%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV417+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 : n020.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 3.97s 6.71s
% Output : CNFRefutation 3.97s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 44 ( 15 unt; 4 def)
% Number of atoms : 129 ( 22 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 94 ( 41 ~; 32 |; 14 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 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 : 11 ( 9 usr; 5 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 62 ( 0 sgn 54 !; 8 ?; 11 :)
% Comments :
%------------------------------------------------------------------------------
fof(f14,axiom,
! [X0,X1] :
( ( issmallestelement_pq(X0,X1)
& contains_pq(X0,X1) )
=> findmin_pq_res(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+1.ax',ax14) ).
fof(f53,axiom,
! [X0] : removemin_cpq_res(X0) = findmin_cpq_res(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax53) ).
fof(f58,axiom,
! [X0,X1] :
( pi_sharp_find_min(X0,X1)
<=> ( issmallestelement_pq(X0,X1)
& contains_pq(X0,X1) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+4.ax',ax58) ).
fof(f63,axiom,
! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> pi_sharp_find_min(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main4_l7) ).
fof(f64,conjecture,
! [X0,X1,X2] :
( pi_find_min(triple(X0,X1,X2))
=> ( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> ? [X3] :
( findmin_cpq_res(triple(X0,X1,X2)) = findmin_pq_res(i(triple(X0,X1,X2)),X3)
& pi_sharp_find_min(i(triple(X0,X1,X2)),X3) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co4) ).
fof(f65,negated_conjecture,
~ ! [X0,X1,X2] :
( pi_find_min(triple(X0,X1,X2))
=> ( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> ? [X3] :
( findmin_cpq_res(triple(X0,X1,X2)) = findmin_pq_res(i(triple(X0,X1,X2)),X3)
& pi_sharp_find_min(i(triple(X0,X1,X2)),X3) ) ) ),
inference(negated_conjecture,[status(cth)],[f64]) ).
fof(f85,plain,
! [X0,X1] :
( ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1)
| findmin_pq_res(X0,X1) = X1 ),
inference(ennf_transformation,[],[f14]) ).
fof(f86,plain,
! [X0,X1] :
( ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1)
| findmin_pq_res(X0,X1) = X1 ),
inference(flattening,[],[f85]) ).
fof(f117,plain,
! [X0,X1,X2] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| pi_sharp_find_min(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f63]) ).
fof(f118,plain,
? [X0,X1,X2] :
( pi_find_min(triple(X0,X1,X2))
& phi(findmin_cpq_eff(triple(X0,X1,X2)))
& ! [X3] :
( findmin_cpq_res(triple(X0,X1,X2)) != findmin_pq_res(i(triple(X0,X1,X2)),X3)
| ~ pi_sharp_find_min(i(triple(X0,X1,X2)),X3) ) ),
inference(ennf_transformation,[],[f65]) ).
fof(f119,plain,
? [X0,X1,X2] :
( pi_find_min(triple(X0,X1,X2))
& phi(findmin_cpq_eff(triple(X0,X1,X2)))
& ! [X3] :
( findmin_cpq_res(triple(X0,X1,X2)) != findmin_pq_res(i(triple(X0,X1,X2)),X3)
| ~ pi_sharp_find_min(i(triple(X0,X1,X2)),X3) ) ),
inference(flattening,[],[f118]) ).
fof(f131,plain,
! [X0,X1] :
( ( ~ pi_sharp_find_min(X0,X1)
| ( issmallestelement_pq(X0,X1)
& contains_pq(X0,X1) ) )
& ( ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1)
| pi_sharp_find_min(X0,X1) ) ),
inference(nnf_transformation,[],[f58]) ).
fof(f132,plain,
! [X0,X1] :
( ( ~ pi_sharp_find_min(X0,X1)
| ( issmallestelement_pq(X0,X1)
& contains_pq(X0,X1) ) )
& ( ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1)
| pi_sharp_find_min(X0,X1) ) ),
inference(flattening,[],[f131]) ).
fof(f137,plain,
( pi_find_min(triple(sK3,sK4,sK5))
& phi(findmin_cpq_eff(triple(sK3,sK4,sK5)))
& ! [X3] :
( findmin_cpq_res(triple(sK3,sK4,sK5)) != findmin_pq_res(i(triple(sK3,sK4,sK5)),X3)
| ~ pi_sharp_find_min(i(triple(sK3,sK4,sK5)),X3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4,sK5]),skolemize(X0,sK3),skolemize(X1,sK4),skolemize(X2,sK5)],[f119]) ).
