! [X9,X10] :
( ( ~ check_cpq(triple(X9,sK0,X10))
| ! [X13,X14] :
( ~ pair_in_list(sK0,X13,X14)
| less_than(X14,X13) ) )
& ( ( pair_in_list(sK0,sK7,sK8)
& ~ less_than(sK8,sK7) )
| check_cpq(triple(X9,sK0,X10)) ) )
& ( check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2))
| ! [X7,X8] :
( ~ pair_in_list(insert_slb(sK0,pair(sK3,sK4)),X7,X8)
| less_than(X8,X7) ) )
& ( ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2))
| ( pair_in_list(insert_slb(sK0,pair(sK3,sK4)),sK5,sK6)
& ~ less_than(sK6,sK5) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X11,sK7),skolemize(X12,sK8)],[f73]) ).
fof(f77,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4) )
& ( ( ( X3 != X4
| X1 != X2 )
& ~ pair_in_list(X0,X2,X4) )
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f78,plain,
! [X0,X1,X2,X3,X4] :
( ( ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4) )
& ( ( ( X3 != X4
| X1 != X2 )
& ~ pair_in_list(X0,X2,X4) )
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(flattening,[],[f77]) ).
fof(f79,plain,
! [X0,X1,X2,X3,X4] :
( ~ less_than(X4,X3)
| ( ( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| check_cpq(triple(X0,X1,X2)) )
& ( ~ check_cpq(triple(X0,X1,X2))
| check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f80,plain,
! [X10,X9,X14,X13] :
( ~ check_cpq(triple(X9,sK0,X10))
| ~ pair_in_list(sK0,X13,X14)
| less_than(X14,X13) ),
inference(cnf_transformation,[],[f74]) ).
fof(f81,plain,
! [X10,X9] :
( pair_in_list(sK0,sK7,sK8)
| check_cpq(triple(X9,sK0,X10)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f82,plain,
! [X10,X9] :
( ~ less_than(sK8,sK7)
| check_cpq(triple(X9,sK0,X10)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f83,plain,
! [X8,X7] :
( check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2))
| ~ pair_in_list(insert_slb(sK0,pair(sK3,sK4)),X7,X8)
| less_than(X8,X7) ),
inference(cnf_transformation,[],[f74]) ).
fof(f84,plain,
( ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2))
| pair_in_list(insert_slb(sK0,pair(sK3,sK4)),sK5,sK6) ),
inference(cnf_transformation,[],[f74]) ).
fof(f85,plain,
( ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2))
| ~ less_than(sK6,sK5) ),
inference(cnf_transformation,[],[f74]) ).
fof(f87,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f92,plain,
! [X2,X3,X0,X1,X4] :
( ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X3 = X4
| pair_in_list(X0,X2,X4) ),
inference(cnf_transformation,[],[f78]) ).
fof(f93,plain,
! [X2,X3,X0,X1,X4] :
( ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X1 = X2
| pair_in_list(X0,X2,X4) ),
inference(cnf_transformation,[],[f78]) ).
fof(f94,plain,
! [X2,X3,X0,X1,X4] :
( X3 != X4
| X1 != X2
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
inference(cnf_transformation,[],[f78]) ).
fof(f95,plain,
! [X2,X3,X0,X1,X4] :
( ~ pair_in_list(X0,X2,X4)
| pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
inference(cnf_transformation,[],[f78]) ).
fof(f97,plain,
! [X2,X3,X0,X1,X4] :
( ~ strictly_less_than(X3,X4)
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(cnf_transformation,[],[f54]) ).
fof(f98,plain,
! [X2,X3,X0,X1,X4] :
( ~ less_than(X4,X3)
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f99,plain,
! [X2,X3,X0,X1,X4] :
( ~ less_than(X4,X3)
| ~ check_cpq(triple(X0,X1,X2))
| check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(cnf_transformation,[],[f79]) ).
fof(f104,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f120,plain,
! [X2,X3,X0,X4] :
( X3 != X4
| pair_in_list(insert_slb(X0,pair(X2,X3)),X2,X4) ),
inference(equality_resolution,[],[f94]) ).
