%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV409+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 : n010.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 3.27s 1.20s
% Output : CNFRefutation 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 55 ( 9 unt; 0 def)
% Number of atoms : 170 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 203 ( 88 ~; 83 |; 26 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 6 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 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-3 aty)
% Number of variables : 117 ( 0 sgn 104 !; 13 ?; 34 :)
% 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(f19,axiom,
! [X0,X1] :
( contains_slb(X0,X1)
=> ? [X2] : pair_in_list(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_li4647) ).
fof(f20,axiom,
! [X0,X1,X2,X3] :
( ( strictly_less_than(X2,X3)
& strictly_less_than(X1,X3)
& pair_in_list(X0,X1,X2) )
=> pair_in_list(update_slb(X0,X3),X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_l48) ).
fof(f21,axiom,
! [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/sandbox/benchmark/theBenchmark.p',l45_l49) ).
fof(f22,conjecture,
! [X0,X1,X2] :
( ( strictly_less_than(X1,X2)
& contains_slb(X0,X1) )
=> ( ? [X3] :
( less_than(X2,X3)
& pair_in_list(update_slb(X0,X2),X1,X3) )
| pair_in_list(update_slb(X0,X2),X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l45_co) ).
fof(f23,negated_conjecture,
~ ! [X0,X1,X2] :
( ( strictly_less_than(X1,X2)
& contains_slb(X0,X1) )
=> ( ? [X3] :
( less_than(X2,X3)
& pair_in_list(update_slb(X0,X2),X1,X3) )
| pair_in_list(update_slb(X0,X2),X1,X2) ) ),
inference(negated_conjecture,[status(cth)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( ~ contains_slb(X0,X1)
| ? [X2] : pair_in_list(X0,X1,X2) ),
inference(ennf_transformation,[],[f19]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ strictly_less_than(X2,X3)
| ~ strictly_less_than(X1,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)
| ~ strictly_less_than(X1,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,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(f28,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,[],[f27]) ).
fof(f29,plain,
? [X0,X1,X2] :
( strictly_less_than(X1,X2)
& contains_slb(X0,X1)
& ! [X3] :
( ~ less_than(X2,X3)
| ~ pair_in_list(update_slb(X0,X2),X1,X3) )
& ~ pair_in_list(update_slb(X0,X2),X1,X2) ),
inference(ennf_transformation,[],[f23]) ).
fof(f30,plain,
? [X0,X1,X2] :
( strictly_less_than(X1,X2)
& contains_slb(X0,X1)
& ! [X3] :
( ~ less_than(X2,X3)
| ~ pair_in_list(update_slb(X0,X2),X1,X3) )
& ~ pair_in_list(update_slb(X0,X2),X1,X2) ),
inference(flattening,[],[f29]) ).
fof(f35,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))],[f24]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2)
| ( less_than(X3,sK1(X0,X1,X3))
& pair_in_list(update_slb(X0,X3),X1,sK1(X0,X1,X3)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(X4,sK1(X0,X1,X3))],[f28]) ).
fof(f37,plain,
( strictly_less_than(sK3,sK4)
& contains_slb(sK2,sK3)
& ! [X3] :
( ~ less_than(sK4,X3)
| ~ pair_in_list(update_slb(sK2,sK4),sK3,X3) )
& ~ pair_in_list(update_slb(sK2,sK4),sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK4]),skolemize(X0,sK2),skolemize(X1,sK3),skolemize(X2,sK4)],[f30]) ).
fof(f42,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(f43,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,[],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( ~ contains_slb(X0,X1)
| pair_in_list(X0,X1,sK0(X0,X1)) ),
inference(cnf_transformation,[],[f35]) ).
fof(f45,plain,
! [X2,X3,X0,X1] :
( ~ strictly_less_than(X2,X3)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2)
| pair_in_list(update_slb(X0,X3),X1,X3) ),
inference(cnf_transformation,[],[f26]) ).
