%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV408+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 : n007.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 3.61s 1.19s
% Output : CNFRefutation 3.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 14 unt; 0 def)
% Number of atoms : 158 ( 16 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 167 ( 67 ~; 69 |; 24 &)
% ( 1 <=>; 6 =>; 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 : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 5 con; 0-3 aty)
% Number of variables : 106 ( 1 sgn 93 !; 13 ?; 24 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1,X2] :
( ( less_than(X1,X2)
& less_than(X0,X1) )
=> less_than(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+0.ax',transitivity) ).
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(f8,axiom,
! [X0] : ~ contains_slb(create_slb,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+2.ax',ax20) ).
fof(f39,axiom,
! [X0,X1,X2,X3] :
( X1 != create_slb
=> findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax51) ).
fof(f42,axiom,
! [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',l44_l45) ).
fof(f43,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/sandbox/benchmark/theBenchmark.p',l44_co) ).
fof(f44,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)],[f43]) ).
fof(f46,plain,
! [X0,X1,X2] :
( X1 != create_slb
=> findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ),
inference(rectify,[],[f39]) ).
fof(f49,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,[],[f42]) ).
fof(f50,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,[],[f49]) ).
fof(f51,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,[],[f44]) ).
fof(f52,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,[],[f51]) ).
fof(f54,plain,
! [X0,X1,X2] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) ),
inference(ennf_transformation,[],[f1]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) ),
inference(flattening,[],[f54]) ).
fof(f59,plain,
! [X0,X1,X2] :
( create_slb = X1
| findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f69,plain,
! [X0,X1,X2] :
( ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1)
| ( less_than(X2,sK0(X0,X1,X2))
& pair_in_list(update_slb(X0,X2),X1,sK0(X0,X1,X2)) )
| pair_in_list(update_slb(X0,X2),X1,X2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1,X2))],[f50]) ).
fof(f70,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)],[f52]) ).
fof(f71,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(f72,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,[],[f71]) ).
fof(f77,plain,
! [X2,X0,X1] :
( ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1)
| less_than(X2,sK0(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f78,plain,
! [X2,X0,X1] :
( ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1)
| pair_in_list(update_slb(X0,X2),X1,sK0(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2) ),
inference(cnf_transformation,[],[f69]) ).
fof(f79,plain,
strictly_less_than(sK4,findmin_cpq_res(triple(sK1,sK2,sK3))),
inference(cnf_transformation,[],[f70]) ).
fof(f80,plain,
contains_slb(sK2,sK4),
inference(cnf_transformation,[],[f70]) ).
fof(f81,plain,
! [X4] :
( ~ less_than(findmin_pqp_res(sK1),X4)
| ~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,X4) ),
inference(cnf_transformation,[],[f70]) ).
fof(f82,plain,
~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)),
inference(cnf_transformation,[],[f70]) ).
fof(f85,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f86,plain,
! [X2,X0,X1] :
( ~ less_than(X1,X2)
| ~ less_than(X0,X1)
| less_than(X0,X2) ),
inference(cnf_transformation,[],[f55]) ).
fof(f89,plain,
! [X0,X1] :
( ~ strictly_less_than(X0,X1)
| ~ less_than(X1,X0) ),
inference(cnf_transformation,[],[f72]) ).
fof(f95,plain,
! [X0] : ~ contains_slb(create_slb,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f102,plain,
! [X2,X0,X1] :
( create_slb = X1
| findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f59]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i] :
( pair_in_list(update_slb(X0,X2),X1,X2)
| pair_in_list(update_slb(X0,X2),X1,sK0(X0,X1,X2))
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(X2,sK0(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
tcf(c_51,negated_conjecture,
~ pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1)),
inference(cnf_transformation,[],[f82]) ).
tcf(c_52,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,[],[f81]) ).
tcf(c_53,negated_conjecture,
contains_slb(sK2,sK4),
inference(cnf_transformation,[],[f80]) ).
tcf(c_54,negated_conjecture,
strictly_less_than(sK4,findmin_cpq_res(triple(sK1,sK2,sK3))),
inference(cnf_transformation,[],[f79]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
tcf(c_63,plain,
! [X0: $i,X1: $i] :
( ~ less_than(X1,X0)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
tcf(c_67,plain,
! [X0: $i] : ~ contains_slb(create_slb,X0),
inference(cnf_transformation,[],[f95]) ).
tcf(c_74,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( X1 = create_slb )
| ( findmin_cpq_res(triple(X0,X1,X2)) = findmin_pqp_res(X0) ) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_1744,plain,
~ less_than(findmin_cpq_res(triple(sK1,sK2,sK3)),sK4),
inference(superposition,[status(thm)],[c_54,c_63]) ).
tcf(c_1746,plain,
less_than(sK4,findmin_cpq_res(triple(sK1,sK2,sK3))),
inference(superposition,[status(thm)],[c_57,c_1744]) ).
tcf(c_1756,plain,
! [X0: $i,X1: $i,X2: $i] :
( less_than(X2,X1)
| less_than(X0,X2)
| ~ less_than(X0,X1) ),
inference(superposition,[status(thm)],[c_57,c_58]) ).