fof(f155,plain,
! [X0,X1] :
( ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1)
| findmin_pq_res(X0,X1) = X1 ),
inference(cnf_transformation,[],[f86]) ).
fof(f201,plain,
! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
inference(cnf_transformation,[],[f53]) ).
fof(f204,plain,
! [X0,X1] :
( ~ pi_sharp_find_min(X0,X1)
| issmallestelement_pq(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f205,plain,
! [X0,X1] :
( ~ pi_sharp_find_min(X0,X1)
| contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
fof(f212,plain,
! [X2,X0,X1] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| pi_sharp_find_min(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
inference(cnf_transformation,[],[f117]) ).
fof(f214,plain,
phi(findmin_cpq_eff(triple(sK3,sK4,sK5))),
inference(cnf_transformation,[],[f137]) ).
fof(f215,plain,
! [X3] :
( findmin_cpq_res(triple(sK3,sK4,sK5)) != findmin_pq_res(i(triple(sK3,sK4,sK5)),X3)
| ~ pi_sharp_find_min(i(triple(sK3,sK4,sK5)),X3) ),
inference(cnf_transformation,[],[f137]) ).
fof(f220,plain,
! [X2,X0,X1] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| pi_sharp_find_min(i(triple(X0,X1,X2)),removemin_cpq_res(triple(X0,X1,X2))) ),
inference(definition_unfolding,[],[f212,f201]) ).
fof(f221,plain,
! [X3] :
( findmin_pq_res(i(triple(sK3,sK4,sK5)),X3) != removemin_cpq_res(triple(sK3,sK4,sK5))
| ~ pi_sharp_find_min(i(triple(sK3,sK4,sK5)),X3) ),
inference(definition_unfolding,[],[f215,f201]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( ( findmin_pq_res(X0,X1) = X1 )
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f155]) ).
tcf(c_114,plain,
! [X0: $i,X1: $i] :
( contains_pq(X0,X1)
| ~ pi_sharp_find_min(X0,X1) ),
inference(cnf_transformation,[],[f205]) ).
tcf(c_115,plain,
! [X0: $i,X1: $i] :
( issmallestelement_pq(X0,X1)
| ~ pi_sharp_find_min(X0,X1) ),
inference(cnf_transformation,[],[f204]) ).
tcf(c_121,plain,
! [X0: $i,X1: $i,X2: $i] :
( pi_sharp_find_min(i(triple(X0,X1,X2)),removemin_cpq_res(triple(X0,X1,X2)))
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(cnf_transformation,[],[f220]) ).
tcf(c_122,negated_conjecture,
! [X0: $i] :
( ~ pi_sharp_find_min(i(triple(sK3,sK4,sK5)),X0)
| ( findmin_pq_res(i(triple(sK3,sK4,sK5)),X0) != removemin_cpq_res(triple(sK3,sK4,sK5)) ) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_123,negated_conjecture,
phi(findmin_cpq_eff(triple(sK3,sK4,sK5))),
inference(cnf_transformation,[],[f214]) ).
tcf(c_2336,definition,
iPr_def_10 = triple(sK3,sK4,sK5),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_2337,definition,
iPr_def_11 = i(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_2339,definition,
iPr_def_13 = findmin_cpq_eff(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_2340,definition,
iPr_def_14 = removemin_cpq_res(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_2342,negated_conjecture,
phi(iPr_def_13),
inference(demodulation,[status(thm)],[c_123,c_2339]) ).
tcf(c_2343,negated_conjecture,
! [X0: $i] :
( ~ pi_sharp_find_min(iPr_def_11,X0)
| ( findmin_pq_res(iPr_def_11,X0) != iPr_def_14 ) ),
inference(demodulation,[status(thm)],[c_122,c_2340]) ).
tcf(c_4219,plain,
( pi_sharp_find_min(i(iPr_def_10),removemin_cpq_res(iPr_def_10))
| ~ phi(findmin_cpq_eff(triple(sK3,sK4,sK5))) ),
inference(superposition,[status(thm)],[c_2336,c_121]) ).
tcf(c_4222,plain,
( pi_sharp_find_min(iPr_def_11,iPr_def_14)
| ~ phi(iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_4219,c_2336,c_2337,c_2339,c_2340]) ).
