%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV822-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 09:09:10 AM UTC 2026
% Result : Unsatisfiable 265.78s 35.22s
% Output : CNFRefutation 265.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 31 ( 9 unt; 0 def)
% Number of atoms : 67 ( 9 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 66 ( 30 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-4 aty)
% Number of variables : 52 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_nat_Oinject_0,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| c_Suc(VAR_0) != c_Suc(VAR_1) ),
file('theBenchmark.p',cls_nat_Oinject_0) ).
cnf(c_590,plain,
( A = B
| c_Suc(A) != c_Suc(B) ),
inference(clausify,[status(thm)],[cls_nat_Oinject_0]) ).
fof(cls_evaln__elim__cases_I6_J_1,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(VAR_0),VAR_1,VAR_2,VAR_3)
| c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(VAR_0),tc_Com_Ocom),VAR_1,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(VAR_0,VAR_2,VAR_1,VAR_3),VAR_3) ),
file('theBenchmark.p',cls_evaln__elim__cases_I6_J_1) ).
cnf(c_591,plain,
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(A),B,C,D)
| c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(A),tc_Com_Ocom),B,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(A,C,B,D),D) ),
inference(clausify,[status(thm)],[cls_evaln__elim__cases_I6_J_1]) ).
fof(cls_evaln_OBody_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(VAR_0),tc_Com_Ocom),VAR_1,VAR_2,VAR_3)
| c_Natural_Oevaln(c_Com_Ocom_OBODY(VAR_0),VAR_1,c_Suc(VAR_2),VAR_3) ),
file('theBenchmark.p',cls_evaln_OBody_0) ).
cnf(c_609,plain,
( ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(A),tc_Com_Ocom),B,C,D)
| c_Natural_Oevaln(c_Com_Ocom_OBODY(A),B,c_Suc(C),D) ),
inference(clausify,[status(thm)],[cls_evaln_OBody_0]) ).
fof(cls_evaln__elim__cases_I6_J_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(VAR_1),VAR_2,VAR_0,VAR_3)
| VAR_0 = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(VAR_1,VAR_0,VAR_2,VAR_3)) ),
file('theBenchmark.p',cls_evaln__elim__cases_I6_J_0) ).
cnf(c_614,plain,
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(B),C,A,D)
| A = c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(B,A,C,D)) ),
inference(clausify,[status(thm)],[cls_evaln__elim__cases_I6_J_0]) ).
cnf(c_615,plain,
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(A),C,B,D)
| c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(A,B,C,D)) = B ),
inference(copy,[status(thm)],[c_614]) ).
fof(cls_conjecture_0,axiom,
( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_626,plain,
( hBOOL(hAPP(hAPP(v_P,v_x),v_xa))
| hBOOL(hAPP(hAPP(v_P,v_x),v_xa)) ),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
cnf(c_627,plain,
hBOOL(hAPP(hAPP(v_P,v_x),v_xa)),
inference(copy,[status(thm)],[c_626]) ).
fof(cls_conjecture_4,axiom,
( c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb)
| c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_628,plain,
( c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb)
| c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
fof(cls_conjecture_8,axiom,
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))
| ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb)) ),
file('theBenchmark.p',cls_conjecture_8) ).
cnf(c_631,plain,
( ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb))
| ~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb)) ),
inference(clausify,[status(thm)],[cls_conjecture_8]) ).
cnf(c_632,plain,
~ hBOOL(hAPP(hAPP(v_Q,v_x),v_xb)),
inference(copy,[status(thm)],[c_631]) ).
fof(cls_conjecture_9,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4,VAR_5] :
( ~ hBOOL(hAPP(hAPP(v_P,VAR_3),VAR_5))
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),VAR_5,c_Suc(v_n),VAR_4)
| hBOOL(hAPP(hAPP(v_Q,VAR_3),VAR_4))
| ~ hBOOL(hAPP(hAPP(v_P,VAR_0),VAR_2))
| ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),VAR_2,v_n,VAR_1)
| hBOOL(hAPP(hAPP(v_Q,VAR_0),VAR_1)) ),
file('theBenchmark.p',cls_conjecture_9) ).
cnf(c_633,plain,
( ~ hBOOL(hAPP(hAPP(v_P,D),F))
| ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),F,c_Suc(v_n),E)
| hBOOL(hAPP(hAPP(v_Q,D),E))
| ~ hBOOL(hAPP(hAPP(v_P,A),C))
| ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),C,v_n,B)
| hBOOL(hAPP(hAPP(v_Q,A),B)) ),
inference(clausify,[status(thm)],[cls_conjecture_9]) ).
cnf(c_792,plain,
( ~ c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),C,c_Suc(v_n),D)
| hBOOL(hAPP(hAPP(v_Q,A),D))
| ~ hBOOL(hAPP(hAPP(v_P,A),C))
| ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),C,v_n,B)
| hBOOL(hAPP(hAPP(v_Q,A),B)) ),
inference(factor,[status(thm)],[c_633]) ).
cnf(c_50072,plain,
( c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb)
| c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb) ),
inference(resolve,[status(thm)],[c_628,c_609]) ).
