%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SCT165+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 : n020.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 08:28:35 AM UTC 2026
% Result : Theorem 138.47s 19.24s
% Output : CNFRefutation 138.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 11
% Syntax : Number of formulae : 58 ( 42 unt; 0 def)
% Number of atoms : 78 ( 45 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 43 ( 23 ~; 15 |; 0 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-5 aty)
% Number of variables : 159 ( 47 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_eq__imp__le,axiom,
! [V_n,V_m] :
( V_m = V_n
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n)) ),
file('theBenchmark.p',fact_eq__imp__le) ).
fof(fact_le__trans,axiom,
! [V_k,V_j,V_i] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_j))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_j),V_k))
=> hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_i),V_k)) ) ),
file('theBenchmark.p',fact_le__trans) ).
fof(fact_le__antisym,axiom,
! [V_n,V_m] :
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_m),V_n))
=> ( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,V_n),V_m))
=> V_m = V_n ) ),
file('theBenchmark.p',fact_le__antisym) ).
fof(fact_n__not__Suc__n,axiom,
! [V_n] : V_n != hAPP(c_Nat_OSuc,V_n),
file('theBenchmark.p',fact_n__not__Suc__n) ).
fof(help_c__COMBB__1,axiom,
! [V_R_2,V_Q_2,V_Pa_2,T_c,T_a,T_b] : hAPP(hAPP(c_COMBB(T_b,T_a,T_c,V_Pa_2),V_Q_2),V_R_2) = hAPP(V_Pa_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_Pa_2,T_a,T_c,T_b] : hAPP(c_COMBS(T_b,T_c,T_a,V_Pa_2,V_Q_2),V_R_2) = hAPP(hAPP(V_Pa_2,V_R_2),hAPP(V_Q_2,V_R_2)),
file('theBenchmark.p',help_c__COMBS__1) ).
fof(help_c__fequal__1,axiom,
! [V_y_2,V_x_2] :
( V_x_2 = V_y_2
| ~ hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2)) ),
file('theBenchmark.p',help_c__fequal__1) ).
fof(help_c__fequal__2,axiom,
! [V_y_2,V_x_2] :
( hBOOL(hAPP(hAPP(c_fequal,V_x_2),V_y_2))
| V_x_2 != V_y_2 ),
file('theBenchmark.p',help_c__fequal__2) ).
fof(fact_nat__size,axiom,
! [V_n] : c_Nat_Osize__class_Osize(tc_Nat_Onat,V_n) = V_n,
file('theBenchmark.p',fact_nat__size) ).
fof(fact_nat__case__Suc,axiom,
! [V_nat_2,V_f2_2,V_f1_2,T_a] : c_Nat_Onat_Onat__case(T_a,V_f1_2,V_f2_2,hAPP(c_Nat_OSuc,V_nat_2)) = hAPP(V_f2_2,V_nat_2),
file('theBenchmark.p',fact_nat__case__Suc) ).
fof(help_c__COMBI__1,axiom,
! [V_P,T_a] : hAPP(c_COMBI(T_a),V_P) = V_P,
file('theBenchmark.p',help_c__COMBI__1) ).
cnf(c_709,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,A) = A,
inference(clausify,[status(thm)],[fact_nat__size]) ).
cnf(c_741,plain,
c_Nat_Onat_Onat__case(A,B,C,hAPP(c_Nat_OSuc,D)) = hAPP(C,D),
inference(clausify,[status(thm)],[fact_nat__case__Suc]) ).
cnf(c_775,plain,
hAPP(c_COMBI(A),B) = B,
inference(clausify,[status(thm)],[help_c__COMBI__1]) ).
cnf(c_916,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),A))
| A != B ),
inference(clausify,[status(thm)],[fact_eq__imp__le]) ).
cnf(c_917,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),C))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),C))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) ),
inference(clausify,[status(thm)],[fact_le__trans]) ).
cnf(c_918,plain,
( B = A
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,B),A))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) ),
inference(clausify,[status(thm)],[fact_le__antisym]) ).
cnf(c_1155,plain,
hAPP(c_Nat_OSuc,A) != A,
inference(clausify,[status(thm)],[fact_n__not__Suc__n]) ).
cnf(c_1270,plain,
hAPP(hAPP(c_COMBB(A,B,C,D),E),F) = hAPP(D,hAPP(E,F)),
inference(clausify,[status(thm)],[help_c__COMBB__1]) ).
cnf(c_1272,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_1273,plain,
( B = A
| ~ hBOOL(hAPP(hAPP(c_fequal,A),B)) ),
inference(clausify,[status(thm)],[help_c__fequal__1]) ).
