%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV390+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n001.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 03:17:31 PM UTC 2026
% Result : Theorem 1.05s 1.93s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 15 unt; 2 def)
% Number of atoms : 151 ( 7 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 140 ( 61 ~; 54 |; 11 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 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; 5 con; 0-3 aty)
% Number of variables : 179 ( 0 sgn 171 !; 8 ?; 60 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).
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/sandbox2/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/sandbox2/benchmark/Axioms/SWV007+3.ax',ax38) ).
fof(f30,axiom,
! [X0,X1,X2,X3] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax42) ).
fof(f42,axiom,
! [X0,X1,X2] :
( check_cpq(triple(X0,X1,X2))
<=> ! [X3,X4] :
( pair_in_list(X1,X3,X4)
=> less_than(X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l26_li4142) ).
fof(f43,conjecture,
! [X0,X1,X2] :
( ~ check_cpq(triple(X0,X1,X2))
=> ! [X3] : ~ check_cpq(insert_cpq(triple(X0,X1,X2),X3)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l26_co) ).
fof(f44,negated_conjecture,
~ ! [X0,X1,X2] :
( ~ check_cpq(triple(X0,X1,X2))
=> ! [X3] : ~ check_cpq(insert_cpq(triple(X0,X1,X2),X3)) ),
inference(negated_conjecture,[status(cth)],[f43]) ).
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(true_and_false_elimination,[],[f26]) ).
fof(f46,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(flattening,[],[f45]) ).
fof(f53,plain,
! [X0,X1] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f56,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f57,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(flattening,[],[f56]) ).
fof(f68,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(f69,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,[],[f46]) ).
fof(f83,plain,
! [X0,X1,X2] :
( check_cpq(triple(X0,X1,X2))
<=> ! [X3,X4] :
( ~ pair_in_list(X1,X3,X4)
| less_than(X4,X3) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f84,plain,
? [X0,X1,X2] :
( ~ check_cpq(triple(X0,X1,X2))
& ? [X3] : check_cpq(insert_cpq(triple(X0,X1,X2),X3)) ),
inference(ennf_transformation,[],[f44]) ).
fof(f89,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,[],[f68]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( ~ check_cpq(triple(X0,X1,X2))
| ! [X3,X4] :
( ~ pair_in_list(X1,X3,X4)
| less_than(X4,X3) ) )
& ( ? [X3,X4] :
( pair_in_list(X1,X3,X4)
& ~ less_than(X4,X3) )
| check_cpq(triple(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f83]) ).
fof(f92,plain,
! [X0,X1,X2] :
( ( ~ check_cpq(triple(X0,X1,X2))
| ! [X5,X6] :
( ~ pair_in_list(X1,X5,X6)
| less_than(X6,X5) ) )
& ( ? [X3,X4] :
( pair_in_list(X1,X3,X4)
& ~ less_than(X4,X3) )
| check_cpq(triple(X0,X1,X2)) ) ),
inference(rectify,[],[f91]) ).
fof(f93,plain,
! [X0,X1,X2] :
( ( ~ check_cpq(triple(X0,X1,X2))
| ! [X5,X6] :
( ~ pair_in_list(X1,X5,X6)
| less_than(X6,X5) ) )
& ( ( pair_in_list(X1,sK0(X1),sK1(X1))
& ~ less_than(sK1(X1),sK0(X1)) )
| check_cpq(triple(X0,X1,X2)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X3,sK0(X1)),skolemize(X4,sK1(X1))],[f92]) ).
fof(f94,plain,
( ~ check_cpq(triple(sK2,sK3,sK4))
& check_cpq(insert_cpq(triple(sK2,sK3,sK4),sK5)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4),skolemize(X3,sK5)],[f84]) ).
fof(f96,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f98,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f124,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,[],[f89]) ).
fof(f126,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,[],[f69]) ).
fof(f131,plain,
! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
inference(cnf_transformation,[],[f30]) ).