tcf(c_4223,plain,
pi_sharp_find_min(iPr_def_11,iPr_def_14),
inference(forward_subsumption_resolution,[status(thm)],[c_4222,c_2342]) ).
tcf(c_4314,plain,
issmallestelement_pq(iPr_def_11,iPr_def_14),
inference(superposition,[status(thm)],[c_4223,c_115]) ).
tcf(c_4315,plain,
contains_pq(iPr_def_11,iPr_def_14),
inference(superposition,[status(thm)],[c_4223,c_114]) ).
tcf(c_4318,plain,
( ( findmin_pq_res(iPr_def_11,iPr_def_14) = iPr_def_14 )
| ~ contains_pq(iPr_def_11,iPr_def_14) ),
inference(superposition,[status(thm)],[c_4314,c_66]) ).
tcf(c_4369,plain,
findmin_pq_res(iPr_def_11,iPr_def_14) = iPr_def_14,
inference(global_subsumption_just,[status(thm)],[c_4318,c_4315,c_4318]) ).
tcf(c_4371,plain,
~ pi_sharp_find_min(iPr_def_11,iPr_def_14),
inference(superposition,[status(thm)],[c_4369,c_2343]) ).
tcf(c_4372,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4371,c_4223]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV417+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.78 % Computer : n020.cluster.edu
% 0.10/5.78 % Model : x86_64 x86_64
% 0.10/5.78 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.78 % Memory : 8046.5625MB
% 0.10/5.78 % OS : Linux 6.8.0-71-generic
% 0.10/5.79 % CPULimit : 300
% 0.10/5.79 % WCLimit : 300
% 0.10/5.79 % DateTime : Thu Sep 24 19:33:09 UTC 2026
% 0.10/5.79 % CPUTime :
% 0.10/5.79 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.13/5.83 Running first-order theorem proving
% 0.13/5.83 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
% 0.13/5.84
% 0.13/5.84 % ======== iProver multi-core TPTP/SMT =========
% 0.13/5.84
% 0.13/5.84 % Detected problem language: tptp
% 0.13/5.85 % Proving...
% 3.97/6.71 % SZS status Started for theBenchmark.p
% 3.97/6.71 % SZS status Theorem for theBenchmark.p
% 3.97/6.71
% 3.97/6.71 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.97/6.71
% 3.97/6.71 % ------ iProver source info
% 3.97/6.71
% 3.97/6.71 % git: date: 2026-07-19 20:42:38 +0200
% 3.97/6.71 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.97/6.71 % git: non_committed_changes: false
% 3.97/6.71
% 3.97/6.71 % ------ Parsing...
% 3.97/6.71 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.97/6.71
% 3.97/6.71 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e sup_sim: 0 sf_s rm: 5 0s sf_e pe_s pe_e %
% 3.97/6.71
% 3.97/6.71 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.97/6.71
% 3.97/6.71 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.97/6.71 % ------ Proving...
% 3.97/6.71 % ------ Problem Properties
% 3.97/6.71
% 3.97/6.71 %
% 3.97/6.71 % clauses 77
% 3.97/6.71 % conjectures 2
% 3.97/6.71 % EPR 15
% 3.97/6.71 % Horn 60
% 3.97/6.71 % unary 30
% 3.97/6.71 % binary 26
% 3.97/6.71 % lits 147
% 3.97/6.71 % lits eq 46
% 3.97/6.71 % fd_pure 0
% 3.97/6.71 % fd_pseudo 0
% 3.97/6.71 % fd_cond 5
% 3.97/6.71 % fd_pseudo_cond 7
% 3.97/6.71 % AC symbols 0
% 3.97/6.71
% 3.97/6.71 % ------ Schedule dynamic 5 is on
% 3.97/6.71
% 3.97/6.71 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.97/6.71
% 3.97/6.71
% 3.97/6.71 % ------
% 3.97/6.71 % Current options:
% 3.97/6.71 % ------
% 3.97/6.71
% 3.97/6.71
% 3.97/6.71 %
% 3.97/6.71
% 3.97/6.71 % ------ Proving...
% 3.97/6.71 %
% 3.97/6.71
% 3.97/6.71 % SZS status Theorem for theBenchmark.p
% 3.97/6.71
% 3.97/6.71 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.97/6.71
% 3.97/6.71
%------------------------------------------------------------------------------