%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV371+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n002.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 : Thu Sep 24 09:03:32 AM UTC 2026
% Result : Theorem 13.78s 19.04s
% Output : Proof 13.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 34 ( 10 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 69 ( 30 ~; 21 |; 13 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 51 ( 0 sgn 34 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax58,axiom,
! [U,V] :
( pi_sharp_find_min(U,V)
<=> ( issmallestelement_pq(U,V)
& contains_pq(U,V) ) ),
file('SWV007+4.ax',ax58) ).
fof(l7_l8,lemma,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> contains_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('theBenchmark.p',l7_l8) ).
fof(l7_lX,lemma,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('theBenchmark.p',l7_lX) ).
fof(l7_co,conjecture,
! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
file('theBenchmark.p',l7_co) ).
fof(f_58_1,plain,
! [U,V] :
( ( pi_sharp_find_min(U,V)
| ~ issmallestelement_pq(U,V)
| ~ contains_pq(U,V) )
& ( ( issmallestelement_pq(U,V)
& contains_pq(U,V) )
| ~ pi_sharp_find_min(U,V) ) ),
inference(fof_nnf,[status(thm)],[ax58]) ).
fof(f_58_2,plain,
! [U_207,U_206] :
( ( pi_sharp_find_min(U_207,U_206)
| ~ issmallestelement_pq(U_207,U_206)
| ~ contains_pq(U_207,U_206) )
& ( ( issmallestelement_pq(U_207,U_206)
& contains_pq(U_207,U_206) )
| ~ pi_sharp_find_min(U_207,U_206) ) ),
inference(variable_rename,[status(thm)],[f_58_1]) ).
fof(f_58_3,plain,
( ! [U_211,U_209] :
( pi_sharp_find_min(U_211,U_209)
| ~ issmallestelement_pq(U_211,U_209)
| ~ contains_pq(U_211,U_209) )
& ! [U_210,U_208] :
( ( issmallestelement_pq(U_210,U_208)
& contains_pq(U_210,U_208) )
| ~ pi_sharp_find_min(U_210,U_208) ) ),
inference(miniscope,[status(thm)],[f_58_2]) ).
cnf(f_58_6,plain,
( pi_sharp_find_min(U_211,U_209)
| ~ issmallestelement_pq(U_211,U_209)
| ~ contains_pq(U_211,U_209) ),
inference(clausify,[status(thm)],[f_58_3]) ).
fof(f_63_1,plain,
! [U,V,W] :
( contains_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W)))
| ~ phi(findmin_cpq_eff(triple(U,V,W))) ),
inference(fof_nnf,[status(thm)],[l7_l8]) ).
fof(f_63_2,plain,
! [U_235,U_234,U_233] :
( contains_pq(i(triple(U_235,U_234,U_233)),findmin_cpq_res(triple(U_235,U_234,U_233)))
| ~ phi(findmin_cpq_eff(triple(U_235,U_234,U_233))) ),
inference(variable_rename,[status(thm)],[f_63_1]) ).
cnf(f_63_3,plain,
( contains_pq(i(triple(U_235,U_234,U_233)),findmin_cpq_res(triple(U_235,U_234,U_233)))
| ~ phi(findmin_cpq_eff(triple(U_235,U_234,U_233))) ),
inference(clausify,[status(thm)],[f_63_2]) ).
fof(f_64_1,plain,
! [U,V,W] :
( issmallestelement_pq(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W)))
| ~ phi(findmin_cpq_eff(triple(U,V,W))) ),
inference(fof_nnf,[status(thm)],[l7_lX]) ).
fof(f_64_2,plain,
! [U_238,U_237,U_236] :
( issmallestelement_pq(i(triple(U_238,U_237,U_236)),findmin_cpq_res(triple(U_238,U_237,U_236)))
| ~ phi(findmin_cpq_eff(triple(U_238,U_237,U_236))) ),
inference(variable_rename,[status(thm)],[f_64_1]) ).
cnf(f_64_3,plain,
( issmallestelement_pq(i(triple(U_238,U_237,U_236)),findmin_cpq_res(triple(U_238,U_237,U_236)))
| ~ phi(findmin_cpq_eff(triple(U_238,U_237,U_236))) ),
inference(clausify,[status(thm)],[f_64_2]) ).
fof(f_65_1,negated_conjecture,
~ ! [U,V,W] :
( phi(findmin_cpq_eff(triple(U,V,W)))
=> pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W))) ),
inference(negate,[status(cth)],[l7_co]) ).
fof(f_65_2,negated_conjecture,
? [U,V,W] :
( ~ pi_sharp_find_min(i(triple(U,V,W)),findmin_cpq_res(triple(U,V,W)))
& phi(findmin_cpq_eff(triple(U,V,W))) ),
inference(fof_nnf,[status(thm)],[f_65_1]) ).
