%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV413+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 : n012.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 03:17:35 PM UTC 2026
% Result : Theorem 0.36s 1.07s
% Output : CNFRefutation 0.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 6 unt; 0 def)
% Number of atoms : 61 ( 2 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 68 ( 29 ~; 20 |; 16 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 0 sgn 36 !; 10 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
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',l49_li3637) ).
fof(f20,conjecture,
! [X0,X1,X2,X3] :
( ( less_than(X3,X2)
& strictly_less_than(X1,X3)
& pair_in_list(X0,X1,X2) )
=> ? [X4] :
( less_than(X3,X4)
& pair_in_list(update_slb(X0,X3),X1,X4) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l49_co) ).
fof(f21,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( less_than(X3,X2)
& strictly_less_than(X1,X3)
& pair_in_list(X0,X1,X2) )
=> ? [X4] :
( less_than(X3,X4)
& pair_in_list(update_slb(X0,X3),X1,X4) ) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f30,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(f31,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,[],[f30]) ).
fof(f32,plain,
? [X0,X1,X2,X3] :
( less_than(X3,X2)
& strictly_less_than(X1,X3)
& pair_in_list(X0,X1,X2)
& ! [X4] :
( ~ less_than(X3,X4)
| ~ pair_in_list(update_slb(X0,X3),X1,X4) ) ),
inference(ennf_transformation,[],[f21]) ).
fof(f33,plain,
? [X0,X1,X2,X3] :
( less_than(X3,X2)
& strictly_less_than(X1,X3)
& pair_in_list(X0,X1,X2)
& ! [X4] :
( ~ less_than(X3,X4)
| ~ pair_in_list(update_slb(X0,X3),X1,X4) ) ),
inference(flattening,[],[f32]) ).
fof(f40,plain,
( less_than(sK3,sK2)
& strictly_less_than(sK1,sK3)
& pair_in_list(sK0,sK1,sK2)
& ! [X4] :
( ~ less_than(sK3,X4)
| ~ pair_in_list(update_slb(sK0,sK3),sK1,X4) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3)],[f33]) ).
fof(f66,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,[],[f31]) ).
fof(f67,plain,
less_than(sK3,sK2),
inference(cnf_transformation,[],[f40]) ).
fof(f69,plain,
pair_in_list(sK0,sK1,sK2),
inference(cnf_transformation,[],[f40]) ).
fof(f70,plain,
! [X4] :
( ~ less_than(sK3,X4)
| ~ pair_in_list(update_slb(sK0,sK3),sK1,X4) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_74,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,[],[f66]) ).
tcf(c_75,negated_conjecture,
! [X0: $i] :
( ~ less_than(sK3,X0)
| ~ pair_in_list(update_slb(sK0,sK3),sK1,X0) ),
inference(cnf_transformation,[],[f70]) ).
tcf(c_76,negated_conjecture,
pair_in_list(sK0,sK1,sK2),
inference(cnf_transformation,[],[f69]) ).
tcf(c_78,negated_conjecture,
less_than(sK3,sK2),
inference(cnf_transformation,[],[f67]) ).
tcf(c_386,plain,
! [X0: $i] :
( ~ less_than(sK3,X0)
| ~ pair_in_list(update_slb(sK0,sK3),sK1,X0) ),
inference(prop_impl_just,[status(thm)],[c_75]) ).
tcf(c_736,plain,
! [X0: $i] :
( ~ pair_in_list(update_slb(sK0,sK3),sK1,X0)
| ( sK3 != sK3 )
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_386,c_78]) ).
tcf(c_737,plain,
~ pair_in_list(update_slb(sK0,sK3),sK1,sK2),
inference(unflattening,[status(thm)],[c_736]) ).
tcf(c_1648,plain,
! [X0: $i] :
( pair_in_list(update_slb(sK0,X0),sK1,sK2)
| ~ less_than(X0,sK2)
| ~ pair_in_list(sK0,sK1,sK2) ),
inference(instantiation,[status(thm)],[c_74]) ).
tcf(c_1936,plain,
( pair_in_list(update_slb(sK0,sK3),sK1,sK2)
| ~ less_than(sK3,sK2)
| ~ pair_in_list(sK0,sK1,sK2) ),
inference(instantiation,[status(thm)],[c_1648]) ).
tcf(c_1937,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_1936,c_737,c_76,c_78]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV413+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.30 % Computer : n012.cluster.edu
% 0.04/0.30 % Model : x86_64 x86_64
% 0.04/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.04/0.30 % Memory : 8046.5625MB
% 0.04/0.30 % OS : Linux 6.8.0-71-generic
% 0.04/0.30 % CPULimit : 300
% 0.04/0.30 % WCLimit : 300
% 0.04/0.30 % DateTime : Thu Sep 24 19:30:50 UTC 2026
% 0.04/0.30 % CPUTime :
% 0.04/0.30 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.04/0.32 Running first-order theorem proving
% 0.04/0.32 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
% 0.04/0.33
% 0.04/0.33 % ======== iProver multi-core TPTP/SMT =========
% 0.04/0.33
% 0.04/0.33 % Detected problem language: tptp
% 0.10/0.34 % Proving...
% 0.36/1.07 % SZS status Started for theBenchmark.p
% 0.36/1.07 % SZS status Theorem for theBenchmark.p
% 0.36/1.07
% 0.36/1.07 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.36/1.07
% 0.36/1.07 % ------ iProver source info
% 0.36/1.07
% 0.36/1.07 % git: date: 2026-07-19 20:42:38 +0200
% 0.36/1.07 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.36/1.07 % git: non_committed_changes: false
% 0.36/1.07
% 0.36/1.07 % ------ Parsing...
% 0.36/1.07 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.36/1.07
% 0.36/1.07 % ------ 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 %
% 0.36/1.07
% 0.36/1.07 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.36/1.07
% 0.36/1.07 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.36/1.07 % ------ Proving...
% 0.36/1.07 % ------ Problem Properties
% 0.36/1.07
% 0.36/1.07 %
% 0.36/1.07 % clauses 29
% 0.36/1.07 % conjectures 4
% 0.36/1.07 % EPR 12
% 0.36/1.07 % Horn 21
% 0.36/1.07 % unary 14
% 0.36/1.07 % binary 8
% 0.36/1.07 % lits 51
% 0.36/1.07 % lits eq 14
% 0.36/1.07 % fd_pure 0
% 0.36/1.07 % fd_pseudo 0
% 0.36/1.07 % fd_cond 0
% 0.36/1.07 % fd_pseudo_cond 5
% 0.36/1.07 % AC symbols 0
% 0.36/1.07
% 0.36/1.07 % ------ Schedule dynamic 5 is on
% 0.36/1.07
% 0.36/1.07 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.36/1.07
% 0.36/1.07
% 0.36/1.07 % ------
% 0.36/1.07 % Current options:
% 0.36/1.07 % ------
% 0.36/1.07
% 0.36/1.07
% 0.36/1.07 %
% 0.36/1.07
% 0.36/1.07 % ------ Proving...
% 0.36/1.07 %
% 0.36/1.07
% 0.36/1.07 % SZS status Theorem for theBenchmark.p
% 0.36/1.07
% 0.36/1.07 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.36/1.07
% 0.36/1.07
%------------------------------------------------------------------------------