%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV408+2 : 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 : n020.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 03:17:34 PM UTC 2026
% Result : Theorem 3.23s 1.18s
% Output : CNFRefutation 3.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 8 unt; 0 def)
% Number of atoms : 119 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 128 ( 54 ~; 48 |; 20 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 101 ( 0 sgn 89 !; 12 ?; 25 :)
% 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(f42,axiom,
! [X0,X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l45_li4647) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ( strictly_less_than(X2,X3)
& pair_in_list(X0,X1,X2) )
=> pair_in_list(update_slb(X0,X3),X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l48_li3839) ).
fof(f44,axiom,
! [X0,X1,X2,X3] :
( ( less_than(X3,X2)
& pair_in_list(X0,X1,X2) )
=> pair_in_list(update_slb(X0,X3),X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l49_li3637) ).
fof(f45,conjecture,
! [X0,X1,X2,X3] :
( ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3) )
=> ( ? [X4] :
( less_than(findmin_pqp_res(X0),X4)
& pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l44_co) ).
fof(f46,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3) )
=> ( ? [X4] :
( less_than(findmin_pqp_res(X0),X4)
& pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
fof(f51,plain,
! [X0,X1] :
( ~ contains_slb(X0,X1)
| ? [X2] : pair_in_list(X0,X1,X2) ),
inference(ennf_transformation,[],[f42]) ).
fof(f52,plain,
! [X0,X1,X2,X3] :
( ~ strictly_less_than(X2,X3)
| ~ pair_in_list(X0,X1,X2)
| pair_in_list(update_slb(X0,X3),X1,X3) ),
inference(ennf_transformation,[],[f43]) ).
fof(f53,plain,
! [X0,X1,X2,X3] :
( ~ strictly_less_than(X2,X3)
| ~ pair_in_list(X0,X1,X2)
| pair_in_list(update_slb(X0,X3),X1,X3) ),
inference(flattening,[],[f52]) ).
fof(f54,plain,
! [X0,X1,X2,X3] :
( ~ less_than(X3,X2)
| ~ pair_in_list(X0,X1,X2)
| pair_in_list(update_slb(X0,X3),X1,X2) ),
inference(ennf_transformation,[],[f44]) ).
fof(f55,plain,
! [X0,X1,X2,X3] :
( ~ less_than(X3,X2)
| ~ pair_in_list(X0,X1,X2)
| pair_in_list(update_slb(X0,X3),X1,X2) ),
inference(flattening,[],[f54]) ).
fof(f56,plain,
? [X0,X1,X2,X3] :
( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3)
& ! [X4] :
( ~ less_than(findmin_pqp_res(X0),X4)
| ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
& ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ),
inference(ennf_transformation,[],[f46]) ).
fof(f57,plain,
? [X0,X1,X2,X3] :
( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3)
& ! [X4] :
( ~ less_than(findmin_pqp_res(X0),X4)
| ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
& ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ),
inference(flattening,[],[f56]) ).
fof(f74,plain,
! [X0,X1] :
( ~ contains_slb(X0,X1)
| pair_in_list(X0,X1,sK0(X0,X1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X2,sK0(X0,X1))],[f51]) ).
fof(f75,plain,
( strictly_less_than(sK4,findmin_cpq_res(triple(sK1,sK2,sK3)))
& contains_slb(sK2,sK4)
& ! [X4] :
( ~ less_than(findmin_pqp_res(sK1),X4)
| ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,X4) )
& ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK3,sK4]),skolemize(X0,sK1),skolemize(X1,sK2),skolemize(X2,sK3),skolemize(X3,sK4)],[f57]) ).
fof(f80,plain,
! [X0,X1] :
( ( ~ strictly_less_than(X0,X1)
| ( ~ less_than(X1,X0)
& less_than(X0,X1) ) )
& ( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f81,plain,
! [X0,X1] :
( ( ~ strictly_less_than(X0,X1)
| ( ~ less_than(X1,X0)
& less_than(X0,X1) ) )
& ( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ) ),
inference(flattening,[],[f80]) ).
fof(f82,plain,
! [X0,X1] :
( ~ contains_slb(X0,X1)
| pair_in_list(X0,X1,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f74]) ).
fof(f83,plain,
! [X2,X3,X0,X1] :
( ~ strictly_less_than(X2,X3)
| ~ pair_in_list(X0,X1,X2)
| pair_in_list(update_slb(X0,X3),X1,X3) ),
inference(cnf_transformation,[],[f53]) ).
fof(f84,plain,
! [X2,X3,X0,X1] :
( ~ less_than(X3,X2)
| ~ pair_in_list(X0,X1,X2)
| pair_in_list(update_slb(X0,X3),X1,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f86,plain,
contains_slb(sK2,sK4),
inference(cnf_transformation,[],[f75]) ).
fof(f87,plain,
! [X4] :
( ~ less_than(findmin_pqp_res(sK1),X4)
| ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,X4) ),
inference(cnf_transformation,[],[f75]) ).