fof(f_65_3,negated_conjecture,
? [U_241,U_240,U_239] :
( ~ pi_sharp_find_min(i(triple(U_241,U_240,U_239)),findmin_cpq_res(triple(U_241,U_240,U_239)))
& phi(findmin_cpq_eff(triple(U_241,U_240,U_239))) ),
inference(variable_rename,[status(thm)],[f_65_2]) ).
fof(f_65_4,negated_conjecture,
? [U_240,U_239] :
( ~ pi_sharp_find_min(i(triple(sK5,U_240,U_239)),findmin_cpq_res(triple(sK5,U_240,U_239)))
& phi(findmin_cpq_eff(triple(sK5,U_240,U_239))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5]),skolemize(U_241,sK5)],[f_65_3]) ).
fof(f_65_5,negated_conjecture,
? [U_239] :
( ~ pi_sharp_find_min(i(triple(sK5,sK6,U_239)),findmin_cpq_res(triple(sK5,sK6,U_239)))
& phi(findmin_cpq_eff(triple(sK5,sK6,U_239))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6]),skolemize(U_240,sK6)],[f_65_4]) ).
fof(f_65_6,negated_conjecture,
( ~ pi_sharp_find_min(i(triple(sK5,sK6,sK7)),findmin_cpq_res(triple(sK5,sK6,sK7)))
& phi(findmin_cpq_eff(triple(sK5,sK6,sK7))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7]),skolemize(U_239,sK7)],[f_65_5]) ).
fof(f_65_7,negated_conjecture,
( ~ pi_sharp_find_min(i(triple(sK5,sK6,sK7)),findmin_cpq_res(triple(sK5,sK6,sK7)))
& phi(findmin_cpq_eff(triple(sK5,sK6,sK7))) ),
inference(definitional_conversion,[status(esa)],[f_65_6]) ).
cnf(f_65_8,negated_conjecture,
phi(findmin_cpq_eff(triple(sK5,sK6,sK7))),
inference(clausify,[status(thm)],[f_65_7]) ).
cnf(f_65_9,negated_conjecture,
~ pi_sharp_find_min(i(triple(sK5,sK6,sK7)),findmin_cpq_res(triple(sK5,sK6,sK7))),
inference(clausify,[status(thm)],[f_65_7]) ).
cnf(t1,plain,
~ pi_sharp_find_min(i(triple(sK5,sK6,sK7)),findmin_cpq_res(triple(sK5,sK6,sK7))),
inference(start,[status(thm),parent(0:0)],[f_65_9]) ).
cnf(t2,plain,
( ~ issmallestelement_pq(i(triple(sK5,sK6,sK7)),findmin_cpq_res(triple(sK5,sK6,sK7)))
| ~ contains_pq(i(triple(sK5,sK6,sK7)),findmin_cpq_res(triple(sK5,sK6,sK7)))
| pi_sharp_find_min(i(triple(sK5,sK6,sK7)),findmin_cpq_res(triple(sK5,sK6,sK7))) ),
inference(extension,[status(thm),parent(t1:1)],[f_58_6]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ phi(findmin_cpq_eff(triple(sK5,sK6,sK7)))
| contains_pq(i(triple(sK5,sK6,sK7)),findmin_cpq_res(triple(sK5,sK6,sK7))) ),
inference(extension,[status(thm),parent(t2:2)],[f_63_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
phi(findmin_cpq_eff(triple(sK5,sK6,sK7))),
inference(extension,[status(thm),parent(t4:2)],[f_65_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ phi(findmin_cpq_eff(triple(sK5,sK6,sK7)))
| issmallestelement_pq(i(triple(sK5,sK6,sK7)),findmin_cpq_res(triple(sK5,sK6,sK7))) ),
inference(extension,[status(thm),parent(t2:3)],[f_64_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
phi(findmin_cpq_eff(triple(sK5,sK6,sK7))),
inference(extension,[status(thm),parent(t8:2)],[f_65_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV371+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.38 % Computer : n002.cluster.edu
% 0.09/5.38 % Model : x86_64 x86_64
% 0.09/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.38 % Memory : 8046.5625MB
% 0.09/5.38 % OS : Linux 6.8.0-71-generic
% 0.09/5.38 % CPULimit : 300
% 0.09/5.38 % WCLimit : 300
% 0.09/5.38 % DateTime : Sun Sep 20 03:30:37 UTC 2026
% 0.09/5.38 % CPUTime :
% 13.78/19.04 % SZS status Theorem for theBenchmark
% 13.78/19.04 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------