%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV381+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 : n015.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 03:17:30 PM UTC 2026
% Result : Theorem 3.74s 11.22s
% Output : CNFRefutation 3.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 8 unt; 0 def)
% Number of atoms : 110 ( 6 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 109 ( 46 ~; 45 |; 8 &)
% ( 3 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 101 ( 0 sgn 96 !; 5 ?; 39 :)
% 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(f10,axiom,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
<=> ! [X2] :
( contains_pq(X0,X2)
=> less_than(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax',ax10) ).
fof(f63,axiom,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
<=> contains_pq(i(triple(X0,X1,X2)),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_li56) ).
fof(f64,axiom,
! [X0,X1,X2] :
( ? [X3] :
( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_cpq(triple(X0,X1,X2),X3) )
=> ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_l18) ).
fof(f65,conjecture,
! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l17_co) ).
fof(f66,negated_conjecture,
~ ! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
fof(f75,plain,
! [X0,X1] :
( ! [X2] :
( contains_pq(X0,X2)
=> less_than(X1,X2) )
=> issmallestelement_pq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f76,plain,
! [X0,X1] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f4]) ).
fof(f77,plain,
! [X0,X1,X2] :
( ! [X3] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3) )
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f64]) ).
fof(f78,plain,
? [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
& ~ issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f66]) ).
fof(f79,plain,
! [X0,X1] :
( ? [X2] :
( contains_pq(X0,X2)
& ~ less_than(X1,X2) )
| issmallestelement_pq(X0,X1) ),
inference(ennf_transformation,[],[f75]) ).
fof(f84,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(ennf_transformation,[],[f76]) ).
fof(f85,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(flattening,[],[f84]) ).
fof(f101,plain,
! [X0,X1,X2,X3] :
( ( ~ contains_cpq(triple(X0,X1,X2),X3)
| contains_pq(i(triple(X0,X1,X2)),X3) )
& ( ~ contains_pq(i(triple(X0,X1,X2)),X3)
| contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f102,plain,
( phi(findmin_cpq_eff(triple(sK0,sK1,sK2)))
& ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f78]) ).
fof(f103,plain,
! [X0,X1] :
( ( contains_pq(X0,sK3(X0,X1))
& ~ less_than(X1,sK3(X0,X1)) )
| issmallestelement_pq(X0,X1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(X2,sK3(X0,X1))],[f79]) ).
fof(f114,plain,
! [X2,X3,X0,X1] :
( ~ contains_pq(i(triple(X0,X1,X2)),X3)
| contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f101]) ).
fof(f115,plain,
! [X2,X3,X0,X1] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3)
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[],[f77]) ).
fof(f116,plain,
phi(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f102]) ).
fof(f117,plain,
~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f102]) ).
fof(f118,plain,
! [X0,X1] :
( contains_pq(X0,sK3(X0,X1))
| issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f119,plain,
! [X0,X1] :
( ~ less_than(X1,sK3(X0,X1))
| issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[],[f103]) ).
fof(f126,plain,
! [X0,X1] :
( less_than(X1,X0)
| ~ less_than(X0,X1)
| strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f85]) ).
fof(f135,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(cnf_transformation,[],[f114]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( ~ phi(findmin_cpq_eff(triple(X1,X2,X3)))
| ~ contains_cpq(triple(X1,X2,X3),X0)
| ~ strictly_less_than(X0,findmin_cpq_res(triple(X1,X2,X3))) ),
inference(cnf_transformation,[],[f115]) ).
tcf(c_52,negated_conjecture,
~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f117]) ).
tcf(c_53,negated_conjecture,
phi(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f116]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( issmallestelement_pq(X1,X0)
| ~ less_than(X0,sK3(X1,X0)) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( issmallestelement_pq(X0,X1)
| contains_pq(X0,sK3(X0,X1)) ),
inference(cnf_transformation,[],[f118]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| strictly_less_than(X0,X1)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f126]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f135]) ).
tcf(c_131,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_62,c_71,c_62]) ).
tcf(c_142,plain,
! [X0: $i,X1: $i] :
( issmallestelement_pq(X1,X0)
| ~ less_than(X0,sK3(X1,X0)) ),
inference(prop_impl_just,[status(thm)],[c_54]) ).
tcf(c_158,plain,
! [X0: $i,X1: $i] :
( less_than(X1,X0)
| strictly_less_than(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_131]) ).
tcf(c_188,plain,
! [X0: $i,X1: $i] :
( issmallestelement_pq(X0,X1)
| contains_pq(X0,sK3(X0,X1)) ),
inference(prop_impl_just,[status(thm)],[c_55]) ).
tcf(c_650,plain,
! [X0: $i,X1: $i] :
( contains_pq(X0,sK3(X0,X1))
| ( findmin_cpq_res(triple(sK0,sK1,sK2)) != X1 )
| ( i(triple(sK0,sK1,sK2)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_188]) ).