fof(f46,plain,
! [X2,X3,X0,X1] :
( ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2)
| less_than(X3,sK1(X0,X1,X3)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f47,plain,
! [X2,X3,X0,X1] :
( ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2)
| pair_in_list(update_slb(X0,X3),X1,sK1(X0,X1,X3)) ),
inference(cnf_transformation,[],[f36]) ).
fof(f48,plain,
strictly_less_than(sK3,sK4),
inference(cnf_transformation,[],[f37]) ).
fof(f49,plain,
contains_slb(sK2,sK3),
inference(cnf_transformation,[],[f37]) ).
fof(f50,plain,
! [X3] :
( ~ less_than(sK4,X3)
| ~ pair_in_list(update_slb(sK2,sK4),sK3,X3) ),
inference(cnf_transformation,[],[f37]) ).
fof(f51,plain,
~ pair_in_list(update_slb(sK2,sK4),sK3,sK4),
inference(cnf_transformation,[],[f37]) ).
fof(f64,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f43]) ).
fof(f68,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,[],[f44]) ).
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)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[],[f45]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( pair_in_list(update_slb(X0,X3),X1,sK1(X0,X1,X3))
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_than(X3,sK1(X0,X1,X3))
| ~ less_than(X3,X2)
| ~ strictly_less_than(X1,X3)
| ~ pair_in_list(X0,X1,X2) ),
inference(cnf_transformation,[],[f46]) ).
tcf(c_53,negated_conjecture,
~ pair_in_list(update_slb(sK2,sK4),sK3,sK4),
inference(cnf_transformation,[],[f51]) ).
tcf(c_54,negated_conjecture,
! [X0: $i] :
( ~ less_than(sK4,X0)
| ~ pair_in_list(update_slb(sK2,sK4),sK3,X0) ),
inference(cnf_transformation,[],[f50]) ).
tcf(c_55,negated_conjecture,
contains_slb(sK2,sK3),
inference(cnf_transformation,[],[f49]) ).
tcf(c_56,negated_conjecture,
strictly_less_than(sK3,sK4),
inference(cnf_transformation,[],[f48]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| strictly_less_than(X0,X1)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
tcf(c_73,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
tcf(c_88,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_358,plain,
! [X0: $i,X1: $i] :
( strictly_less_than(X0,X1)
| less_than(X1,X0) ),
inference(prop_impl_just,[status(thm)],[c_88]) ).
tcf(c_359,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(renaming,[status(thm)],[c_358]) ).
tcf(c_1601,plain,
! [X0: $i,X1: $i] :
( less_than(sK4,sK1(X0,sK3,sK4))
| ~ strictly_less_than(sK3,sK4)
| ~ less_than(sK4,X1)
| ~ pair_in_list(X0,sK3,X1) ),
inference(instantiation,[status(thm)],[c_52]) ).
tcf(c_1682,plain,
! [X0: $i,X1: $i] :
( pair_in_list(update_slb(X0,sK4),sK3,sK1(X0,sK3,sK4))
| ~ strictly_less_than(sK3,sK4)
| ~ less_than(sK4,X1)
| ~ pair_in_list(X0,sK3,X1) ),
inference(instantiation,[status(thm)],[c_51]) ).
tcf(c_1967,plain,
! [X0: $i,X1: $i,X2: $i] :
( pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1)
| ~ strictly_less_than(sK0(X0,X1),X2) ),
inference(superposition,[status(thm)],[c_49,c_50]) ).
tcf(c_2009,plain,
! [X0: $i] :
( less_than(sK4,sK1(X0,sK3,sK4))
| ~ strictly_less_than(sK3,sK4)
| ~ less_than(sK4,sK0(X0,sK3))
| ~ pair_in_list(X0,sK3,sK0(X0,sK3)) ),
inference(instantiation,[status(thm)],[c_1601]) ).
tcf(c_2010,plain,
! [X0: $i] :
( pair_in_list(X0,sK3,sK0(X0,sK3))
| ~ contains_slb(X0,sK3) ),
inference(instantiation,[status(thm)],[c_49]) ).
tcf(c_2454,plain,
( ~ strictly_less_than(sK3,sK4)
| ~ contains_slb(sK2,sK3)
| ~ strictly_less_than(sK0(sK2,sK3),sK4) ),
inference(superposition,[status(thm)],[c_1967,c_53]) ).