fof(f121,plain,
! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
inference(equality_resolution,[],[f120]) ).
tcf(c_49,negated_conjecture,
( ~ less_than(sK6,sK5)
| ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_50,negated_conjecture,
( pair_in_list(insert_slb(sK0,pair(sK3,sK4)),sK5,sK6)
| ~ check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2))
| ~ pair_in_list(insert_slb(sK0,pair(sK3,sK4)),X0,X1) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_52,negated_conjecture,
! [X0: $i,X1: $i] :
( check_cpq(triple(X0,sK0,X1))
| ~ less_than(sK8,sK7) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_53,negated_conjecture,
! [X0: $i,X1: $i] :
( pair_in_list(sK0,sK7,sK8)
| check_cpq(triple(X0,sK0,X1)) ),
inference(cnf_transformation,[],[f81]) ).
tcf(c_54,negated_conjecture,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_than(X3,X2)
| ~ pair_in_list(sK0,X2,X3)
| ~ check_cpq(triple(X0,sK0,X1)) ),
inference(cnf_transformation,[],[f80]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( pair_in_list(insert_slb(X0,pair(X3,X4)),X1,X2)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[],[f95]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i,X2: $i] : pair_in_list(insert_slb(X0,pair(X1,X2)),X1,X2),
inference(cnf_transformation,[],[f121]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( pair_in_list(X0,X3,X4)
| ( X1 = X3 )
| ~ pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4) ),
inference(cnf_transformation,[],[f93]) ).
tcf(c_64,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( pair_in_list(X0,X3,X4)
| ( X2 = X4 )
| ~ pair_in_list(insert_slb(X0,pair(X1,X2)),X3,X4) ),
inference(cnf_transformation,[],[f92]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( ~ strictly_less_than(X2,X3)
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X2,X3)),X4)) ),
inference(cnf_transformation,[],[f97]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( check_cpq(triple(X0,insert_slb(X1,pair(X4,X3)),X2))
| ~ less_than(X3,X4)
| ~ check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f99]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( check_cpq(triple(X0,X1,X4))
| ~ less_than(X3,X2)
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X2,X3)),X4)) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f104]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_73,c_56,c_73]) ).
tcf(c_116,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_115]) ).
tcf(c_427,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i,X6: $i] :
( less_than(X3,X1)
| ~ check_cpq(triple(X4,insert_slb(X5,pair(X0,X2)),X6))
| ( X2 != X3 )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_66,c_116]) ).
tcf(c_428,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_than(X3,X2)
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X2,X3)),X4)) ),
inference(unflattening,[status(thm)],[c_427]) ).
tcf(c_457,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( check_cpq(triple(X0,X1,X4))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X2,X3)),X4)) ),
inference(backward_subsumption_resolution,[status(thm)],[c_68,c_428]) ).
tcf(c_738,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_10
| less_than(X1,X0)
| ~ pair_in_list(sK0,X0,X1) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_10])],[c_54]) ).
tcf(c_739,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ iPr_def_11
| ~ check_cpq(triple(X0,sK0,X1)) ),
inference(splitting,[splitting(split),new_symbols(definition,[iPr_def_11])],[c_54]) ).
tcf(c_740,negated_conjecture,
( iPr_def_11
| iPr_def_10 ),
inference(splitting,[splitting(split),new_symbols(definition,[])],[c_54]) ).
tcf(c_1247,plain,
( ~ iPr_def_11
| ~ less_than(sK8,sK7) ),
inference(superposition,[status(thm)],[c_52,c_739]) ).
tcf(c_1254,plain,
( pair_in_list(sK0,sK7,sK8)
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_53,c_739]) ).
tcf(c_1313,plain,
( less_than(sK4,sK3)
| check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)) ),
inference(superposition,[status(thm)],[c_62,c_51]) ).
tcf(c_1318,plain,
less_than(sK4,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_1313,c_428]) ).
tcf(c_1353,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2))
| ~ pair_in_list(sK0,X0,X1) ),
inference(superposition,[status(thm)],[c_61,c_51]) ).
tcf(c_1421,plain,
( less_than(sK8,sK7)
| check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2))
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_1254,c_1353]) ).