fof(f143,plain,
! [X2,X0,X1,X6,X5] :
( ~ check_cpq(triple(X0,X1,X2))
| ~ pair_in_list(X1,X5,X6)
| less_than(X6,X5) ),
inference(cnf_transformation,[],[f93]) ).
fof(f144,plain,
! [X2,X0,X1] :
( pair_in_list(X1,sK0(X1),sK1(X1))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f145,plain,
! [X2,X0,X1] :
( ~ less_than(sK1(X1),sK0(X1))
| check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f93]) ).
fof(f146,plain,
~ check_cpq(triple(sK2,sK3,sK4)),
inference(cnf_transformation,[],[f94]) ).
fof(f147,plain,
check_cpq(insert_cpq(triple(sK2,sK3,sK4),sK5)),
inference(cnf_transformation,[],[f94]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
tcf(c_79,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,[],[f124]) ).
tcf(c_80,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,[],[f126]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] : triple(insert_pqp(X0,X1),insert_slb(X2,pair(X1,bottom)),X3) = insert_cpq(triple(X0,X2,X3),X1),
inference(cnf_transformation,[],[f131]) ).
tcf(c_95,plain,
! [X0: $i,X1: $i,X2: $i] :
( check_cpq(triple(X1,X0,X2))
| ~ less_than(sK1(X0),sK0(X0)) ),
inference(cnf_transformation,[],[f145]) ).
tcf(c_96,plain,
! [X0: $i,X1: $i,X2: $i] :
( check_cpq(triple(X1,X0,X2))
| pair_in_list(X0,sK0(X0),sK1(X0)) ),
inference(cnf_transformation,[],[f144]) ).
tcf(c_97,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i] :
( less_than(X4,X3)
| ~ pair_in_list(X1,X3,X4)
| ~ check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_98,negated_conjecture,
check_cpq(insert_cpq(triple(sK2,sK3,sK4),sK5)),
inference(cnf_transformation,[],[f147]) ).
tcf(c_99,negated_conjecture,
~ check_cpq(triple(sK2,sK3,sK4)),
inference(cnf_transformation,[],[f146]) ).
tcf(c_133,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_52,c_50,c_52]) ).
tcf(c_134,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_133]) ).
tcf(c_550,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_80,c_134]) ).
tcf(c_551,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_550]) ).
tcf(c_585,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_79,c_551]) ).
tcf(c_938,definition,
iPr_def_10 = triple(sK2,sK3,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_939,definition,
iPr_def_11 = insert_cpq(iPr_def_10,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_940,negated_conjecture,
~ check_cpq(iPr_def_10),
inference(demodulation,[status(thm)],[c_99,c_938]) ).
tcf(c_941,negated_conjecture,
check_cpq(iPr_def_11),
inference(demodulation,[status(thm)],[c_98,c_939]) ).
tcf(c_1577,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( check_cpq(triple(insert_pqp(X0,X3),X1,X2))
| ~ check_cpq(insert_cpq(triple(X0,X1,X2),X3)) ),
inference(superposition,[status(thm)],[c_85,c_585]) ).
tcf(c_1936,plain,
! [X0: $i] :
( check_cpq(triple(insert_pqp(sK2,X0),sK3,sK4))
| ~ check_cpq(insert_cpq(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_938,c_1577]) ).
tcf(c_1948,plain,
( check_cpq(iPr_def_10)
| pair_in_list(sK3,sK0(sK3),sK1(sK3)) ),
inference(superposition,[status(thm)],[c_938,c_96]) ).
tcf(c_1951,plain,
pair_in_list(sK3,sK0(sK3),sK1(sK3)),
inference(forward_subsumption_resolution,[status(thm)],[c_1948,c_940]) ).
tcf(c_2478,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(X1,X0)
| ~ check_cpq(insert_cpq(iPr_def_10,X2))
| ~ pair_in_list(sK3,X0,X1) ),
inference(superposition,[status(thm)],[c_1936,c_97]) ).
