%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWW297+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n016.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 09:05:02 AM UTC 2026
% Result : Theorem 55.86s 66.18s
% Output : Proof 55.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 26 ( 10 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 30 ~; 21 |; 19 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 46 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_evaln__Suc,axiom,
! [V_s_H,V_n,V_s,V_c] :
( c_Natural_Oevaln(V_c,V_s,V_n,V_s_H)
=> c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H) ),
file('theBenchmark.p',fact_evaln__Suc) ).
fof(conj_0,conjecture,
( ! [B_Z,B_s] :
( v_fun1(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(v_com,B_s,hAPP(c_Nat_OSuc,v_n),B_s_H)
=> v_fun2(B_Z,B_s_H) ) )
=> ! [B_Z,B_s] :
( v_fun1(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(v_com,B_s,v_n,B_s_H)
=> v_fun2(B_Z,B_s_H) ) ) ),
file('theBenchmark.p',conj_0) ).
fof(f_2_1,plain,
! [V_s_H,V_n,V_s,V_c] :
( c_Natural_Oevaln(V_c,V_s,hAPP(c_Nat_OSuc,V_n),V_s_H)
| ~ c_Natural_Oevaln(V_c,V_s,V_n,V_s_H) ),
inference(fof_nnf,[status(thm)],[fact_evaln__Suc]) ).
fof(f_2_2,plain,
! [U_6,U_5,U_4,U_3] :
( c_Natural_Oevaln(U_3,U_4,hAPP(c_Nat_OSuc,U_5),U_6)
| ~ c_Natural_Oevaln(U_3,U_4,U_5,U_6) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
! [U_3,U_4,U_5,U_6] :
( c_Natural_Oevaln(U_3,U_4,hAPP(c_Nat_OSuc,U_5),U_6)
| ~ c_Natural_Oevaln(U_3,U_4,U_5,U_6) ),
inference(definitional_conversion,[status(esa)],[f_2_2]) ).
cnf(f_2_4,plain,
( c_Natural_Oevaln(U_3,U_4,hAPP(c_Nat_OSuc,U_5),U_6)
| ~ c_Natural_Oevaln(U_3,U_4,U_5,U_6) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_5225_1,negated_conjecture,
( ~ ! [B_Z,B_s] :
( v_fun1(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(v_com,B_s,v_n,B_s_H)
=> v_fun2(B_Z,B_s_H) ) )
& ! [B_Z,B_s] :
( v_fun1(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(v_com,B_s,hAPP(c_Nat_OSuc,v_n),B_s_H)
=> v_fun2(B_Z,B_s_H) ) ) ),
inference(negate,[status(cth)],[conj_0]) ).
fof(f_5225_2,negated_conjecture,
( ? [B_Z,B_s] :
( ? [B_s_H] :
( ~ v_fun2(B_Z,B_s_H)
& c_Natural_Oevaln(v_com,B_s,v_n,B_s_H) )
& v_fun1(B_Z,B_s) )
& ! [B_Z,B_s] :
( ! [B_s_H] :
( v_fun2(B_Z,B_s_H)
| ~ c_Natural_Oevaln(v_com,B_s,hAPP(c_Nat_OSuc,v_n),B_s_H) )
| ~ v_fun1(B_Z,B_s) ) ),
inference(fof_nnf,[status(thm)],[f_5225_1]) ).
fof(f_5225_3,negated_conjecture,
( ? [U_20848,U_20847] :
( ? [U_20846] :
( ~ v_fun2(U_20848,U_20846)
& c_Natural_Oevaln(v_com,U_20847,v_n,U_20846) )
& v_fun1(U_20848,U_20847) )
& ! [U_20845,U_20844] :
( ! [U_20843] :
( v_fun2(U_20845,U_20843)
| ~ c_Natural_Oevaln(v_com,U_20844,hAPP(c_Nat_OSuc,v_n),U_20843) )
| ~ v_fun1(U_20845,U_20844) ) ),
inference(variable_rename,[status(thm)],[f_5225_2]) ).
fof(f_5225_4,negated_conjecture,
( ? [U_20847] :
( ? [U_20846] :
( ~ v_fun2(sK567,U_20846)
& c_Natural_Oevaln(v_com,U_20847,v_n,U_20846) )
& v_fun1(sK567,U_20847) )
& ! [U_20845,U_20844] :
( ! [U_20843] :
( v_fun2(U_20845,U_20843)
| ~ c_Natural_Oevaln(v_com,U_20844,hAPP(c_Nat_OSuc,v_n),U_20843) )
| ~ v_fun1(U_20845,U_20844) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK567]),skolemize(U_20848,sK567)],[f_5225_3]) ).