cnf(c_2669,plain,
c_Natural_Oevaln(c_Com_Ocom_OBODY(v_pn),v_xa,c_Suc(v_n),v_xb),
inference(copy,[status(thm)],[c_50072]) ).
cnf(c_4470,plain,
( hBOOL(hAPP(hAPP(v_Q,A),v_xb))
| ~ hBOOL(hAPP(hAPP(v_P,A),v_xa))
| ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,B)
| hBOOL(hAPP(hAPP(v_Q,A),B)) ),
inference(resolve,[status(thm)],[c_2669,c_792]) ).
cnf(c_4475,plain,
c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb)) = c_Suc(v_n),
inference(resolve,[status(thm)],[c_2669,c_615]) ).
cnf(c_4482,plain,
c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb),v_xb),
inference(resolve,[status(thm)],[c_2669,c_591]) ).
cnf(c_4485,plain,
( ~ hBOOL(hAPP(hAPP(v_P,A),v_xa))
| ~ c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb)
| hBOOL(hAPP(hAPP(v_Q,A),v_xb)) ),
inference(factor,[status(thm)],[c_4470]) ).
cnf(c_13476,plain,
c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_pn,c_Suc(v_n),v_xa,v_xb) = v_n,
inference(resolve,[status(thm)],[c_4475,c_590]) ).
cnf(c_13478,plain,
c_Natural_Oevaln(c_Option_Othe(c_Com_Obody(v_pn),tc_Com_Ocom),v_xa,v_n,v_xb),
inference(paramod,[status(thm)],[c_13476,c_4482]) ).
cnf(c_13479,plain,
( ~ hBOOL(hAPP(hAPP(v_P,A),v_xa))
| hBOOL(hAPP(hAPP(v_Q,A),v_xb)) ),
inference(resolve,[status(thm)],[c_13478,c_4485]) ).
cnf(c_50073,plain,
hBOOL(hAPP(hAPP(v_Q,v_x),v_xb)),
inference(resolve,[status(thm)],[c_13479,c_627]) ).
cnf(c_50071,plain,
$false,
inference(resolve,[status(thm)],[c_632,c_50073]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV822-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.13/0.40 % Computer : n019.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.40 % CPULimit : 300
% 0.13/0.40 % WCLimit : 300
% 0.13/0.40 % DateTime : Sat Sep 26 15:01:19 UTC 2026
% 0.13/0.40 % CPUTime :
% 0.13/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/0.41 % Process 1604526 was started by sandbox2 on n019,
% 0.13/0.41 % Sat Sep 26 15:01:19 2026
% 0.13/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 265.78/35.22
% 265.78/35.22 % given #500 (A,wt=30): 817 c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(c_HOL_Otimes__class_Otimes(B,C,tc_nat),c_HOL_Oplus__class_Oplus(D,c_HOL_Otimes__class_Otimes(E,C,tc_nat),tc_nat),tc_nat),tc_nat) = c_HOL_Oplus__class_Oplus(A,c_HOL_Oplus__class_Oplus(D,c_HOL_Otimes__class_Otimes(c_HOL_Oplus__class_Oplus(B,E,tc_nat),C,tc_nat),tc_nat),tc_nat). [para(292(a,1),291(a,1,2,2)),flip(a)].
% 265.78/35.22
% 265.78/35.22 % given #1000 (T,wt=11): 1302 c_Suc(c_HOL_Oplus__class_Oplus(A,B,tc_nat)) != C | c_HOL_Oord__class_Oless(A,C,tc_nat). [resolve(429,a,300,b),rewrite([597(3),293(7)])].
% 265.78/35.22
% 265.78/35.22 % given #1500 (F,wt=12): 8718 -c_lessequals(c_Suc(c_Suc(A)),c_Orderings_Oord__class_Omin(B,c_Orderings_Oord__class_Omin(A,C,tc_nat),tc_nat),tc_nat). [para(711(a,1),6066(a,2))].
% 265.78/35.22
% 265.78/35.22 % given #2000 (T,wt=12): 1501 c_HOL_Oord__class_Oless(A,B,tc_nat) | A = B | c_lessequals(c_Suc(B),A,tc_nat). [resolve(458,a,314,b)].
% 265.78/35.22
% 265.78/35.22 % given #2500 (F,wt=12): 30649 c_Orderings_Oord__class_Omin(A,B,tc_nat) != c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(A),c_Suc(C),tc_nat)). [para(691(a,1),18860(a,1,1,1,1)),flip(a)].
% 265.78/35.22
% 265.78/35.22 % given #3000 (T,wt=12): 11728 c_HOL_Oord__class_Oless(A,c_Suc(c_Suc(c_Suc(c_HOL_Otimes__class_Otimes(c_Suc(B),c_Suc(A),tc_nat)))),tc_nat). [resolve(2560,a,7128,a)].
% 265.78/35.22
% 265.78/35.22 % SZS status Unsatisfiable for theBenchmark
% 265.78/35.22
% 265.78/35.22 % Proof 1 at 26.55 (+ 7.81) seconds.
% 265.78/35.22 % Length of proof is 21.
% 265.78/35.22 % Level of proof is 6.
% 265.78/35.22 % Maximum clause weight is 39.000.
% 265.78/35.22 % Given clauses 3261.
% 265.78/35.22
% 265.78/35.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------