0.03/0.11 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.03/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s 0.11/0.33 % Computer : n022.cluster.edu 0.11/0.33 % Model : x86_64 x86_64 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.11/0.33 % Memory : 8042.1875MB 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64 0.11/0.33 % CPULimit : 960 0.11/0.33 % WCLimit : 120 0.11/0.33 % DateTime : Tue Aug 9 04:04:31 EDT 2022 0.11/0.33 % CPUTime : 0.54/0.61 start to proof:theBenchmark 0.57/0.72 %------------------------------------------- 0.57/0.72 % File :CSE---1.5 0.57/0.72 % Problem :theBenchmark 0.57/0.72 % Transform :cnf 0.57/0.72 % Format :tptp:raw 0.57/0.72 % Command :java -jar mcs_scs.jar %d %s 0.57/0.72 0.57/0.72 % Result :Theorem 0.000000s 0.57/0.72 % Output :CNFRefutation 0.000000s 0.57/0.72 %------------------------------------------- 0.57/0.73 fof(thm_2Ebool_2EIMP__F,axiom, 0.57/0.73 ! [V0t_2E0] : 0.57/0.73 ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0)) 0.57/0.73 => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) 0.57/0.73 => ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ). 0.57/0.73 0.57/0.73 fof(arityeq2_2Ec_2Epred__set_2ECROSS_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom, 0.57/0.73 ! [X0_2E0,X1_2E0] : s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool))),c_2Epred__set_2ECROSS_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) = s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))) ). 0.57/0.73 0.57/0.73 fof(thm_2Esat_2EOR__DUAL2,axiom, 0.57/0.73 ! [V0B_2E0,V1A_2E0] : 0.57/0.73 ( ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) 0.57/0.73 <= p(s(tyop_2Emin_2Ebool,V1A_2E0)) ) 0.57/0.73 => ( ~ p(s(tyop_2Emin_2Ebool,V0B_2E0)) 0.57/0.73 => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) 0.57/0.73 <=> ( ~ ( p(s(tyop_2Emin_2Ebool,V1A_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V0B_2E0)) ) 0.57/0.73 => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Esat_2EAND__INV2,axiom, 0.57/0.73 ! [V0A_2E0] : 0.57/0.73 ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) 0.57/0.73 <= ( p(s(tyop_2Emin_2Ebool,V0A_2E0)) 0.57/0.73 => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) ) 0.57/0.73 <= ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) 0.57/0.73 <= ~ p(s(tyop_2Emin_2Ebool,V0A_2E0)) ) ) ). 0.57/0.73 0.57/0.73 fof(reserved_2Equant_2E_3F,axiom, 0.57/0.73 ! [A_27a,V0f_2E0] : 0.57/0.73 ( ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) 0.57/0.73 <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) ) ). 0.57/0.73 0.57/0.73 fof(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom, 0.57/0.73 ! [A_27a,X0_2E0,X1_2E0] : 0.57/0.73 ( s(A_27a,X1_2E0) = s(A_27a,X0_2E0) 0.57/0.73 <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_2E0),s(A_27a,X0_2E0))),s(A_27a,X1_2E0)))) ) ). 0.57/0.73 0.57/0.73 fof(reserved_2Elogic_2E_3D_3D_3E,axiom, 0.57/0.73 ! [V0_2E0,V1_2E0] : 0.57/0.73 ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_3D_3E_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) 0.57/0.73 <=> ( p(s(tyop_2Emin_2Ebool,V0_2E0)) 0.57/0.73 => p(s(tyop_2Emin_2Ebool,V1_2E0)) ) ) ). 0.57/0.73 0.57/0.73 fof(reserved_2Elogic_2E_2F_5C,axiom, 0.57/0.73 ! [V0_2E0,V1_2E0] : 0.57/0.73 ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_2F_5C_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) 0.57/0.73 <=> ( p(s(tyop_2Emin_2Ebool,V1_2E0)) 0.57/0.73 & p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Ebool_2ESKOLEM__THM,axiom, 0.57/0.73 ! [A_27a,A_27b,V0P_2E0] : 0.57/0.73 ( ? [V3f_2E0] : 0.57/0.73 ! [V4x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V4x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V3f_2E0),s(A_27a,V4x_2E0)))))) 