tcf(c_4848,plain,
( check_cpq(triple(sK2,sK3,sK4))
| ~ less_than(sK1(sK3),sK0(sK3)) ),
inference(instantiation,[status(thm)],[c_95]) ).
tcf(c_5535,plain,
! [X0: $i] :
( less_than(sK1(sK3),sK0(sK3))
| ~ check_cpq(insert_cpq(iPr_def_10,X0)) ),
inference(superposition,[status(thm)],[c_1951,c_2478]) ).
tcf(c_5542,plain,
! [X0: $i] : ~ check_cpq(insert_cpq(iPr_def_10,X0)),
inference(global_subsumption_just,[status(thm)],[c_5535,c_99,c_4848,c_5535]) ).
tcf(c_5545,plain,
~ check_cpq(iPr_def_11),
inference(superposition,[status(thm)],[c_939,c_5542]) ).
tcf(c_5546,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5545,c_941]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV390+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.53 % Computer : n001.cluster.edu
% 0.10/0.53 % Model : x86_64 x86_64
% 0.10/0.53 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.53 % Memory : 8046.5625MB
% 0.10/0.53 % OS : Linux 6.8.0-71-generic
% 0.10/0.54 % CPULimit : 300
% 0.10/0.54 % WCLimit : 300
% 0.10/0.54 % DateTime : Thu Sep 24 19:33:26 UTC 2026
% 0.10/0.54 % CPUTime :
% 0.10/0.54 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.57 Running first-order theorem proving
% 0.14/0.57 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
% 0.14/0.58
% 0.14/0.58 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.58
% 0.14/0.58 % Detected problem language: tptp
% 0.14/0.59 % Proving...
% 1.05/1.93 % SZS status Started for theBenchmark.p
% 1.05/1.93 % SZS status Theorem for theBenchmark.p
% 1.05/1.93
% 1.05/1.93 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.05/1.93
% 1.05/1.93 % ------ iProver source info
% 1.05/1.93
% 1.05/1.93 % git: date: 2026-07-19 20:42:38 +0200
% 1.05/1.93 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.05/1.93 % git: non_committed_changes: false
% 1.05/1.93
% 1.05/1.93 % ------ Parsing...
% 1.05/1.93 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.05/1.93
% 1.05/1.93 % ------ Preprocessing... sup_sim: 0 sf_s rm: 7 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 %
% 1.05/1.93
% 1.05/1.93 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.05/1.93
% 1.05/1.93 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.05/1.93 % ------ Proving...
% 1.05/1.93 % ------ Problem Properties
% 1.05/1.93
% 1.05/1.93 %
% 1.05/1.93 % clauses 46
% 1.05/1.93 % conjectures 2
% 1.05/1.93 % EPR 8
% 1.05/1.93 % Horn 31
% 1.05/1.93 % unary 19
% 1.05/1.93 % binary 14
% 1.05/1.93 % lits 87
% 1.05/1.93 % lits eq 30
% 1.05/1.93 % fd_pure 0
% 1.05/1.93 % fd_pseudo 0
% 1.05/1.93 % fd_cond 5
% 1.05/1.93 % fd_pseudo_cond 5
% 1.05/1.93 % AC symbols 0
% 1.05/1.93
% 1.05/1.93 % ------ Schedule dynamic 5 is on
% 1.05/1.93
% 1.05/1.93 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.05/1.93
% 1.05/1.93
% 1.05/1.93 % ------
% 1.05/1.93 % Current options:
% 1.05/1.93 % ------
% 1.05/1.93
% 1.05/1.93
% 1.05/1.93 %
% 1.05/1.93
% 1.05/1.93 % ------ Proving...
% 1.05/1.93 %
% 1.05/1.93
% 1.05/1.93 % SZS status Theorem for theBenchmark.p
% 1.05/1.93
% 1.05/1.93 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.05/1.93
% 1.05/1.93
%------------------------------------------------------------------------------