%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW196+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 : Sun Sep 27 09:13:55 AM UTC 2026
% Result : Theorem 0.38s 0.79s
% Output : CNFRefutation 0.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 34 unt; 0 def)
% Number of atoms : 70 ( 48 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 38 ( 20 ~; 17 |; 0 &)
% ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 2 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-3 aty)
% Number of variables : 38 ( 18 sgn 7 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact__096EX_Am_O_An_A_061_A2_A_K_Am_096,axiom,
? [B_m] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m),
file('theBenchmark.p',fact__096EX_Am_O_An_A_061_A2_A_K_Am_096) ).
fof(fact_nat__mult__commute,axiom,
! [V_n,V_m] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_m,V_n) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,V_n,V_m),
file('theBenchmark.p',fact_nat__mult__commute) ).
fof(fact_zadd__commute,axiom,
! [V_w,V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_z,V_w) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_w,V_z),
file('theBenchmark.p',fact_zadd__commute) ).
fof(fact_zadd__0,axiom,
! [V_z] : c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),V_z) = V_z,
file('theBenchmark.p',fact_zadd__0) ).
fof(fact_Bit0__def,axiom,
! [V_k] : c_Int_OBit0(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,V_k,V_k),
file('theBenchmark.p',fact_Bit0__def) ).
fof(fact_Bit1__def,axiom,
! [V_k] : c_Int_OBit1(V_k) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),V_k),V_k),
file('theBenchmark.p',fact_Bit1__def) ).
fof(conj_0,axiom,
( ? [B_m] : v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m)
=> v_thesis____ ),
file('theBenchmark.p',conj_0) ).
fof(conj_1,conjecture,
v_thesis____,
file('theBenchmark.p',conj_1) ).
fof(conj_1_neg,negated_conjecture,
~ v_thesis____,
inference(assume_negation,[status(cth)],[conj_1]) ).
fof(nnf_1,plain,
? [B_m] : c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),B_m) = v_na____,
inference(fof_nnf,[status(thm)],[fact__096EX_Am_O_An_A_061_A2_A_K_Am_096]) ).
fof(sk_fact__096EX_Am_O_An_A_061_A2_A_K_Am_096,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK0) = v_na____,
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B_m,sK0)],[nnf_1]) ).
cnf(c_1499,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK0) = v_na____,
inference(split_conjunct,[status(thm)],[sk_fact__096EX_Am_O_An_A_061_A2_A_K_Am_096]) ).
cnf(c_1500,plain,
v_na____ = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK0),
inference(copy,[status(thm)],[c_1499]) ).
fof(fact_Pls__def,axiom,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
file('theBenchmark.p',fact_Pls__def) ).
cnf(c_1556,plain,
c_Int_OPls = c_Groups_Ozero__class_Ozero(tc_Int_Oint),
inference(clausify,[status(thm)],[fact_Pls__def]) ).
cnf(c_1558,plain,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,A,B) = c_Groups_Otimes__class_Otimes(tc_Nat_Onat,B,A),
inference(clausify,[status(thm)],[fact_nat__mult__commute]) ).
cnf(c_1833,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,B) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,B,A),
inference(clausify,[status(thm)],[fact_zadd__commute]) ).
cnf(c_1846,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),A) = A,
inference(clausify,[status(thm)],[fact_zadd__0]) ).
cnf(c_1851,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A) = c_Int_OBit0(A),
inference(clausify,[status(thm)],[fact_Bit0__def]) ).
cnf(c_1852,plain,
c_Int_OBit0(A) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,A),
inference(copy,[status(thm)],[c_1851]) ).
cnf(c_2294,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A),A) = c_Int_OBit1(A),
inference(clausify,[status(thm)],[fact_Bit1__def]) ).
cnf(c_2989,plain,
c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)) = c_Int_OBit1(A),
inference(paramod,[status(thm)],[c_1833,c_2294]) ).
cnf(c_2295,plain,
c_Int_OBit1(A) = c_Groups_Oplus__class_Oplus(tc_Int_Oint,A,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),A)),
inference(copy,[status(thm)],[c_2989]) ).
fof(fact_nat__1__add__1,axiom,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
file('theBenchmark.p',fact_nat__1__add__1) ).
cnf(c_2501,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),
inference(clausify,[status(thm)],[fact_nat__1__add__1]) ).
cnf(c_2990,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),
inference(paramod,[status(thm)],[c_1556,c_2501]) ).
cnf(c_2991,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),
inference(paramod,[status(thm)],[c_2295,c_2990]) ).
cnf(c_2992,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),
inference(paramod,[status(thm)],[c_1833,c_2991]) ).
