%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWW206+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 : n007.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 09:13:56 AM UTC 2026
% Result : Theorem 156.27s 21.69s
% Output : CNFRefutation 156.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 6
% Syntax : Number of formulae : 20 ( 20 unt; 0 def)
% Number of atoms : 20 ( 19 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 2 con; 0-5 aty)
% Number of variables : 81 ( 36 sgn 21 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_o__def,axiom,
! [V_x_2,V_gb_2,V_fa_2,T_c,T_a,T_b] : hAPP(c_Fun_Ocomp(T_b,T_a,T_c,V_fa_2,V_gb_2),V_x_2) = hAPP(V_fa_2,hAPP(V_gb_2,V_x_2)),
file('theBenchmark.p',fact_o__def) ).
fof(fact_complex__cnj__cnj,axiom,
! [V_z] : hAPP(c_Complex_Ocnj,hAPP(c_Complex_Ocnj,V_z)) = V_z,
file('theBenchmark.p',fact_complex__cnj__cnj) ).
fof(fact_n__not__Suc__n,axiom,
! [V_n] : V_n != c_Nat_OSuc(V_n),
file('theBenchmark.p',fact_n__not__Suc__n) ).
fof(fact_Suc__eq__plus1__left,axiom,
! [V_n] : c_Nat_OSuc(V_n) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),V_n),
file('theBenchmark.p',fact_Suc__eq__plus1__left) ).
fof(help_c__COMBB__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_c,T_a,T_b] : hAPP(c_COMBB(T_b,T_a,T_c,V_P_2,V_Q_2),V_R_2) = hAPP(V_P_2,hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBB__1) ).
fof(help_c__COMBS__1,axiom,
! [V_R_2,V_Q_2,V_P_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_P_2,V_Q_2),V_R_2) = hAPP(hAPP(V_P_2,V_R_2),hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBS__1) ).
cnf(c_1649,plain,
hAPP(c_COMBS(A,B,C,D,E),F) = hAPP(hAPP(D,F),hAPP(E,F)),
inference(clausify,[status(thm)],[help_c__COMBS__1]) ).
cnf(c_1894,plain,
hAPP(c_Fun_Ocomp(A,B,C,D,E),F) = hAPP(D,hAPP(E,F)),
inference(clausify,[status(thm)],[fact_o__def]) ).
cnf(c_1967,plain,
hAPP(c_Complex_Ocnj,hAPP(c_Complex_Ocnj,A)) = A,
inference(clausify,[status(thm)],[fact_complex__cnj__cnj]) ).
cnf(c_2659,plain,
c_Nat_OSuc(A) != A,
inference(clausify,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_2662,plain,
c_Nat_OSuc(A) = hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A),
inference(clausify,[status(thm)],[fact_Suc__eq__plus1__left]) ).
cnf(c_2753,plain,
hAPP(c_COMBB(A,B,C,D,E),F) = hAPP(D,hAPP(E,F)),
inference(clausify,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_2848,plain,
hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),A) != A,
inference(paramod,[status(thm)],[c_2662,c_2659]) ).
cnf(c_6342,plain,
hAPP(c_COMBB(A,B,C,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),D),E) != hAPP(D,E),
inference(paramod,[status(thm)],[c_2753,c_2848]) ).
cnf(c_16716,plain,
hAPP(c_COMBB(A,B,C,D,c_Complex_Ocnj),hAPP(c_Complex_Ocnj,E)) = hAPP(D,E),
inference(paramod,[status(thm)],[c_1967,c_2753]) ).
cnf(c_16721,plain,
hAPP(c_Fun_Ocomp(A,B,C,c_Complex_Ocnj,c_Complex_Ocnj),D) = D,
inference(paramod,[status(thm)],[c_1967,c_1894]) ).
cnf(c_16746,plain,
hAPP(c_COMBS(A,B,C,c_Fun_Ocomp(D,E,F,c_Complex_Ocnj,c_Complex_Ocnj),V6),V7) = hAPP(V7,hAPP(V6,V7)),
inference(paramod,[status(thm)],[c_16721,c_1649]) ).
cnf(c_16764,plain,
hAPP(c_COMBB(A,B,C,hAPP(c_Groups_Oplus__class_Oplus(tc_Nat_Onat),c_Groups_Oone__class_Oone(tc_Nat_Onat)),c_COMBB(D,E,F,V6,c_Complex_Ocnj)),hAPP(c_Complex_Ocnj,V7)) != hAPP(V6,V7),
inference(paramod,[status(thm)],[c_16716,c_6342]) ).
cnf(c_16766,plain,
hAPP(V7,hAPP(V6,V7)) = hAPP(c_COMBS(A,B,C,c_Fun_Ocomp(D,E,F,c_Complex_Ocnj,c_Complex_Ocnj),V6),V7),
inference(copy,[status(thm)],[c_16746]) ).
cnf(c_16765,plain,
$false,
inference(resolve,[status(thm)],[c_16764,c_16766]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW206+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37 % Computer : n007.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 26 15:25:38 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.38 % Process 4069038 was started by sandbox on n007,
% 0.12/0.38 % Sat Sep 26 15:25:38 2026
% 0.12/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.32/0.61
% 0.32/0.61 % From the command line: assign(max_seconds, 300).
% 0.32/0.61
% 0.32/0.61 % SInE: 803 to sos, 468 to usable, of 1271 axioms (tolerance 2.00, depth 0 fixpoint).
% 156.27/21.69
% 156.27/21.69 % given #500 (F,wt=36): 8226 hAPP(hAPP(c_Groups_Oplus__class_Oplus(tc_RealDef_Oreal),c_Groups_Oabs__class_Oabs(tc_RealDef_Oreal,c4)),c_RealVector_Onorm__class_Onorm(tc_Complex_Ocomplex,c_Groups_Oone__class_Oone(tc_Complex_Ocomplex))) != c_Groups_Ozero__class_Ozero(tc_RealDef_Oreal). [resolve(7261,a,7665,a)].
% 156.27/21.69
% 156.27/21.69 % given #1000 (W,wt=31): 14190 c_Complex_Ocomplex_OComplex(c_Nat__Transfer_Otsub(A,B),C) = c_Complex_Ocomplex_OComplex(c_Groups_Ozero__class_Ozero(tc_Int_Oint),C) | hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Int_Oint,B),A)). [resolve(13733,b,1410,b)].
% 156.27/21.69
% 156.27/21.69 % SZS status Theorem for theBenchmark
% 156.27/21.69
% 156.27/21.69 % Proof 1 at 4.15 (+ 0.54) seconds.
% 156.27/21.69 % Length of proof is 19.
% 156.27/21.69 % Level of proof is 5.
% 156.27/21.69 % Maximum clause weight is 232.000.
% 156.27/21.69 % Given clauses 1050.
% 156.27/21.69
% 156.27/21.69 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------