cnf(c_1274,plain,
( hBOOL(hAPP(hAPP(c_fequal,B),A))
| A != B ),
inference(clausify,[status(thm)],[help_c__fequal__2]) ).
cnf(c_1392,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),hAPP(c_COMBI(B),A))),
inference(resolve,[status(thm)],[c_916,c_775]) ).
cnf(c_1396,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),c_Nat_Osize__class_Osize(tc_Nat_Onat,A))),
inference(resolve,[status(thm)],[c_916,c_709]) ).
cnf(c_6680,plain,
B = hAPP(c_COMBI(A),B),
inference(copy,[status(thm)],[c_775]) ).
cnf(c_1400,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_COMBI(A),B)),B)),
inference(resolve,[status(thm)],[c_916,c_6680]) ).
cnf(c_6681,plain,
A = c_Nat_Osize__class_Osize(tc_Nat_Onat,A),
inference(copy,[status(thm)],[c_709]) ).
cnf(c_1405,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,A)),A)),
inference(resolve,[status(thm)],[c_916,c_6681]) ).
cnf(c_1413,plain,
hBOOL(hAPP(hAPP(c_fequal,hAPP(A,B)),c_Nat_Onat_Onat__case(C,D,A,hAPP(c_Nat_OSuc,B)))),
inference(resolve,[status(thm)],[c_1274,c_741]) ).
cnf(c_6682,plain,
B = hAPP(c_COMBI(A),B),
inference(copy,[status(thm)],[c_775]) ).
cnf(c_1421,plain,
hBOOL(hAPP(hAPP(c_fequal,hAPP(c_COMBI(A),B)),B)),
inference(resolve,[status(thm)],[c_1274,c_6682]) ).
cnf(c_2052,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,A)),B))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) ),
inference(resolve,[status(thm)],[c_917,c_1405]) ).
cnf(c_2065,plain,
( hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),c_Nat_Osize__class_Osize(tc_Nat_Onat,B)))
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,A),B)) ),
inference(resolve,[status(thm)],[c_917,c_1396]) ).
cnf(c_2672,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_COMBI(A),B)),c_Nat_Osize__class_Osize(tc_Nat_Onat,B))),
inference(resolve,[status(thm)],[c_1400,c_2065]) ).
cnf(c_2885,plain,
hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,c_Nat_Osize__class_Osize(tc_Nat_Onat,A)),hAPP(c_COMBI(B),A))),
inference(resolve,[status(thm)],[c_2052,c_1392]) ).
cnf(c_6683,plain,
( c_Nat_Osize__class_Osize(tc_Nat_Onat,B) = hAPP(c_COMBI(A),B)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_COMBI(A),B)),c_Nat_Osize__class_Osize(tc_Nat_Onat,B))) ),
inference(resolve,[status(thm)],[c_2885,c_918]) ).
cnf(c_6684,plain,
( hAPP(c_COMBI(A),B) = c_Nat_Osize__class_Osize(tc_Nat_Onat,B)
| ~ hBOOL(hAPP(c_Orderings_Oord__class_Oless__eq(tc_Nat_Onat,hAPP(c_COMBI(A),B)),c_Nat_Osize__class_Osize(tc_Nat_Onat,B))) ),
inference(copy,[status(thm)],[c_6683]) ).
cnf(c_2893,plain,
hAPP(c_COMBI(A),B) = c_Nat_Osize__class_Osize(tc_Nat_Onat,B),
inference(resolve,[status(thm)],[c_2672,c_6684]) ).
cnf(c_3474,plain,
hAPP(hAPP(c_COMBB(A,B,C,D),c_COMBI(E)),F) = hAPP(D,F),
inference(paramod,[status(thm)],[c_775,c_1270]) ).
cnf(c_3491,plain,
hAPP(hAPP(c_COMBB(A,B,C,D),c_COMBS(E,F,V6,V7,V8)),V9) = hAPP(D,hAPP(hAPP(V7,V9),hAPP(V8,V9))),
inference(paramod,[status(thm)],[c_1272,c_1270]) ).
cnf(c_6685,plain,
hAPP(A,B) = hAPP(A,hAPP(c_COMBI(C),B)),
inference(paramod,[status(thm)],[c_3474,c_1270]) ).
cnf(c_3585,plain,
hAPP(A,hAPP(c_COMBI(B),C)) = hAPP(A,C),
inference(copy,[status(thm)],[c_6685]) ).
cnf(c_6686,plain,
hAPP(c_Nat_OSuc,A) != hAPP(c_COMBI(B),A),
inference(paramod,[status(thm)],[c_3585,c_1155]) ).