fof(f88,plain,
~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)),
inference(cnf_transformation,[],[f75]) ).
fof(f102,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f81]) ).
fof(f106,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( pair_in_list(X0,X1,sK0(X0,X1))
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( pair_in_list(update_slb(X0,X3),X1,X3)
| ~ strictly_less_than(X2,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[],[f83]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( pair_in_list(update_slb(X0,X3),X1,X2)
| ~ less_than(X3,X2)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[],[f84]) ).
tcf(c_52,negated_conjecture,
~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)),
inference(cnf_transformation,[],[f88]) ).
tcf(c_53,negated_conjecture,
! [X0: $i] :
( ~ less_than(findmin_pqp_res(sK1),X0)
| ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,X0) ),
inference(cnf_transformation,[],[f87]) ).
tcf(c_54,negated_conjecture,
contains_slb(sK2,sK4),
inference(cnf_transformation,[],[f86]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| strictly_less_than(X0,X1)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f106]) ).
tcf(c_107,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_73,c_67]) ).
tcf(c_552,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_107]) ).
tcf(c_553,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_552]) ).
tcf(c_1845,plain,
! [X0: $i,X1: $i,X2: $i] :
( pair_in_list(update_slb(X0,X2),X1,X2)
| ~ contains_slb(X0,X1)
| ~ strictly_less_than(sK0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_49,c_50]) ).
tcf(c_2147,plain,
( ~ contains_slb(sK2,sK4)
| ~ strictly_less_than(sK0(sK2,sK4),findmin_pqp_res(sK1)) ),
inference(superposition,[status(thm)],[c_1845,c_52]) ).
tcf(c_2149,plain,
~ strictly_less_than(sK0(sK2,sK4),findmin_pqp_res(sK1)),
inference(forward_subsumption_resolution,[status(thm)],[c_2147,c_54]) ).
tcf(c_2154,plain,
( pair_in_list(sK2,sK4,sK0(sK2,sK4))
| ~ contains_slb(sK2,sK4) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_2166,plain,
! [X0: $i] :
( ~ less_than(findmin_pqp_res(sK1),X0)
| ~ pair_in_list(sK2,sK4,X0) ),
inference(superposition,[status(thm)],[c_51,c_53]) ).
tcf(c_2212,plain,
less_than(findmin_pqp_res(sK1),sK0(sK2,sK4)),
inference(superposition,[status(thm)],[c_553,c_2149]) ).
tcf(c_2270,plain,
~ pair_in_list(sK2,sK4,sK0(sK2,sK4)),
inference(superposition,[status(thm)],[c_2212,c_2166]) ).
tcf(c_2282,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2270,c_2154,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV408+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n020.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 19:31:33 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.41 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.23/1.18 % SZS status Started for theBenchmark.p
% 3.23/1.18 % SZS status Theorem for theBenchmark.p
% 3.23/1.18
% 3.23/1.18 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.23/1.18
% 3.23/1.18 % ------ iProver source info
% 3.23/1.18
% 3.23/1.18 % git: date: 2026-07-19 20:42:38 +0200
% 3.23/1.18 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.23/1.18 % git: non_committed_changes: false
% 3.23/1.18
% 3.23/1.18 % ------ Parsing...
% 3.23/1.18 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.23/1.18
% 3.23/1.18 % ------ Preprocessing... sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 3.23/1.18
% 3.23/1.18 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.23/1.18
% 3.23/1.18 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.23/1.18 % ------ Proving...
% 3.23/1.18 % ------ Problem Properties
% 3.23/1.18
% 3.23/1.18 %
% 3.23/1.18 % clauses 32
% 3.23/1.18 % conjectures 4
% 3.23/1.18 % EPR 8
% 3.23/1.18 % Horn 20
% 3.23/1.18 % unary 11
% 3.23/1.18 % binary 11
% 3.23/1.18 % lits 64
% 3.23/1.18 % lits eq 19
% 3.23/1.18 % fd_pure 0
% 3.23/1.18 % fd_pseudo 0
% 3.23/1.18 % fd_cond 4
% 3.23/1.18 % fd_pseudo_cond 4
% 3.23/1.18 % AC symbols 0
% 3.23/1.18
% 3.23/1.18 % ------ Schedule dynamic 5 is on
% 3.23/1.18
% 3.23/1.18 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.23/1.18
% 3.23/1.18
% 3.23/1.18 % ------
% 3.23/1.18 % Current options:
% 3.23/1.18 % ------
% 3.23/1.18
% 3.23/1.18
% 3.23/1.18 %
% 3.23/1.18
% 3.23/1.18 % ------ Proving...
% 3.23/1.18 %
% 3.23/1.18
% 3.23/1.18 % SZS status Theorem for theBenchmark.p
% 3.23/1.18
% 3.23/1.18 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.23/1.19
% 3.23/1.19
%------------------------------------------------------------------------------