fof(f_5225_5,negated_conjecture,
( ? [U_20846] :
( ~ v_fun2(sK567,U_20846)
& c_Natural_Oevaln(v_com,sK568,v_n,U_20846) )
& v_fun1(sK567,sK568)
& ! [U_20845,U_20844] :
( ! [U_20843] :
( v_fun2(U_20845,U_20843)
| ~ c_Natural_Oevaln(v_com,U_20844,hAPP(c_Nat_OSuc,v_n),U_20843) )
| ~ v_fun1(U_20845,U_20844) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK568]),skolemize(U_20847,sK568)],[f_5225_4]) ).
fof(f_5225_6,negated_conjecture,
( ~ v_fun2(sK567,sK569)
& c_Natural_Oevaln(v_com,sK568,v_n,sK569)
& v_fun1(sK567,sK568)
& ! [U_20845,U_20844] :
( ! [U_20843] :
( v_fun2(U_20845,U_20843)
| ~ c_Natural_Oevaln(v_com,U_20844,hAPP(c_Nat_OSuc,v_n),U_20843) )
| ~ v_fun1(U_20845,U_20844) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK569]),skolemize(U_20846,sK569)],[f_5225_5]) ).
fof(f_5225_7,negated_conjecture,
( ~ v_fun2(sK567,sK569)
& c_Natural_Oevaln(v_com,sK568,v_n,sK569)
& v_fun1(sK567,sK568)
& ! [U_20843,U_20844,U_20845] :
( v_fun2(U_20845,U_20843)
| ~ c_Natural_Oevaln(v_com,U_20844,hAPP(c_Nat_OSuc,v_n),U_20843)
| ~ v_fun1(U_20845,U_20844) ) ),
inference(definitional_conversion,[status(esa)],[f_5225_6]) ).
cnf(f_5225_8,negated_conjecture,
( v_fun2(U_20845,U_20843)
| ~ c_Natural_Oevaln(v_com,U_20844,hAPP(c_Nat_OSuc,v_n),U_20843)
| ~ v_fun1(U_20845,U_20844) ),
inference(clausify,[status(thm)],[f_5225_7]) ).
cnf(f_5225_9,negated_conjecture,
v_fun1(sK567,sK568),
inference(clausify,[status(thm)],[f_5225_7]) ).
cnf(f_5225_10,negated_conjecture,
c_Natural_Oevaln(v_com,sK568,v_n,sK569),
inference(clausify,[status(thm)],[f_5225_7]) ).
cnf(f_5225_11,negated_conjecture,
~ v_fun2(sK567,sK569),
inference(clausify,[status(thm)],[f_5225_7]) ).
cnf(t1,plain,
( ~ c_Natural_Oevaln(v_com,sK568,hAPP(c_Nat_OSuc,v_n),sK569)
| v_fun2(sK567,sK569)
| ~ v_fun1(sK567,sK568) ),
inference(start,[status(thm),parent(0:0)],[f_5225_8]) ).
cnf(t2,plain,
v_fun1(sK567,sK568),
inference(extension,[status(thm),parent(t1:1)],[f_5225_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
~ v_fun2(sK567,sK569),
inference(extension,[status(thm),parent(t1:2)],[f_5225_11]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
( ~ c_Natural_Oevaln(v_com,sK568,v_n,sK569)
| c_Natural_Oevaln(v_com,sK568,hAPP(c_Nat_OSuc,v_n),sK569) ),
inference(extension,[status(thm),parent(t1:3)],[f_2_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t1:3]) ).
cnf(t8,plain,
c_Natural_Oevaln(v_com,sK568,v_n,sK569),
inference(extension,[status(thm),parent(t6:2)],[f_5225_10]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW297+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/10.40 % Computer : n016.cluster.edu
% 0.10/10.40 % Model : x86_64 x86_64
% 0.10/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.40 % Memory : 8046.5625MB
% 0.10/10.40 % OS : Linux 6.8.0-71-generic
% 0.10/10.40 % CPULimit : 300
% 0.10/10.40 % WCLimit : 300
% 0.10/10.40 % DateTime : Sun Sep 20 05:25:36 UTC 2026
% 0.14/10.40 % CPUTime :
% 55.86/66.18 % SZS status Theorem for theBenchmark
% 55.86/66.18 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------