tcf(c_1425,plain,
( ~ iPr_def_11
| check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2)) ),
inference(global_subsumption_just,[status(thm)],[c_1421,c_1247,c_1421]) ).
tcf(c_1426,plain,
( check_cpq(triple(sK1,insert_slb(sK0,pair(sK3,sK4)),sK2))
| ~ iPr_def_11 ),
inference(renaming,[status(thm)],[c_1425]) ).
tcf(c_1433,plain,
( check_cpq(triple(sK1,sK0,sK2))
| ~ iPr_def_11 ),
inference(superposition,[status(thm)],[c_1426,c_457]) ).
tcf(c_1465,plain,
~ iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_1433,c_739]) ).
tcf(c_1466,plain,
iPr_def_10,
inference(backward_subsumption_resolution,[status(thm)],[c_740,c_1465]) ).
tcf(c_1863,plain,
( pair_in_list(insert_slb(sK0,pair(sK3,sK4)),sK5,sK6)
| ~ less_than(sK4,sK3)
| ~ check_cpq(triple(sK1,sK0,sK2)) ),
inference(superposition,[status(thm)],[c_67,c_50]) ).
tcf(c_1864,plain,
( ~ less_than(sK4,sK3)
| ~ less_than(sK6,sK5)
| ~ check_cpq(triple(sK1,sK0,sK2)) ),
inference(superposition,[status(thm)],[c_67,c_49]) ).
tcf(c_1867,plain,
( ~ less_than(sK6,sK5)
| ~ check_cpq(triple(sK1,sK0,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1864,c_1318]) ).
tcf(c_1870,plain,
( pair_in_list(insert_slb(sK0,pair(sK3,sK4)),sK5,sK6)
| ~ check_cpq(triple(sK1,sK0,sK2)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_1863,c_1318]) ).
tcf(c_1963,plain,
( less_than(sK6,sK5)
| ~ iPr_def_10
| ~ pair_in_list(sK0,sK5,sK6) ),
inference(instantiation,[status(thm)],[c_738]) ).
tcf(c_1964,plain,
( less_than(sK8,sK7)
| ~ iPr_def_10
| ~ pair_in_list(sK0,sK7,sK8) ),
inference(instantiation,[status(thm)],[c_738]) ).
tcf(c_1983,plain,
( pair_in_list(sK0,sK7,sK8)
| ~ less_than(sK6,sK5) ),
inference(superposition,[status(thm)],[c_53,c_1867]) ).
tcf(c_1984,plain,
( ~ less_than(sK8,sK7)
| ~ less_than(sK6,sK5) ),
inference(superposition,[status(thm)],[c_52,c_1867]) ).
tcf(c_1993,plain,
~ less_than(sK6,sK5),
inference(global_subsumption_just,[status(thm)],[c_1983,c_1466,c_1964,c_1984,c_1983]) ).
tcf(c_2316,plain,
( pair_in_list(sK0,sK5,sK6)
| ( sK6 = sK4 )
| ~ check_cpq(triple(sK1,sK0,sK2)) ),
inference(superposition,[status(thm)],[c_1870,c_64]) ).
tcf(c_2317,plain,
( pair_in_list(sK0,sK5,sK6)
| ( sK5 = sK3 )
| ~ check_cpq(triple(sK1,sK0,sK2)) ),
inference(superposition,[status(thm)],[c_1870,c_63]) ).
tcf(c_4239,plain,
( ~ check_cpq(triple(sK1,sK0,sK2))
| ( sK6 = sK4 ) ),
inference(global_subsumption_just,[status(thm)],[c_2316,c_1466,c_1963,c_1964,c_1984,c_1983,c_2316]) ).
tcf(c_4240,plain,
( ( sK6 = sK4 )
| ~ check_cpq(triple(sK1,sK0,sK2)) ),
inference(renaming,[status(thm)],[c_4239]) ).
tcf(c_4245,plain,
( pair_in_list(sK0,sK7,sK8)
| ( sK6 = sK4 ) ),
inference(superposition,[status(thm)],[c_53,c_4240]) ).
