%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW294+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n006.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 09:14:03 AM UTC 2026
% Result : Theorem 3.41s 1.00s
% Output : CNFRefutation 3.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 15 ( 6 unt; 0 def)
% Number of atoms : 33 ( 9 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 31 ( 13 ~; 5 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 9 con; 0-4 aty)
% Number of variables : 38 ( 2 sgn 28 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_Suc__neq__Zero,axiom,
! [V_m] : hAPP(c_Nat_OSuc,V_m) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
file('theBenchmark.p',fact_Suc__neq__Zero) ).
fof(fact_evaln__elim__cases_I6_J,axiom,
! [V_s1,V_n,V_s,V_P] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1)
=> ~ ! [B_n] :
( V_n = hAPP(c_Nat_OSuc,B_n)
=> ~ c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1) ) ),
file('theBenchmark.p',fact_evaln__elim__cases_I6_J) ).
fof(conj_0,conjecture,
! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),B_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_s_H)
=> v_Q(B_Z,B_s_H) ) ),
file('theBenchmark.p',conj_0) ).
fof(conj_0_neg,negated_conjecture,
~ ! [B_Z,B_s] :
( v_P(B_Z,B_s)
=> ! [B_s_H] :
( c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),B_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_s_H)
=> v_Q(B_Z,B_s_H) ) ),
inference(assume_negation,[status(cth)],[conj_0]) ).
fof(nnf_344,plain,
! [V_s1,V_n,V_s,V_P] :
( ? [B_n] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,B_n,V_s1)
& hAPP(c_Nat_OSuc,B_n) = V_n )
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1) ),
inference(fof_nnf,[status(thm)],[fact_evaln__elim__cases_I6_J]) ).
fof(sk_fact_evaln__elim__cases_I6_J_sk,plain,
! [V_s1,V_n,V_s,V_P] :
( ( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,V_P)),V_s,sK0(V_s1,V_n,V_s,V_P),V_s1)
& hAPP(c_Nat_OSuc,sK0(V_s1,V_n,V_s,V_P)) = V_n )
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,V_P),V_s,V_n,V_s1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(B_n,sK0(V_s1,V_n,V_s,V_P))],[nnf_344]) ).
fof(sk_fact_evaln__elim__cases_I6_J,plain,
( ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,VAR_0)),VAR_1,sK0(VAR_3,VAR_2,VAR_1,VAR_0),VAR_3)
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,VAR_0),VAR_1,VAR_2,VAR_3) )
& ! [VAR_0,VAR_1,VAR_2,VAR_3] :
( hAPP(c_Nat_OSuc,sK0(VAR_3,VAR_2,VAR_1,VAR_0)) = VAR_2
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,VAR_0),VAR_1,VAR_2,VAR_3) ) ),
inference(cnf_transformation,[status(thm)],[sk_fact_evaln__elim__cases_I6_J_sk]) ).
cnf(c_1177,plain,
( hAPP(c_Nat_OSuc,sK0(D,C,B,A)) = C
| ~ c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,A),B,C,D) ),
inference(split_conjunct,[status(thm)],[sk_fact_evaln__elim__cases_I6_J]) ).
cnf(c_2905,plain,
c_Groups_Ozero__class_Ozero(tc_Nat_Onat) != hAPP(c_Nat_OSuc,A),
inference(clausify,[status(thm)],[fact_Suc__neq__Zero]) ).
cnf(c_2906,plain,
hAPP(c_Nat_OSuc,A) != c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(copy,[status(thm)],[c_2905]) ).
fof(nnf_1129,plain,
? [B_Z,B_s] :
( ? [B_s_H] :
( ~ v_Q(B_Z,B_s_H)
& c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),B_s,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),B_s_H) )
& v_P(B_Z,B_s) ),
inference(fof_nnf,[status(thm)],[conj_0_neg]) ).
fof(sk_conj_0_neg,plain,
( ~ v_Q(sK3,sK2)
& c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),sK1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK2)
& v_P(sK3,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK1,sK2]),skolemize(B_Z,sK3),skolemize(B_s,sK1),skolemize(B_s_H,sK2)],[nnf_1129]) ).
cnf(c_3142,negated_conjecture,
c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_pn),sK1,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK2),
inference(split_conjunct,[status(thm)],[sk_conj_0_neg]) ).
cnf(c_3273,negated_conjecture,
hAPP(c_Nat_OSuc,sK0(sK2,c_Groups_Ozero__class_Ozero(tc_Nat_Onat),sK1,v_pn)) = c_Groups_Ozero__class_Ozero(tc_Nat_Onat),
inference(resolve,[status(thm)],[c_3142,c_1177]) ).
cnf(c_3272,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_2906,c_3273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW294+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n006.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Sat Sep 26 15:35:55 UTC 2026
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.36 % Process 1575141 was started by sandbox2 on n006,
% 0.15/0.36 % Sat Sep 26 15:35:55 2026
% 0.15/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 3.41/1.00
% 3.41/1.00 % SInE (scan): 862 to sos (tol 1.5x), 319 to usable (tol 2.0x), 4025 zapped, of 5206 axioms (depth 3).
% 3.41/1.00
% 3.41/1.00 % From the command line: assign(max_seconds, 300).
% 3.41/1.00
% 3.41/1.00 % SZS status Theorem for theBenchmark
% 3.41/1.00
% 3.41/1.00 % Proof 1 at 0.25 (+ 0.08) seconds.
% 3.41/1.00 % Length of proof is 8.
% 3.41/1.00 % Level of proof is 3.
% 3.41/1.00 % Maximum clause weight is 116.000.
% 3.41/1.00 % Given clauses 9.
% 3.41/1.00
% 3.41/1.00 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------