0.57/0.73 <=> ! [V1x_2E0] : 0.57/0.73 ? [V2y_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool)),V0P_2E0),s(A_27a,V1x_2E0))),s(A_27b,V2y_2E0)))) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Ebool_2EDISJ__SYM,axiom, 0.57/0.73 ! [V0A_2E0,V1B_2E0] : 0.57/0.73 ( ( p(s(tyop_2Emin_2Ebool,V1B_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V0A_2E0)) ) 0.57/0.73 <=> ( p(s(tyop_2Emin_2Ebool,V1B_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V0A_2E0)) ) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Epred__set_2EBIJ__SYM,axiom, 0.57/0.73 ! [A_27a,A_27b,V0s_2E0,V1t_2E0] : 0.57/0.73 ( ? [V2f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),V2f_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0)))) 0.57/0.73 <=> ? [V3g_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),V3g_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),V1t_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0s_2E0)))) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Esat_2Edc__imp,axiom, 0.57/0.73 ! [V0r_2E0,V1q_2E0,V2p_2E0] : 0.57/0.73 ( ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V1q_2E0)) ) 0.57/0.73 & ( ~ p(s(tyop_2Emin_2Ebool,V1q_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V0r_2E0)) 0.57/0.73 | ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) 0.57/0.73 & ( ~ p(s(tyop_2Emin_2Ebool,V0r_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) ) 0.57/0.73 <=> ( p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.73 <=> ( p(s(tyop_2Emin_2Ebool,V1q_2E0)) 0.57/0.73 => p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) ) ) ). 0.57/0.73 0.57/0.73 fof(reserved_2Elogic_2E_3D,axiom, 0.57/0.73 ! [A_27a,V0_2E0,V1_2E0] : 0.57/0.73 ( p(s(tyop_2Emin_2Ebool,c_2Emin_2E_3D_2E2(s(A_27a,V0_2E0),s(A_27a,V1_2E0)))) 0.57/0.73 <=> s(A_27a,V1_2E0) = s(A_27a,V0_2E0) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Ebool_2ETRUTH,axiom, 0.57/0.73 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ). 0.57/0.73 0.57/0.73 fof(thm_2Esat_2Edc__disj,axiom, 0.57/0.73 ! [V0r_2E0,V1q_2E0,V2p_2E0] : 0.57/0.73 ( ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.73 | ~ p(s(tyop_2Emin_2Ebool,V1q_2E0)) ) 0.57/0.73 & ( p(s(tyop_2Emin_2Ebool,V1q_2E0)) 0.57/0.73 | ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) 0.57/0.73 & ( p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.73 | ~ p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) ) 0.57/0.73 <=> ( ( p(s(tyop_2Emin_2Ebool,V0r_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V1q_2E0)) ) 0.57/0.73 <=> p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Esat_2ENOT__NOT,axiom, 0.57/0.73 ! [V0t_2E0] : 0.57/0.73 ( ~ ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) 0.57/0.73 <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ). 0.57/0.73 0.57/0.73 fof(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom, 0.57/0.73 ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_3F_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ). 0.57/0.73 0.57/0.73 fof(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom, 0.57/0.73 ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27a,A_27b),X0_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X2_2E0))) ). 0.57/0.73 0.57/0.73 fof(reserved_2Eho_2Enotfalse,axiom, 0.57/0.73 ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ). 0.57/0.73 0.57/0.73 fof(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29,axiom, 0.57/0.73 ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X2_2E0))) ). 