tcf(c_1757,plain,
! [X0: $i] :
( less_than(sK4,X0)
| ~ less_than(findmin_cpq_res(triple(sK1,sK2,sK3)),X0) ),
inference(superposition,[status(thm)],[c_1746,c_58]) ).
tcf(c_1931,plain,
! [X0: $i] :
( less_than(sK4,X0)
| ( sK2 = create_slb )
| ~ less_than(findmin_pqp_res(sK1),X0) ),
inference(superposition,[status(thm)],[c_74,c_1757]) ).
tcf(c_1934,plain,
( strictly_less_than(sK4,findmin_pqp_res(sK1))
| ( sK2 = create_slb ) ),
inference(superposition,[status(thm)],[c_74,c_54]) ).
tcf(c_3367,plain,
( less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ~ contains_slb(sK2,sK4)
| ~ strictly_less_than(sK4,findmin_pqp_res(sK1)) ),
inference(superposition,[status(thm)],[c_50,c_51]) ).
tcf(c_3369,plain,
( less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ~ strictly_less_than(sK4,findmin_pqp_res(sK1)) ),
inference(forward_subsumption_resolution,[status(thm)],[c_3367,c_53]) ).
tcf(c_3737,plain,
( less_than(sK4,sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ( sK2 = create_slb )
| ~ strictly_less_than(sK4,findmin_pqp_res(sK1)) ),
inference(superposition,[status(thm)],[c_3369,c_1931]) ).
tcf(c_4148,plain,
( less_than(sK4,sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ( sK2 = create_slb ) ),
inference(global_subsumption_just,[status(thm)],[c_3737,c_1934,c_3737]) ).
tcf(c_4156,plain,
! [X0: $i] :
( less_than(sK4,X0)
| less_than(X0,sK0(sK2,sK4,findmin_pqp_res(sK1)))
| ( sK2 = create_slb ) ),
inference(superposition,[status(thm)],[c_4148,c_1756]) ).
tcf(c_4869,plain,
( pair_in_list(update_slb(sK2,findmin_pqp_res(sK1)),sK4,findmin_pqp_res(sK1))
| ~ contains_slb(sK2,sK4)
| ~ strictly_less_than(sK4,findmin_pqp_res(sK1))
| ~ less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1))) ),
inference(superposition,[status(thm)],[c_49,c_52]) ).
tcf(c_4870,plain,
( ~ strictly_less_than(sK4,findmin_pqp_res(sK1))
| ~ less_than(findmin_pqp_res(sK1),sK0(sK2,sK4,findmin_pqp_res(sK1))) ),
inference(forward_subsumption_resolution,[status(thm)],[c_4869,c_51,c_53]) ).
tcf(c_5098,plain,
sK2 = create_slb,
inference(global_subsumption_just,[status(thm)],[c_4156,c_1934,c_3369,c_4870]) ).
tcf(c_5123,plain,
contains_slb(create_slb,sK4),
inference(demodulation,[status(thm)],[c_53,c_5098]) ).
tcf(c_5124,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_5123,c_67]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV408+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 : n007.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 19:28:07 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.40 Running first-order theorem proving
% 0.09/0.40 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...
% 3.61/1.19 % SZS status Started for theBenchmark.p
% 3.61/1.19 % SZS status Theorem for theBenchmark.p
% 3.61/1.19
% 3.61/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.61/1.19
% 3.61/1.19 % ------ iProver source info
% 3.61/1.19
% 3.61/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.61/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.61/1.19 % git: non_committed_changes: false
% 3.61/1.19
% 3.61/1.19 % ------ Parsing...
% 3.61/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.61/1.19
% 3.61/1.19 % ------ 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 %
% 3.61/1.19
% 3.61/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.61/1.19
% 3.61/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.61/1.19 % ------ Proving...
% 3.61/1.19 % ------ Problem Properties
% 3.61/1.19
% 3.61/1.19 %
% 3.61/1.19 % clauses 31
% 3.61/1.19 % conjectures 4
% 3.61/1.19 % EPR 8
% 3.61/1.19 % Horn 17
% 3.61/1.19 % unary 11
% 3.61/1.19 % binary 10
% 3.61/1.19 % lits 64
% 3.61/1.19 % lits eq 19
% 3.61/1.19 % fd_pure 0
% 3.61/1.19 % fd_pseudo 0
% 3.61/1.19 % fd_cond 4
% 3.61/1.19 % fd_pseudo_cond 4
% 3.61/1.19 % AC symbols 0
% 3.61/1.19
% 3.61/1.19 % ------ Schedule dynamic 5 is on
% 3.61/1.19
% 3.61/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.61/1.19
% 3.61/1.19
% 3.61/1.19 % ------
% 3.61/1.19 % Current options:
% 3.61/1.19 % ------
% 3.61/1.19
% 3.61/1.19
% 3.61/1.19 %
% 3.61/1.19
% 3.61/1.19 % ------ Proving...
% 3.61/1.19 %
% 3.61/1.19
% 3.61/1.19 % SZS status Theorem for theBenchmark.p
% 3.61/1.19
% 3.61/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.61/1.19
% 3.61/1.19
%------------------------------------------------------------------------------