%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV399+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 : n004.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 4.32s 1.51s
% Output : CNFRefutation 4.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 59 ( 8 unt; 0 def)
% Number of atoms : 150 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 158 ( 67 ~; 67 |; 18 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 139 ( 0 sgn 123 !; 16 ?; 51 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( ( less_than(X1,X2)
& less_than(X0,X1) )
=> less_than(X0,X2) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',transitivity) ).
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(f19,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',l35_li3637) ).
fof(f20,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',l35_li3839) ).
fof(f21,conjecture,
! [X0] :
( ? [X1,X2] :
( strictly_less_than(X1,X2)
& pair_in_list(X0,X1,X2) )
=> ! [X3] :
? [X4,X5] :
( strictly_less_than(X4,X5)
& pair_in_list(update_slb(X0,X3),X4,X5) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l35_co) ).
fof(f22,negated_conjecture,
~ ! [X0] :
( ? [X1,X2] :
( strictly_less_than(X1,X2)
& pair_in_list(X0,X1,X2) )
=> ! [X3] :
? [X4,X5] :
( strictly_less_than(X4,X5)
& pair_in_list(update_slb(X0,X3),X4,X5) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
fof(f23,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,[],[f19]) ).
fof(f24,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,[],[f23]) ).
fof(f25,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,[],[f20]) ).
fof(f26,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,[],[f25]) ).
fof(f27,plain,
? [X0] :
( ? [X1,X2] :
( strictly_less_than(X1,X2)
& pair_in_list(X0,X1,X2) )
& ? [X3] :
! [X4,X5] :
( ~ strictly_less_than(X4,X5)
| ~ pair_in_list(update_slb(X0,X3),X4,X5) ) ),
inference(ennf_transformation,[],[f22]) ).
fof(f29,plain,
! [X0,X1,X2] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f30,plain,
! [X0,X1,X2] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) ),
inference(flattening,[],[f29]) ).
fof(f32,plain,
? [X0] :
( ? [X4,X5] :
( strictly_less_than(X4,X5)
& pair_in_list(X0,X4,X5) )
& ? [X1] :
! [X2,X3] :
( ~ strictly_less_than(X2,X3)
| ~ pair_in_list(update_slb(X0,X1),X2,X3) ) ),
inference(rectify,[],[f27]) ).
fof(f33,plain,
( strictly_less_than(sK2,sK3)
& pair_in_list(sK0,sK2,sK3)
& ! [X2,X3] :
( ~ strictly_less_than(X2,X3)
| ~ pair_in_list(update_slb(sK0,sK1),X2,X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X4,sK2),skolemize(X5,sK3)],[f32]) ).
fof(f36,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(f37,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,[],[f36]) ).
fof(f40,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,[],[f24]) ).
fof(f41,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,[],[f26]) ).
fof(f42,plain,
strictly_less_than(sK2,sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f43,plain,
pair_in_list(sK0,sK2,sK3),
inference(cnf_transformation,[],[f33]) ).
fof(f44,plain,
! [X2,X3] :
( ~ strictly_less_than(X2,X3)
| ~ pair_in_list(update_slb(sK0,sK1),X2,X3) ),
inference(cnf_transformation,[],[f33]) ).
fof(f47,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f48,plain,
! [X2,X0,X1] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f56,plain,
! [X0,X1] :
( ~ strictly_less_than(X0,X1)
| ~ less_than(X1,X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f57,plain,
! [X0,X1] :
( ~ strictly_less_than(X0,X1)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
fof(f58,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_49,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,[],[f40]) ).
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,[],[f41]) ).
tcf(c_51,negated_conjecture,
! [X0: $i,X1: $i] :
( ~ strictly_less_than(X0,X1)
| ~ pair_in_list(update_slb(sK0,sK1),X0,X1) ),
inference(cnf_transformation,[],[f44]) ).
tcf(c_52,negated_conjecture,
pair_in_list(sK0,sK2,sK3),
inference(cnf_transformation,[],[f43]) ).
tcf(c_53,negated_conjecture,
strictly_less_than(sK2,sK3),
inference(cnf_transformation,[],[f42]) ).
tcf(c_56,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f48]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( less_than(X0,X1)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( ~ strictly_less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
tcf(c_84,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(global_subsumption_just,[status(thm)],[c_65,c_56,c_65]) ).
tcf(c_85,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_84]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_88]) ).
tcf(c_98,plain,
! [X0: $i,X1: $i] :
( ~ strictly_less_than(X1,X0)
| ~ strictly_less_than(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_66,c_67]) ).
tcf(c_154,plain,
! [X0: $i,X1: $i,X2: $i] :
( strictly_less_than(X0,X2)
| less_than(X2,X1)
| ~ less_than(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_57,c_89]) ).
tcf(c_317,plain,
! [X0: $i,X1: $i] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_85]) ).
tcf(c_318,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X1,X0)
| less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_317]) ).