0.57/0.73 0.57/0.73 fof(thm_2Ebool_2EF__IMP,axiom, 0.57/0.73 ! [V0t_2E0] : 0.57/0.73 ( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) 0.57/0.73 => ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) 0.57/0.73 <= p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Ebool_2ELEFT__OR__EXISTS__THM,axiom, 0.57/0.73 ! [A_27a,V0P_2E0,V1Q_2E0] : 0.57/0.73 ( ? [V3x_2E0] : 0.57/0.73 ( p(s(tyop_2Emin_2Ebool,V1Q_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) ) 0.57/0.73 <=> ( ? [V2x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V1Q_2E0)) ) ) ). 0.57/0.73 0.57/0.73 fof(reserved_2Eho_2Ek__thm,axiom, 0.57/0.73 ! [A_27a,A_27b,V0x_2E0,V1y_2E0] : s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27a),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)),combin_k_2E0),s(A_27a,V0x_2E0))),s(A_27b,V1y_2E0))) = s(A_27a,V0x_2E0) ). 0.57/0.73 0.57/0.73 fof(thm_2Eutil__prob_2ENUM__2D__BIJ__INV,conjecture, 0.57/0.73 ? [V0f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))))) ). 0.57/0.73 0.57/0.73 fof(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom, 0.57/0.73 ! [A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0))),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(A_27b,A_27a),X0_2E0),s(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X2_2E0))) ). 0.57/0.73 0.57/0.73 fof(thm_2Esat_2Edc__eq,axiom, 0.57/0.73 ! [V0r_2E0,V1q_2E0,V2p_2E0] : 0.57/0.73 ( ( ( p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V1q_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) 0.57/0.73 & ( p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.73 | ~ p(s(tyop_2Emin_2Ebool,V0r_2E0)) 0.57/0.73 | ~ p(s(tyop_2Emin_2Ebool,V1q_2E0)) ) 0.57/0.73 & ( p(s(tyop_2Emin_2Ebool,V1q_2E0)) 0.57/0.73 | ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.73 | ~ p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) 0.57/0.73 & ( ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.73 | ~ p(s(tyop_2Emin_2Ebool,V1q_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) ) 0.57/0.73 <=> ( p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.73 <=> s(tyop_2Emin_2Ebool,V0r_2E0) = s(tyop_2Emin_2Ebool,V1q_2E0) ) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Esat_2Edc__neg,axiom, 0.57/0.73 ! [V0q_2E0,V1p_2E0] : 0.57/0.73 ( ( ( p(s(tyop_2Emin_2Ebool,V0q_2E0)) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V1p_2E0)) ) 0.57/0.73 & ( ~ p(s(tyop_2Emin_2Ebool,V1p_2E0)) 0.57/0.73 | ~ p(s(tyop_2Emin_2Ebool,V0q_2E0)) ) ) 0.57/0.73 <=> ( ~ p(s(tyop_2Emin_2Ebool,V0q_2E0)) 0.57/0.73 <=> p(s(tyop_2Emin_2Ebool,V1p_2E0)) ) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Ebool_2ERIGHT__OR__EXISTS__THM,axiom, 0.57/0.73 ! [A_27a,V0P_2E0,V1Q_2E0] : 0.57/0.73 ( ? [V3x_2E0] : 0.57/0.73 ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V0P_2E0)) ) 0.57/0.73 <=> ( ? [V2x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))) 0.57/0.73 | p(s(tyop_2Emin_2Ebool,V0P_2E0)) ) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Ebool_2EEQ__SYM__EQ,axiom, 0.57/0.73 ! [A_27a,V0x_2E0,V1y_2E0] : 0.57/0.73 ( s(A_27a,V0x_2E0) = s(A_27a,V1y_2E0) 0.57/0.73 <=> s(A_27a,V1y_2E0) = s(A_27a,V0x_2E0) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Ebool_2ENOT__CLAUSES,axiom, 0.57/0.73 ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) 0.57/0.73 <=> ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) 0.57/0.73 & ( ~ p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) 0.57/0.73 <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) 0.57/0.73 & ! [V0t_2E0] : 0.57/0.73 ( p(s(tyop_2Emin_2Ebool,V0t_2E0)) 0.57/0.73 <=> ~ ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Esat_2EOR__DUAL3,axiom, 0.57/0.73 ! [V0B_2E0,V1A_2E0] : 0.57/0.73 ( ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) 0.57/0.73 <= ~ p(s(tyop_2Emin_2Ebool,V0B_2E0)) ) 0.57/0.73 <= p(s(tyop_2Emin_2Ebool,V1A_2E0)) ) 0.57/0.73 <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) 0.57/0.73 <= ~ ( p(s(tyop_2Emin_2Ebool,V0B_2E0)) 0.57/0.73 | ~ p(s(tyop_2Emin_2Ebool,V1A_2E0)) ) ) ) ). 