%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV861-1 : TPTP v9.3.1. Released v4.1.0.
% 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 09:09:14 AM UTC 2026
% Result : Unsatisfiable 56.49s 15.48s
% Output : CNFRefutation 56.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 9
% Syntax : Number of formulae : 26 ( 13 unt; 0 def)
% Number of atoms : 47 ( 0 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 19 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-4 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-2 aty)
% Number of variables : 36 ( 0 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_not__less__eq__eq_0,axiom,
! [VAR_0,VAR_1] :
( c_lessequals(VAR_1,VAR_0,tc_nat)
| c_lessequals(c_Suc(VAR_0),VAR_1,tc_nat) ),
file('theBenchmark.p',cls_not__less__eq__eq_0) ).
cnf(c_385,plain,
( c_lessequals(B,A,tc_nat)
| c_lessequals(c_Suc(A),B,tc_nat) ),
inference(clausify,[status(thm)],[cls_not__less__eq__eq_0]) ).
fof(cls_Suc__n__not__le__n_0,axiom,
! [VAR_0] : ~ c_lessequals(c_Suc(VAR_0),VAR_0,tc_nat),
file('theBenchmark.p',cls_Suc__n__not__le__n_0) ).
cnf(c_475,plain,
~ c_lessequals(c_Suc(A),A,tc_nat),
inference(clausify,[status(thm)],[cls_Suc__n__not__le__n_0]) ).
fof(cls_evaln__nonstrict_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3,VAR_4] :
( ~ c_Natural_Oevaln(VAR_0,VAR_1,VAR_4,VAR_3)
| ~ c_lessequals(VAR_4,VAR_2,tc_nat)
| c_Natural_Oevaln(VAR_0,VAR_1,VAR_2,VAR_3) ),
file('theBenchmark.p',cls_evaln__nonstrict_0) ).
cnf(c_593,plain,
( ~ c_Natural_Oevaln(A,B,E,D)
| ~ c_lessequals(E,C,tc_nat)
| c_Natural_Oevaln(A,B,C,D) ),
inference(clausify,[status(thm)],[cls_evaln__nonstrict_0]) ).
fof(cls_conjecture_0,axiom,
hBOOL(hAPP(hAPP(v_P,v_Z),v_s)),
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_621,plain,
hBOOL(hAPP(hAPP(v_P,v_Z),v_s)),
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
c_Natural_Oevaln(v_c,v_s,v_n,v_s1),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_622,plain,
c_Natural_Oevaln(v_c,v_s,v_n,v_s1),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_2,axiom,
c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H),
file('theBenchmark.p',cls_conjecture_2) ).
cnf(c_623,plain,
c_Natural_Oevaln(v_d,v_s1,v_n,v_s_H),
inference(clausify,[status(thm)],[cls_conjecture_2]) ).
fof(cls_conjecture_3,axiom,
~ hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_624,plain,
~ hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
fof(cls_conjecture_5,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(hAPP(v_P,VAR_0),VAR_2))
| ~ c_Natural_Oevaln(v_c,VAR_2,v_n,VAR_1)
| hBOOL(hAPP(hAPP(v_Q,VAR_0),VAR_1)) ),
file('theBenchmark.p',cls_conjecture_5) ).
cnf(c_626,plain,
( ~ hBOOL(hAPP(hAPP(v_P,A),C))
| ~ c_Natural_Oevaln(v_c,C,v_n,B)
| hBOOL(hAPP(hAPP(v_Q,A),B)) ),
inference(clausify,[status(thm)],[cls_conjecture_5]) ).
fof(cls_conjecture_6,axiom,
! [VAR_0,VAR_1,VAR_2] :
( ~ hBOOL(hAPP(hAPP(v_Q,VAR_0),VAR_2))
| ~ c_Natural_Oevaln(v_d,VAR_2,v_n,VAR_1)
| hBOOL(hAPP(hAPP(v_R,VAR_0),VAR_1)) ),
file('theBenchmark.p',cls_conjecture_6) ).