tcf(c_4246,plain,
( ( sK6 = sK4 )
| ~ less_than(sK8,sK7) ),
inference(superposition,[status(thm)],[c_52,c_4240]) ).
tcf(c_4251,plain,
sK6 = sK4,
inference(global_subsumption_just,[status(thm)],[c_4245,c_1466,c_1964,c_4246,c_4245]) ).
tcf(c_4277,plain,
~ less_than(sK4,sK5),
inference(demodulation,[status(thm)],[c_1993,c_4251]) ).
tcf(c_7021,plain,
( ~ check_cpq(triple(sK1,sK0,sK2))
| ( sK5 = sK3 ) ),
inference(global_subsumption_just,[status(thm)],[c_2317,c_1466,c_1963,c_1964,c_1984,c_1983,c_2317]) ).
tcf(c_7022,plain,
( ( sK5 = sK3 )
| ~ check_cpq(triple(sK1,sK0,sK2)) ),
inference(renaming,[status(thm)],[c_7021]) ).
tcf(c_7027,plain,
( pair_in_list(sK0,sK7,sK8)
| ( sK5 = sK3 ) ),
inference(superposition,[status(thm)],[c_53,c_7022]) ).
tcf(c_7028,plain,
( ( sK5 = sK3 )
| ~ less_than(sK8,sK7) ),
inference(superposition,[status(thm)],[c_52,c_7022]) ).
tcf(c_7033,plain,
sK5 = sK3,
inference(global_subsumption_just,[status(thm)],[c_7027,c_1466,c_1964,c_7028,c_7027]) ).
tcf(c_7056,plain,
~ less_than(sK4,sK3),
inference(demodulation,[status(thm)],[c_4277,c_7033]) ).
tcf(c_7059,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7056,c_1318]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV406+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.08/0.34 % Computer : n002.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Thu Sep 24 19:32:34 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.34 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.38 Running first-order theorem proving
% 0.12/0.38 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
% 0.12/0.39
% 0.12/0.39 % ======== iProver multi-core TPTP/SMT =========
% 0.12/0.39
% 0.12/0.39 % Detected problem language: tptp
% 0.12/0.41 % Proving...
% 3.70/1.18 % SZS status Started for theBenchmark.p
% 3.70/1.18 % SZS status Theorem for theBenchmark.p
% 3.70/1.18
% 3.70/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.70/1.18
% 3.70/1.18 % ------ iProver source info
% 3.70/1.18
% 3.70/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.70/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.70/1.18 % git: non_committed_changes: false
% 3.70/1.18
% 3.70/1.18 % ------ Parsing...
% 3.70/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.70/1.18
% 3.70/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 3.70/1.18
% 3.70/1.18 % ------ Preprocessing... gs_s sp: 2 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.70/1.18
% 3.70/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.70/1.18 % ------ Proving...
% 3.70/1.18 % ------ Problem Properties
% 3.70/1.18
% 3.70/1.18 %
% 3.70/1.18 % clauses 37
% 3.70/1.18 % conjectures 8
% 3.70/1.18 % EPR 8
% 3.70/1.18 % Horn 23
% 3.70/1.18 % unary 11
% 3.70/1.18 % binary 15
% 3.70/1.18 % lits 75
% 3.70/1.18 % lits eq 20
% 3.70/1.18 % fd_pure 0
% 3.70/1.18 % fd_pseudo 0
% 3.70/1.18 % fd_cond 4
% 3.70/1.18 % fd_pseudo_cond 4
% 3.70/1.18 % AC symbols 0
% 3.70/1.18
% 3.70/1.18 % ------ Schedule dynamic 5 is on
% 3.70/1.18
% 3.70/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.70/1.18
% 3.70/1.18
% 3.70/1.18 % ------
% 3.70/1.18 % Current options:
% 3.70/1.18 % ------
% 3.70/1.18
% 3.70/1.18
% 3.70/1.18 %
% 3.70/1.18
% 3.70/1.18 % ------ Proving...
% 3.70/1.18 %
% 3.70/1.18
% 3.70/1.18 % SZS status Theorem for theBenchmark.p
% 3.70/1.18
% 3.70/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.70/1.19
% 3.70/1.19
%------------------------------------------------------------------------------