%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SWV865-1 : 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 : n001.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 0.17s 0.50s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 8 unt; 0 def)
% Number of atoms : 57 ( 39 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 47 ( 18 ~; 29 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 2 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 32 ( 2 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cls_com__det_0,axiom,
! [VAR_0,VAR_1,VAR_2,VAR_3] :
( ~ c_Natural_Oevalc(VAR_2,VAR_3,VAR_1)
| ~ c_Natural_Oevalc(VAR_2,VAR_3,VAR_0)
| VAR_0 = VAR_1 ),
file('theBenchmark.p',cls_com__det_0) ).
cnf(c_15,plain,
( ~ c_Natural_Oevalc(C,D,B)
| ~ c_Natural_Oevalc(C,D,A)
| A = B ),
inference(clausify,[status(thm)],[cls_com__det_0]) ).
fof(cls_single__stateE_0,axiom,
! [VAR_0] :
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| v_sko__Hoare__Mirabelle__Xsingle__stateE__1(VAR_0) != VAR_0 ),
file('theBenchmark.p',cls_single__stateE_0) ).
cnf(c_20,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| v_sko__Hoare__Mirabelle__Xsingle__stateE__1(A) != A ),
inference(clausify,[status(thm)],[cls_single__stateE_0]) ).
fof(cls_conjecture_0,axiom,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(c_27,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(clausify,[status(thm)],[cls_conjecture_0]) ).
fof(cls_conjecture_1,axiom,
~ c_Natural_Oevalc(v_c,v_Z,v_s_H),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(c_28,plain,
~ c_Natural_Oevalc(v_c,v_Z,v_s_H),
inference(clausify,[status(thm)],[cls_conjecture_1]) ).
fof(cls_conjecture_3,axiom,
! [VAR_0] :
( c_Natural_Oevalc(v_c,v_Z,v_Z_H(VAR_0))
| VAR_0 = v_s_H ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(c_30,plain,
( c_Natural_Oevalc(v_c,v_Z,v_Z_H(A))
| A = v_s_H ),
inference(clausify,[status(thm)],[cls_conjecture_3]) ).
cnf(c_31,plain,
( c_Natural_Oevalc(v_c,v_Z,v_Z_H(A))
| v_s_H = A ),
inference(copy,[status(thm)],[c_30]) ).
fof(cls_conjecture_4,axiom,
! [VAR_0] :
( VAR_0 = v_s_H
| VAR_0 != v_Z_H(VAR_0) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(c_32,plain,
( A = v_s_H
| A != v_Z_H(A) ),
inference(clausify,[status(thm)],[cls_conjecture_4]) ).
cnf(c_199,plain,
( A = v_s_H
| v_Z_H(A) != A ),
inference(copy,[status(thm)],[c_32]) ).
cnf(c_33,plain,
( v_s_H = A
| v_Z_H(A) != A ),
inference(copy,[status(thm)],[c_199]) ).
cnf(c_37,plain,
v_sko__Hoare__Mirabelle__Xsingle__stateE__1(A) != A,
inference(resolve,[status(thm)],[c_27,c_20]) ).
cnf(c_200,plain,
( ~ c_Natural_Oevalc(v_c,v_Z,B)
| B = v_Z_H(A)
| v_s_H = A ),
inference(resolve,[status(thm)],[c_31,c_15]) ).
cnf(c_58,plain,
( ~ c_Natural_Oevalc(v_c,v_Z,B)
| v_Z_H(A) = B
| v_s_H = A ),
inference(copy,[status(thm)],[c_200]) ).
cnf(c_193,plain,
( v_s_H = B
| v_Z_H(A) = v_Z_H(B)
| v_s_H = A ),
inference(resolve,[status(thm)],[c_58,c_31]) ).
cnf(c_201,plain,
( v_s_H = v_Z_H(A)
| v_s_H = A
| v_s_H = v_Z_H(A) ),
inference(resolve,[status(thm)],[c_193,c_33]) ).
cnf(c_202,plain,
( v_s_H = v_Z_H(A)
| v_s_H = A
| v_Z_H(A) = v_s_H ),
inference(copy,[status(thm)],[c_201]) ).
cnf(c_203,plain,
( v_Z_H(A) = v_s_H
| v_s_H = A
| v_Z_H(A) = v_s_H ),
inference(copy,[status(thm)],[c_202]) ).
cnf(c_195,plain,
( v_s_H = A
| v_Z_H(A) = v_s_H ),
inference(copy,[status(thm)],[c_203]) ).
cnf(c_204,plain,
( c_Natural_Oevalc(v_c,v_Z,v_s_H)
| v_s_H = A
| v_s_H = A ),
inference(paramod,[status(thm)],[c_195,c_31]) ).
cnf(c_205,plain,
( c_Natural_Oevalc(v_c,v_Z,v_s_H)
| v_s_H = A ),
inference(copy,[status(thm)],[c_204]) ).
cnf(c_197,plain,
v_s_H = A,
inference(resolve,[status(thm)],[c_28,c_205]) ).
cnf(c_206,plain,
A != v_sko__Hoare__Mirabelle__Xsingle__stateE__1(A),
inference(copy,[status(thm)],[c_37]) ).
cnf(c_198,plain,
$false,
inference(resolve,[status(thm)],[c_197,c_206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV865-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n001.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Sat Sep 26 15:10:43 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 2070837 was started by sandbox2 on n001,
% 0.17/0.44 % Sat Sep 26 15:10:43 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 0.17/0.50
% 0.17/0.50 % SZS status Unsatisfiable for theBenchmark
% 0.17/0.50
% 0.17/0.50 % Proof 1 at 0.03 (+ 0.01) seconds.
% 0.17/0.50 % Length of proof is 14.
% 0.17/0.50 % Level of proof is 6.
% 0.17/0.50 % Maximum clause weight is 21.000.
% 0.17/0.50 % Given clauses 77.
% 0.17/0.50
% 0.17/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------