%------------------------------------------------------------------------------
% File : hopCoP---0.1
% Problem : SWW297+1 : TPTP v9.0.0. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Jul 25 05:04:08 PM UTC 2025
% Result : Theorem 6.91s 1.49s
% Output : CNFRefutation 6.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 20 ( 13 unt; 0 def)
% Number of atoms : 37 ( 6 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 26 ( 9 ~; 6 |; 0 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 41 ( 0 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(conj_0,plain,
( ! [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('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
fof(conj_0_negated,plain,
~ ( ! [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) ) ) ),
inference(negate_conjecture,[status(cth)],[conj_0]) ).
cnf(7459,plain,
( ~ c_Natural_Oevaln(v_com,X0,hAPP(c_Nat_OSuc,v_n),X1)
| ~ v_fun1(X2,X0)
| v_fun2(X2,X1) ),
inference(cnf,[status(esa)],[conj_0_negated]) ).
cnf(l0,plain,
( ~ c_Natural_Oevaln(v_com,sK669,hAPP(c_Nat_OSuc,v_n),sK670)
| ~ v_fun1(hAPP(hAPP(c_Product__Type_OPair(X0_5,X1_5),hAPP(c_Product__Type_Ofst(X0_5,X1_5),sK668)),hAPP(c_Product__Type_Osnd(X0_5,X1_5),sK668)),sK669)
| v_fun2(hAPP(hAPP(c_Product__Type_OPair(X0_5,X1_5),hAPP(c_Product__Type_Ofst(X0_5,X1_5),sK668)),hAPP(c_Product__Type_Osnd(X0_5,X1_5),sK668)),sK670) ),
inference(instantiation,[status(thm)],[7459]) ).
cnf(7462,plain,
~ v_fun2(sK668,sK670),
inference(cnf,[status(esa)],[conj_0_negated]) ).
cnf(l11,plain,
~ v_fun2(sK668,sK670),
inference(instantiation,[status(thm)],[7462]) ).
cnf(7460,plain,
v_fun1(sK668,sK669),
inference(cnf,[status(esa)],[conj_0_negated]) ).
cnf(l6,plain,
v_fun1(sK668,sK669),
inference(instantiation,[status(thm)],[7460]) ).
fof(fact_evaln__Suc,plain,
! [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('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__Suc) ).
cnf(1,plain,
( ~ c_Natural_Oevaln(X0,X1,X2,X3)
| c_Natural_Oevaln(X0,X1,hAPP(c_Nat_OSuc,X2),X3) ),
inference(cnf,[status(esa)],[fact_evaln__Suc]) ).
cnf(l2,plain,
( ~ c_Natural_Oevaln(v_com,sK669,v_n,sK670)
| c_Natural_Oevaln(v_com,sK669,hAPP(c_Nat_OSuc,v_n),sK670) ),
inference(instantiation,[status(thm)],[1]) ).
cnf(7461,plain,
c_Natural_Oevaln(v_com,sK669,v_n,sK670),
inference(cnf,[status(esa)],[conj_0_negated]) ).
cnf(l8,plain,
c_Natural_Oevaln(v_com,sK669,v_n,sK670),
inference(instantiation,[status(thm)],[7461]) ).
fof(fact_surjective__pairing,plain,
! [T_b,T_a,V_t] : V_t = hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_t)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_t)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_surjective__pairing) ).
cnf(2432,plain,
X0 = hAPP(hAPP(c_Product__Type_OPair(X1,X2),hAPP(c_Product__Type_Ofst(X1,X2),X0)),hAPP(c_Product__Type_Osnd(X1,X2),X0)),
inference(cnf,[status(esa)],[fact_surjective__pairing]) ).
cnf(l3,plain,
sK668 = hAPP(hAPP(c_Product__Type_OPair(X0_5,X1_5),hAPP(c_Product__Type_Ofst(X0_5,X1_5),sK668)),hAPP(c_Product__Type_Osnd(X0_5,X1_5),sK668)),
inference(instantiation,[status(thm)],[2432]) ).
fof(fact_pair__collapse,plain,
! [V_p,T_b,T_a] : hAPP(hAPP(c_Product__Type_OPair(T_a,T_b),hAPP(c_Product__Type_Ofst(T_a,T_b),V_p)),hAPP(c_Product__Type_Osnd(T_a,T_b),V_p)) = V_p,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__collapse) ).
cnf(2433,plain,
hAPP(hAPP(c_Product__Type_OPair(X0,X1),hAPP(c_Product__Type_Ofst(X0,X1),X2)),hAPP(c_Product__Type_Osnd(X0,X1),X2)) = X2,
inference(cnf,[status(esa)],[fact_pair__collapse]) ).
cnf(l5,plain,
hAPP(hAPP(c_Product__Type_OPair(X0_5,X1_5),hAPP(c_Product__Type_Ofst(X0_5,X1_5),sK668)),hAPP(c_Product__Type_Osnd(X0_5,X1_5),sK668)) = sK668,
inference(instantiation,[status(thm)],[2433]) ).
cnf(final,plain,
$false,
inference(ground_refutation,[status(thm)],[l0,l11,l6,l2,l8,l3,l5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : SWW297+1 : TPTP v9.0.0. Released v5.2.0.
% 0.10/0.13 % Command : /export/starexec/sandbox2/solver/bin/execute.py 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Jul 22 13:18:04 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.46/0.66 % launching worker at depth: 7
% 0.46/0.66 % launching worker at depth: 1
% 0.46/0.66 % launching worker at depth: 2
% 0.46/0.66 % launching worker at depth: 3
% 0.46/0.66 % launching worker at depth: 4
% 0.46/0.66 % launching worker at depth: 6
% 0.46/0.66 % launching worker at depth: 5
% 0.46/0.66 % launching worker at depth: 8
% 0.46/0.66 % launching worker at depth: 9
% 6.91/1.49 % SZS status Theorem for theBenchmark
% 6.91/1.49 % SZS output start CNFRefutation
% See solution above
%------------------------------------------------------------------------------