tcf(c_2456,plain,
~ strictly_less_than(sK0(sK2,sK3),sK4),
inference(forward_subsumption_resolution,[status(thm)],[c_2454,c_56,c_55]) ).
tcf(c_2487,plain,
less_than(sK4,sK0(sK2,sK3)),
inference(superposition,[status(thm)],[c_359,c_2456]) ).
tcf(c_2700,plain,
( pair_in_list(sK2,sK3,sK0(sK2,sK3))
| ~ contains_slb(sK2,sK3) ),
inference(instantiation,[status(thm)],[c_2010]) ).
tcf(c_3744,plain,
( pair_in_list(update_slb(sK2,sK4),sK3,sK1(sK2,sK3,sK4))
| ~ strictly_less_than(sK3,sK4)
| ~ less_than(sK4,sK0(sK2,sK3))
| ~ pair_in_list(sK2,sK3,sK0(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_1682]) ).
tcf(c_4164,plain,
( less_than(sK4,sK1(sK2,sK3,sK4))
| ~ strictly_less_than(sK3,sK4)
| ~ less_than(sK4,sK0(sK2,sK3))
| ~ pair_in_list(sK2,sK3,sK0(sK2,sK3)) ),
inference(instantiation,[status(thm)],[c_2009]) ).
tcf(c_7559,plain,
( ~ less_than(sK4,sK1(sK2,sK3,sK4))
| ~ pair_in_list(update_slb(sK2,sK4),sK3,sK1(sK2,sK3,sK4)) ),
inference(instantiation,[status(thm)],[c_54]) ).
tcf(c_7560,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_7559,c_4164,c_3744,c_2700,c_2487,c_55,c_56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV409+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n010.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 19:30:43 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.41 Running first-order theorem proving
% 0.09/0.41 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
% 0.09/0.42
% 0.09/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.09/0.42
% 0.09/0.42 % Detected problem language: tptp
% 0.09/0.43 % Proving...
% 3.27/1.20 % SZS status Started for theBenchmark.p
% 3.27/1.20 % SZS status Theorem for theBenchmark.p
% 3.27/1.20
% 3.27/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.27/1.20
% 3.27/1.20 % ------ iProver source info
% 3.27/1.20
% 3.27/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.27/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.27/1.20 % git: non_committed_changes: false
% 3.27/1.20
% 3.27/1.20 % ------ Parsing...
% 3.27/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.27/1.20
% 3.27/1.20 % ------ 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 %
% 3.27/1.20
% 3.27/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.27/1.20
% 3.27/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.27/1.20 % ------ Proving...
% 3.27/1.20 % ------ Problem Properties
% 3.27/1.20
% 3.27/1.20 %
% 3.27/1.20 % clauses 25
% 3.27/1.20 % conjectures 4
% 3.27/1.20 % EPR 9
% 3.27/1.20 % Horn 19
% 3.27/1.20 % unary 9
% 3.27/1.20 % binary 9
% 3.27/1.20 % lits 51
% 3.27/1.20 % lits eq 6
% 3.27/1.20 % fd_pure 0
% 3.27/1.20 % fd_pseudo 0
% 3.27/1.20 % fd_cond 0
% 3.27/1.20 % fd_pseudo_cond 3
% 3.27/1.20 % AC symbols 0
% 3.27/1.20
% 3.27/1.20 % ------ Schedule dynamic 5 is on
% 3.27/1.20
% 3.27/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.27/1.20
% 3.27/1.20
% 3.27/1.20 % ------
% 3.27/1.20 % Current options:
% 3.27/1.20 % ------
% 3.27/1.20
% 3.27/1.20
% 3.27/1.20 %
% 3.27/1.20
% 3.27/1.20 % ------ Proving...
% 3.27/1.20 %
% 3.27/1.20
% 3.27/1.20 % SZS status Theorem for theBenchmark.p
% 3.27/1.20
% 3.27/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.27/1.20
% 3.27/1.20
%------------------------------------------------------------------------------