tcf(c_651,plain,
contains_pq(i(triple(sK0,sK1,sK2)),sK3(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(unflattening,[status(thm)],[c_650]) ).
tcf(c_655,plain,
! [X0: $i,X1: $i] :
( ~ less_than(X1,sK3(X0,X1))
| ( findmin_cpq_res(triple(sK0,sK1,sK2)) != X1 )
| ( i(triple(sK0,sK1,sK2)) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_52,c_142]) ).
tcf(c_656,plain,
~ less_than(findmin_cpq_res(triple(sK0,sK1,sK2)),sK3(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(unflattening,[status(thm)],[c_655]) ).
tcf(c_670,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i,X4: $i,X5: $i] :
( less_than(X3,X5)
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X4)
| ( X4 != X5 )
| ( findmin_cpq_res(triple(X0,X1,X2)) != X3 ) ),
inference(resolution_lifted,[status(thm)],[c_51,c_158]) ).
tcf(c_671,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( less_than(findmin_cpq_res(triple(X0,X1,X2)),X3)
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(unflattening,[status(thm)],[c_670]) ).
tcf(c_2980,plain,
contains_cpq(triple(sK0,sK1,sK2),sK3(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))),
inference(superposition,[status(thm)],[c_651,c_49]) ).
tcf(c_3412,plain,
! [X0: $i] :
( less_than(findmin_cpq_res(triple(sK0,sK1,sK2)),X0)
| ~ phi(findmin_cpq_eff(triple(sK0,sK1,sK2)))
| ~ contains_cpq(triple(sK0,sK1,sK2),X0) ),
inference(instantiation,[status(thm)],[c_671]) ).
tcf(c_3784,plain,
( less_than(findmin_cpq_res(triple(sK0,sK1,sK2)),sK3(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))))
| ~ phi(findmin_cpq_eff(triple(sK0,sK1,sK2)))
| ~ contains_cpq(triple(sK0,sK1,sK2),sK3(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))) ),
inference(instantiation,[status(thm)],[c_3412]) ).
tcf(c_3785,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3784,c_2980,c_656,c_53]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV381+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.12/10.40 % Computer : n015.cluster.edu
% 0.12/10.40 % Model : x86_64 x86_64
% 0.12/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.40 % Memory : 8046.5625MB
% 0.12/10.40 % OS : Linux 6.8.0-71-generic
% 0.12/10.40 % CPULimit : 300
% 0.12/10.40 % WCLimit : 300
% 0.16/10.40 % DateTime : Thu Sep 24 19:28:24 UTC 2026
% 0.16/10.40 % CPUTime :
% 0.16/10.40 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.16/10.44 Running first-order theorem proving
% 0.16/10.44 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
% 0.16/10.45
% 0.16/10.45 % ======== iProver multi-core TPTP/SMT =========
% 0.16/10.45
% 0.16/10.45 % Detected problem language: tptp
% 0.16/10.46 % Proving...
% 3.74/11.22 % SZS status Started for theBenchmark.p
% 3.74/11.22 % SZS status Theorem for theBenchmark.p
% 3.74/11.22
% 3.74/11.22 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.74/11.22
% 3.74/11.22 % ------ iProver source info
% 3.74/11.22
% 3.74/11.22 % git: date: 2026-07-19 20:42:38 +0200
% 3.74/11.22 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.74/11.22 % git: non_committed_changes: false
% 3.74/11.22
% 3.74/11.22 % ------ Parsing...
% 3.74/11.22 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.74/11.22
% 3.74/11.22 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 3.74/11.22
% 3.74/11.22 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.74/11.22
% 3.74/11.22 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.74/11.22 % ------ Proving...
% 3.74/11.22 % ------ Problem Properties
% 3.74/11.22
% 3.74/11.22 %
% 3.74/11.22 % clauses 44
% 3.74/11.22 % conjectures 1
% 3.74/11.22 % EPR 6
% 3.74/11.22 % Horn 33
% 3.74/11.22 % unary 15
% 3.74/11.22 % binary 19
% 3.74/11.22 % lits 85
% 3.74/11.23 % lits eq 21
% 3.74/11.23 % fd_pure 0
% 3.74/11.23 % fd_pseudo 0
% 3.74/11.23 % fd_cond 5
% 3.74/11.23 % fd_pseudo_cond 3
% 3.74/11.23 % AC symbols 0
% 3.74/11.23
% 3.74/11.23 % ------ Schedule dynamic 5 is on
% 3.74/11.23
% 3.74/11.23 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.74/11.23
% 3.74/11.23
% 3.74/11.23 % ------
% 3.74/11.23 % Current options:
% 3.74/11.23 % ------
% 3.74/11.23
% 3.74/11.23
% 3.74/11.23 %
% 3.74/11.23
% 3.74/11.23 % ------ Proving...
% 3.74/11.23 %
% 3.74/11.23
% 3.74/11.23 % SZS status Theorem for theBenchmark.p
% 3.74/11.23
% 3.74/11.23 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.74/11.23
%------------------------------------------------------------------------------