cnf(c_627,plain,
( ~ hBOOL(hAPP(hAPP(v_Q,A),C))
| ~ c_Natural_Oevaln(v_d,C,v_n,B)
| hBOOL(hAPP(hAPP(v_R,A),B)) ),
inference(clausify,[status(thm)],[cls_conjecture_6]) ).
cnf(c_11931,plain,
( c_lessequals(c_Suc(C),E,tc_nat)
| ~ c_Natural_Oevaln(A,B,E,D)
| c_Natural_Oevaln(A,B,C,D) ),
inference(resolve,[status(thm)],[c_593,c_385]) ).
cnf(c_2460,plain,
( c_lessequals(c_Suc(A),v_n,tc_nat)
| c_Natural_Oevaln(v_d,v_s1,A,v_s_H) ),
inference(resolve,[status(thm)],[c_11931,c_623]) ).
cnf(c_11932,plain,
( ~ hBOOL(hAPP(hAPP(v_P,A),v_s))
| hBOOL(hAPP(hAPP(v_Q,A),v_s1)) ),
inference(resolve,[status(thm)],[c_626,c_622]) ).
cnf(c_2465,plain,
hBOOL(hAPP(hAPP(v_Q,v_Z),v_s1)),
inference(resolve,[status(thm)],[c_11932,c_621]) ).
cnf(c_11933,plain,
( c_lessequals(c_Suc(v_n),v_n,tc_nat)
| ~ hBOOL(hAPP(hAPP(v_Q,A),v_s1))
| hBOOL(hAPP(hAPP(v_R,A),v_s_H)) ),
inference(resolve,[status(thm)],[c_627,c_2460]) ).
cnf(c_11934,plain,
( c_lessequals(c_Suc(v_n),v_n,tc_nat)
| hBOOL(hAPP(hAPP(v_R,v_Z),v_s_H)) ),
inference(resolve,[status(thm)],[c_11933,c_2465]) ).
cnf(c_11935,plain,
c_lessequals(c_Suc(v_n),v_n,tc_nat),
inference(resolve,[status(thm)],[c_624,c_11934]) ).
cnf(c_11930,plain,
$false,
inference(resolve,[status(thm)],[c_475,c_11935]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV861-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.39 % Computer : n002.cluster.edu
% 0.07/0.39 % Model : x86_64 x86_64
% 0.07/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.39 % Memory : 8046.5625MB
% 0.07/0.39 % OS : Linux 6.8.0-71-generic
% 0.07/0.39 % CPULimit : 300
% 0.07/0.39 % WCLimit : 300
% 0.07/0.39 % DateTime : Sat Sep 26 15:07:05 UTC 2026
% 0.07/0.40 % CPUTime :
% 0.07/0.40 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/0.40 % Process 2025024 was started by sandbox on n002,
% 0.07/0.40 % Sat Sep 26 15:07:05 2026
% 0.07/0.40 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.07/0.41
% 0.07/0.41 % From the command line: assign(max_seconds, 300).
% 56.49/15.48
% 56.49/15.48 % given #500 (I,wt=65): 803 hBOOL(hAPP(hAPP(c_in(A),c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3(B,C,hAPP(c_in(A),hAPP(C,D)),E,A)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(B,C,E,tc_fun(A,tc_bool)))) | -hBOOL(hAPP(hAPP(c_in(A),hAPP(C,D)),hAPP(C,D))) | -hBOOL(hAPP(hAPP(c_in(E),D),B)). [factor(456,b,c)].
% 56.49/15.48
% 56.49/15.48 % SZS status Unsatisfiable for theBenchmark
% 56.49/15.48
% 56.49/15.48 % Proof 1 at 3.01 (+ 0.70) seconds.
% 56.49/15.48 % Length of proof is 12.
% 56.49/15.48 % Level of proof is 2.
% 56.49/15.48 % Maximum clause weight is 27.000.
% 56.49/15.48 % Given clauses 811.
% 56.49/15.48
% 56.49/15.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------