cnf(c_2993,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),
inference(paramod,[status(thm)],[c_1846,c_2992]) ).
cnf(c_2994,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(paramod,[status(thm)],[c_1846,c_2993]) ).
cnf(c_2995,plain,
c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)) = c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),
inference(paramod,[status(thm)],[c_1852,c_2994]) ).
cnf(c_2502,plain,
c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))) = c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),
inference(copy,[status(thm)],[c_2995]) ).
cnf(c_2702,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),A) != v_na____ ),
inference(clausify,[status(thm)],[conj_0]) ).
cnf(c_2996,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),A) != v_na____ ),
inference(paramod,[status(thm)],[c_1556,c_2702]) ).
cnf(c_2997,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),A) != v_na____ ),
inference(paramod,[status(thm)],[c_2295,c_2996]) ).
cnf(c_2998,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),A) != v_na____ ),
inference(paramod,[status(thm)],[c_1833,c_2997]) ).
cnf(c_2999,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),A) != v_na____ ),
inference(paramod,[status(thm)],[c_1846,c_2998]) ).
cnf(c_3000,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oone__class_Oone(tc_Int_Oint))),A) != v_na____ ),
inference(paramod,[status(thm)],[c_1846,c_2999]) ).
cnf(c_3001,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),A) != v_na____ ),
inference(paramod,[status(thm)],[c_1852,c_3000]) ).
cnf(c_3002,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != v_na____ ),
inference(paramod,[status(thm)],[c_2502,c_3001]) ).
cnf(c_3003,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Int_OPls))),sK0) ),
inference(paramod,[status(thm)],[c_1500,c_3002]) ).
cnf(c_3004,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Int_OBit1(c_Groups_Ozero__class_Ozero(tc_Int_Oint)))),sK0) ),
inference(paramod,[status(thm)],[c_1556,c_3003]) ).
cnf(c_3005,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Ozero__class_Ozero(tc_Int_Oint))))),sK0) ),
inference(paramod,[status(thm)],[c_2295,c_3004]) ).
cnf(c_3006,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))))),sK0) ),
inference(paramod,[status(thm)],[c_1833,c_3005]) ).
cnf(c_3007,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Ozero__class_Ozero(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint)))),sK0) ),
inference(paramod,[status(thm)],[c_1846,c_3006]) ).
cnf(c_3008,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Int_OBit0(c_Groups_Oone__class_Oone(tc_Int_Oint))),sK0) ),
inference(paramod,[status(thm)],[c_1846,c_3007]) ).
cnf(c_3009,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Int_Onumber__class_Onumber__of(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Int_Oint,c_Groups_Oone__class_Oone(tc_Int_Oint),c_Groups_Oone__class_Oone(tc_Int_Oint))),sK0) ),
inference(paramod,[status(thm)],[c_1852,c_3008]) ).
cnf(c_3010,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),sK0) ),
inference(paramod,[status(thm)],[c_2502,c_3009]) ).
cnf(c_2703,plain,
( v_thesis____
| c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,sK0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))) ),
inference(paramod,[status(thm)],[c_1558,c_3010]) ).
cnf(c_2704,negated_conjecture,
~ v_thesis____,
inference(clausify,[status(thm)],[conj_1_neg]) ).
cnf(c_2987,negated_conjecture,
c_Groups_Otimes__class_Otimes(tc_Nat_Onat,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != c_Groups_Otimes__class_Otimes(tc_Nat_Onat,sK0,c_Groups_Oplus__class_Oplus(tc_Nat_Onat,c_Groups_Oone__class_Oone(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat))),
inference(resolve,[status(thm)],[c_2704,c_2703]) ).
cnf(c_2988,plain,
$false,
inference(resolve,[status(thm)],[c_2987,c_1558]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW196+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n002.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 15:28:35 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2063044 was started by sandbox on n002,
% 0.09/0.37 % Sat Sep 26 15:28:35 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.32/0.59
% 0.32/0.59 % From the command line: assign(max_seconds, 300).
% 0.32/0.59
% 0.32/0.59 % SInE: 797 to sos, 374 to usable, of 1171 axioms (tolerance 2.00, depth 0 fixpoint).
% 0.38/0.79
% 0.38/0.79 % SZS status Theorem for theBenchmark
% 0.38/0.79
% 0.38/0.79 % Proof 1 at 0.13 (+ 0.03) seconds.
% 0.38/0.79 % Length of proof is 25.
% 0.38/0.79 % Level of proof is 6.
% 0.38/0.79 % Maximum clause weight is 222.000.
% 0.38/0.79 % Given clauses 0.
% 0.38/0.79
% 0.38/0.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
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