%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : SWV865-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 : Thu Sep 24 09:04:26 AM UTC 2026
% Result : Unsatisfiable 12.78s 23.13s
% Output : Proof 12.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 10
% Syntax : Number of clauses : 41 ( 24 unt; 3 nHn; 37 RR)
% Number of literals : 66 ( 20 equ; 26 neg)
% Maximal clause size : 5 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 25 ( 6 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(cls_evaln_OSkip_0,axiom,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,V_s,V_n,V_s),
file('theBenchmark.p',cls_evaln_OSkip_0) ).
cnf(cls_com__det_0,axiom,
( ~ c_Natural_Oevalc(V_c,V_s,V_t)
| ~ c_Natural_Oevalc(V_c,V_s,V_u)
| V_u = V_t ),
file('theBenchmark.p',cls_com__det_0) ).
cnf(cls_single__stateE_0,axiom,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| v_sko__Hoare__Mirabelle__Xsingle__stateE__1(V_t) != V_t ),
file('theBenchmark.p',cls_single__stateE_0) ).
cnf(cls_evalc__elim__cases_I1_J_0,axiom,
( ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,V_s,V_t)
| V_t = V_s ),
file('theBenchmark.p',cls_evalc__elim__cases_I1_J_0) ).
cnf(cls_eval__eq_1,axiom,
( ~ c_Natural_Oevaln(V_c,V_s,V_x,V_t)
| c_Natural_Oevalc(V_c,V_s,V_t) ),
file('theBenchmark.p',cls_eval__eq_1) ).
cnf(cls_conjecture_0,negated_conjecture,
c_Hoare__Mirabelle_Ostate__not__singleton,
file('theBenchmark.p',cls_conjecture_0) ).
cnf(cls_conjecture_1,negated_conjecture,
~ c_Natural_Oevalc(v_c,v_Z,v_s_H),
file('theBenchmark.p',cls_conjecture_1) ).
cnf(cls_conjecture_3,negated_conjecture,
( c_Natural_Oevalc(v_c,v_Z,v_Z_H(V_Z_Ha))
| V_Z_Ha = v_s_H ),
file('theBenchmark.p',cls_conjecture_3) ).
cnf(cls_conjecture_4,negated_conjecture,
( V_Z_Ha = v_s_H
| V_Z_Ha != v_Z_H(V_Z_Ha) ),
file('theBenchmark.p',cls_conjecture_4) ).
cnf(equality_14,axiom,
( c_Natural_Oevalc(Eq_y_0,Eq_y_1,Eq_y_2)
| ~ c_Natural_Oevalc(Eq_x_0,Eq_x_1,Eq_x_2)
| Eq_x_2 != Eq_y_2
| Eq_x_1 != Eq_y_1
| Eq_x_0 != Eq_y_0 ),
theory(equality,[substitution_predicates]) ).
cnf(t1,plain,
~ c_Natural_Oevalc(v_c,v_Z,v_s_H),
inference(start,[status(thm),parent(0:0)],[cls_conjecture_1]) ).
cnf(t2,plain,
( v_Z != v_Z
| v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H)) != v_s_H
| ~ c_Natural_Oevalc(v_c,v_Z,v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H)))
| v_c != v_c
| c_Natural_Oevalc(v_c,v_Z,v_s_H) ),
inference(extension,[status(thm),parent(t1:1)],[equality_14]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,v_c,v_c)
| v_c = v_c ),
inference(extension,[status(thm),parent(t2:2)],[cls_evalc__elim__cases_I1_J_0]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
( ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_c,U_738,v_c)
| c_Natural_Oevalc(c_Com_Ocom_OSKIP,v_c,v_c) ),
inference(extension,[status(thm),parent(t4:2)],[cls_eval__eq_1]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_c,U_738,v_c),
inference(extension,[status(thm),parent(t6:2)],[cls_evaln_OSkip_0]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
( v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H) = v_s_H
| c_Natural_Oevalc(v_c,v_Z,v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H))) ),
inference(extension,[status(thm),parent(t2:3)],[cls_conjecture_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
( ~ c_Hoare__Mirabelle_Ostate__not__singleton
| v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H) != v_s_H ),
inference(extension,[status(thm),parent(t10:2)],[cls_single__stateE_0]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
c_Hoare__Mirabelle_Ostate__not__singleton,
inference(extension,[status(thm),parent(t12:2)],[cls_conjecture_0]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t12:2]) ).
cnf(l5,lemma,
c_Natural_Oevalc(v_c,v_Z,v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H))),
inference(lemma,[status(cth),parent(t2:3),below(t1:1)],[t2:3]) ).
cnf(t16,plain,
( v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H)) != v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H)))
| v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H)) = v_s_H ),
inference(extension,[status(thm),parent(t2:4)],[cls_conjecture_4]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:4]) ).
cnf(t18,plain,
( ~ c_Natural_Oevalc(v_c,v_Z,v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H)))
| ~ c_Natural_Oevalc(v_c,v_Z,v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H))))
| v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H)) = v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H))) ),
inference(extension,[status(thm),parent(t16:2)],[cls_com__det_0]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
( v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H)) = v_s_H
| c_Natural_Oevalc(v_c,v_Z,v_Z_H(v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H)))) ),
inference(extension,[status(thm),parent(t18:2)],[cls_conjecture_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t18:2]) ).
cnf(t22,plain,
$false,
inference(reduction,[status(thm),parent(t20:2)],[t20:2,t2:4]) ).
cnf(t23,plain,
c_Natural_Oevalc(v_c,v_Z,v_Z_H(v_sko__Hoare__Mirabelle__Xsingle__stateE__1(v_s_H))),
inference(lemma_extension,[status(thm),parent(t18:3)],[l5:1]) ).
cnf(t24,plain,
$false,
inference(connection,[status(thm),parent(t23:1)],[t23:1,t18:3]) ).
cnf(t25,plain,
( ~ c_Natural_Oevalc(c_Com_Ocom_OSKIP,v_Z,v_Z)
| v_Z = v_Z ),
inference(extension,[status(thm),parent(t2:5)],[cls_evalc__elim__cases_I1_J_0]) ).
cnf(t26,plain,
$false,
inference(connection,[status(thm),parent(t25:1)],[t25:1,t2:5]) ).
cnf(t27,plain,
( ~ c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_Z,U_754,v_Z)
| c_Natural_Oevalc(c_Com_Ocom_OSKIP,v_Z,v_Z) ),
inference(extension,[status(thm),parent(t25:2)],[cls_eval__eq_1]) ).
cnf(t28,plain,
$false,
inference(connection,[status(thm),parent(t27:1)],[t27:1,t25:2]) ).
cnf(t29,plain,
c_Natural_Oevaln(c_Com_Ocom_OSKIP,v_Z,U_754,v_Z),
inference(extension,[status(thm),parent(t27:2)],[cls_evaln_OSkip_0]) ).
cnf(t30,plain,
$false,
inference(connection,[status(thm),parent(t29:1)],[t29:1,t27:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV865-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a CNF_UNS_RFO_SEQ_NHN problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n026.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Sun Sep 20 04:53:15 UTC 2026
% 0.09/10.37 % CPUTime :
% 12.78/23.13 % SZS status Unsatisfiable for theBenchmark
% 12.78/23.13 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------