cnf(c_3743,plain,
hAPP(c_COMBI(A),B) != hAPP(c_Nat_OSuc,B),
inference(copy,[status(thm)],[c_6686]) ).
cnf(c_3904,plain,
hAPP(A,c_Nat_Osize__class_Osize(tc_Nat_Onat,B)) = hAPP(A,B),
inference(paramod,[status(thm)],[c_2893,c_3585]) ).
cnf(c_3954,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,A) != hAPP(c_Nat_OSuc,A),
inference(paramod,[status(thm)],[c_2893,c_3743]) ).
cnf(c_4101,plain,
c_Nat_Onat_Onat__case(A,B,C,hAPP(c_Nat_OSuc,D)) = hAPP(C,c_Nat_Osize__class_Osize(tc_Nat_Onat,D)),
inference(paramod,[status(thm)],[c_3904,c_741]) ).
cnf(c_6687,plain,
( B = c_Nat_Osize__class_Osize(tc_Nat_Onat,A)
| ~ hBOOL(hAPP(hAPP(c_fequal,A),B)) ),
inference(paramod,[status(thm)],[c_3904,c_1273]) ).
cnf(c_4107,plain,
( c_Nat_Osize__class_Osize(tc_Nat_Onat,A) = B
| ~ hBOOL(hAPP(hAPP(c_fequal,A),B)) ),
inference(copy,[status(thm)],[c_6687]) ).
cnf(c_4420,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_COMBI(A),B)) = B,
inference(resolve,[status(thm)],[c_4107,c_1421]) ).
cnf(c_6688,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(A,B)) = c_Nat_Onat_Onat__case(C,D,A,hAPP(c_Nat_OSuc,B)),
inference(resolve,[status(thm)],[c_4107,c_1413]) ).
cnf(c_4421,plain,
c_Nat_Onat_Onat__case(A,B,C,hAPP(c_Nat_OSuc,D)) = c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(C,D)),
inference(copy,[status(thm)],[c_6688]) ).
cnf(c_6486,plain,
c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(A,B)) = hAPP(A,c_Nat_Osize__class_Osize(tc_Nat_Onat,B)),
inference(paramod,[status(thm)],[c_4421,c_4101]) ).
cnf(c_6689,plain,
hAPP(A,c_Nat_Osize__class_Osize(tc_Nat_Onat,B)) != hAPP(c_Nat_OSuc,hAPP(A,B)),
inference(paramod,[status(thm)],[c_6486,c_3954]) ).
cnf(c_6565,plain,
hAPP(c_Nat_OSuc,hAPP(A,B)) != hAPP(A,c_Nat_Osize__class_Osize(tc_Nat_Onat,B)),
inference(copy,[status(thm)],[c_6689]) ).
cnf(c_6678,plain,
hAPP(c_Nat_OSuc,hAPP(A,hAPP(c_COMBI(B),C))) != hAPP(A,C),
inference(paramod,[status(thm)],[c_4420,c_6565]) ).
cnf(c_6690,plain,
hAPP(D,hAPP(hAPP(V7,V9),hAPP(V8,V9))) = hAPP(hAPP(c_COMBB(A,B,C,D),c_COMBS(E,F,V6,V7,V8)),V9),
inference(copy,[status(thm)],[c_3491]) ).
cnf(c_6679,plain,
$false,
inference(resolve,[status(thm)],[c_6678,c_6690]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SCT165+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n020.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Sat Sep 26 06:36:05 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 871731 was started by sandbox on n020,
% 0.19/0.45 % Sat Sep 26 06:36:05 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.41/0.69
% 0.41/0.69 % From the command line: assign(max_seconds, 300).
% 0.41/0.69
% 0.41/0.69 % SInE: 332 to sos, 200 to usable, of 532 axioms (tolerance 2.00, depth 0 fixpoint).
% 138.47/19.24
% 138.47/19.24 % given #500 (W,wt=27): 6177 -hBOOL(c_Nat_Osize__class_Osize(tc_Nat_Onat,hAPP(c_COMBI(A),c_fFalse))). [para(4260(a,1),5135(a,1,2))].
% 138.47/19.24
% 138.47/19.24 % SZS status Theorem for theBenchmark
% 138.47/19.24
% 138.47/19.24 % Proof 1 at 2.09 (+ 0.19) seconds.
% 138.47/19.24 % Length of proof is 47.
% 138.47/19.24 % Level of proof is 12.
% 138.47/19.24 % Maximum clause weight is 115.000.
% 138.47/19.24 % Given clauses 510.
% 138.47/19.24
% 138.47/19.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------