tcf(c_329,plain,
! [X0: $i,X1: $i] :
( ~ strictly_less_than(X1,X0)
| ~ strictly_less_than(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_98]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i,X2: $i] :
( strictly_less_than(X2,X0)
| strictly_less_than(X1,X2)
| less_than(X0,X1) ),
inference(bin_hyper_res,[status(thm)],[c_154,c_318]) ).
tcf(c_1082,plain,
! [X0: $i,X1: $i,X2: $i] :
( strictly_less_than(X2,X1)
| strictly_less_than(X0,X2)
| ~ strictly_less_than(X0,X1) ),
inference(superposition,[status(thm)],[c_378,c_67]) ).
tcf(c_1192,plain,
! [X0: $i] :
( strictly_less_than(sK2,X0)
| strictly_less_than(X0,sK3) ),
inference(superposition,[status(thm)],[c_53,c_1082]) ).
tcf(c_1227,plain,
! [X0: $i,X1: $i] :
( ~ less_than(sK1,X1)
| ~ strictly_less_than(X0,X1)
| ~ pair_in_list(sK0,X0,X1) ),
inference(superposition,[status(thm)],[c_49,c_51]) ).
tcf(c_1239,plain,
! [X0: $i] :
( pair_in_list(update_slb(sK0,X0),sK2,X0)
| ~ strictly_less_than(sK3,X0) ),
inference(superposition,[status(thm)],[c_52,c_50]) ).
tcf(c_1276,plain,
! [X0: $i] :
( strictly_less_than(sK2,X0)
| ~ strictly_less_than(sK3,X0) ),
inference(superposition,[status(thm)],[c_1192,c_329]) ).
tcf(c_1356,plain,
( ~ strictly_less_than(sK3,sK1)
| ~ strictly_less_than(sK2,sK1) ),
inference(superposition,[status(thm)],[c_1239,c_51]) ).
tcf(c_1367,plain,
~ strictly_less_than(sK3,sK1),
inference(forward_subsumption_resolution,[status(thm)],[c_1356,c_1276]) ).
tcf(c_1368,plain,
less_than(sK1,sK3),
inference(superposition,[status(thm)],[c_318,c_1367]) ).
tcf(c_1400,plain,
( ~ strictly_less_than(sK2,sK3)
| ~ less_than(sK1,sK3) ),
inference(superposition,[status(thm)],[c_52,c_1227]) ).
tcf(c_1401,plain,
~ less_than(sK1,sK3),
inference(forward_subsumption_resolution,[status(thm)],[c_1400,c_53]) ).
tcf(c_1402,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1401,c_1368]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV399+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.44 % Computer : n004.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Thu Sep 24 19:28:36 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.50 Running first-order theorem proving
% 0.19/0.50 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
% 0.26/0.52
% 0.26/0.52 % ======== iProver multi-core TPTP/SMT =========
% 0.26/0.52
% 0.26/0.52 % Detected problem language: tptp
% 0.26/0.54 % Proving...
% 4.32/1.51 % SZS status Started for theBenchmark.p
% 4.32/1.51 % SZS status Theorem for theBenchmark.p
% 4.32/1.51
% 4.32/1.51 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.32/1.51
% 4.32/1.51 % ------ iProver source info
% 4.32/1.51
% 4.32/1.51 % git: date: 2026-07-19 20:42:38 +0200
% 4.32/1.51 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.32/1.51 % git: non_committed_changes: false
% 4.32/1.51
% 4.32/1.51 % ------ Parsing...
% 4.32/1.51 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.32/1.51
% 4.32/1.51 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.32/1.51
% 4.32/1.51 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.32/1.51
% 4.32/1.51 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.32/1.51 % ------ Proving...
% 4.32/1.51 % ------ Problem Properties
% 4.32/1.51
% 4.32/1.51 %
% 4.32/1.51 % clauses 22
% 4.32/1.51 % conjectures 3
% 4.32/1.51 % EPR 9
% 4.32/1.51 % Horn 16
% 4.32/1.51 % unary 8
% 4.32/1.51 % binary 8
% 4.32/1.51 % lits 42
% 4.32/1.51 % lits eq 6
% 4.32/1.51 % fd_pure 0
% 4.32/1.51 % fd_pseudo 0
% 4.32/1.51 % fd_cond 0
% 4.32/1.51 % fd_pseudo_cond 3
% 4.32/1.51 % AC symbols 0
% 4.32/1.51
% 4.32/1.51 % ------ Schedule dynamic 5 is on
% 4.32/1.51
% 4.32/1.51 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.32/1.51
% 4.32/1.51
% 4.32/1.51 % ------
% 4.32/1.51 % Current options:
% 4.32/1.51 % ------
% 4.32/1.51
% 4.32/1.51
% 4.32/1.51 %
% 4.32/1.51
% 4.32/1.51 % ------ Proving...
% 4.32/1.51 %
% 4.32/1.51
% 4.32/1.51 % SZS status Theorem for theBenchmark.p
% 4.32/1.51
% 4.32/1.51 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.32/1.51
% 4.32/1.51
%------------------------------------------------------------------------------