0.57/0.73 0.57/0.73 fof(thm_2Ebool_2ELEFT__AND__FORALL__THM,axiom, 0.57/0.73 ! [A_27a,V0P_2E0,V1Q_2E0] : 0.57/0.73 ( ! [V3x_2E0] : 0.57/0.73 ( p(s(tyop_2Emin_2Ebool,V1Q_2E0)) 0.57/0.73 & p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) ) 0.57/0.73 <=> ( p(s(tyop_2Emin_2Ebool,V1Q_2E0)) 0.57/0.73 & ! [V2x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) ) ) ). 0.57/0.73 0.57/0.73 fof(reserved_2Eho_2Eboolext,axiom, 0.57/0.73 ! [V0_2E0,V1_2E0] : 0.57/0.73 ( ( p(s(tyop_2Emin_2Ebool,V1_2E0)) 0.57/0.73 <=> p(s(tyop_2Emin_2Ebool,V0_2E0)) ) 0.57/0.73 => s(tyop_2Emin_2Ebool,V1_2E0) = s(tyop_2Emin_2Ebool,V0_2E0) ) ). 0.57/0.74 0.57/0.74 fof(reserved_2Eho_2Etruth,axiom, 0.57/0.74 p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ). 0.57/0.74 0.57/0.74 fof(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom, 0.57/0.74 ! [X0_2E0] : 0.57/0.74 ( ~ p(s(tyop_2Emin_2Ebool,X0_2E0)) 0.57/0.74 <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_7E_2E0),s(tyop_2Emin_2Ebool,X0_2E0)))) ) ). 0.57/0.74 0.57/0.74 fof(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom, 0.57/0.74 ! [A_27a,X0_2E0] : s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2E_21_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) = s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X0_2E0))) ). 0.57/0.74 0.57/0.74 fof(reserved_2Elogic_2E_7E,axiom, 0.57/0.74 ! [V0_2E0] : 0.57/0.74 ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E1(s(tyop_2Emin_2Ebool,V0_2E0)))) 0.57/0.74 <=> ~ p(s(tyop_2Emin_2Ebool,V0_2E0)) ) ). 0.57/0.74 0.57/0.74 fof(reserved_2Eho_2Ei__thm,axiom, 0.57/0.74 ! [A_27a,V0x_2E0] : s(A_27a,V0x_2E0) = s(A_27a,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27a),combin_i_2E0),s(A_27a,V0x_2E0))) ). 0.57/0.74 0.57/0.74 fof(thm_2Ebool_2EIMP__ANTISYM__AX,axiom, 0.57/0.74 ! [V0t1_2E0,V1t2_2E0] : 0.57/0.74 ( ( s(tyop_2Emin_2Ebool,V0t1_2E0) = s(tyop_2Emin_2Ebool,V1t2_2E0) 0.57/0.74 <= ( p(s(tyop_2Emin_2Ebool,V1t2_2E0)) 0.57/0.74 => p(s(tyop_2Emin_2Ebool,V0t1_2E0)) ) ) 0.57/0.74 <= ( p(s(tyop_2Emin_2Ebool,V0t1_2E0)) 0.57/0.74 => p(s(tyop_2Emin_2Ebool,V1t2_2E0)) ) ) ). 0.57/0.74 0.57/0.74 fof(thm_2Esat_2EAND__INV__IMP,axiom, 0.57/0.74 ! [V0A_2E0] : 0.57/0.74 ( p(s(tyop_2Emin_2Ebool,V0A_2E0)) 0.57/0.74 => ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) 0.57/0.74 <= ~ p(s(tyop_2Emin_2Ebool,V0A_2E0)) ) ) ). 0.57/0.74 0.57/0.74 fof(thm_2Ebool_2ELEFT__FORALL__OR__THM,axiom, 0.57/0.74 ! [A_27a,V0Q_2E0,V1P_2E0] : 0.57/0.74 ( ( ! [V3x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V3x_2E0)))) 0.57/0.74 | p(s(tyop_2Emin_2Ebool,V0Q_2E0)) ) 0.57/0.74 <=> ! [V2x_2E0] : 0.57/0.74 ( p(s(tyop_2Emin_2Ebool,V0Q_2E0)) 0.57/0.74 | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1P_2E0),s(A_27a,V2x_2E0)))) ) ) ). 0.57/0.74 0.57/0.74 fof(arityeq3_2Ec_2Epred__set_2EBIJ_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Enum_2Enum_29_20mono_2Etyop_2Enum_2Enum,axiom, 0.57/0.74 ! [X0_2E0,X1_2E0,X2_2E0] : s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0))) = s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool))),c_2Epred__set_2EBIJ_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),X0_2E0))),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),X1_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X2_2E0))) ). 0.57/0.74 0.57/0.74 fof(thm_2Ebool_2ELEFT__EXISTS__AND__THM,axiom, 0.57/0.74 ! [A_27a,V0P_2E0,V1Q_2E0] : 0.57/0.74 ( ? [V2x_2E0] : 0.57/0.74 ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) 0.57/0.74 & p(s(tyop_2Emin_2Ebool,V1Q_2E0)) ) 0.57/0.74 <=> ( p(s(tyop_2Emin_2Ebool,V1Q_2E0)) 0.57/0.74 & ? [V3x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V3x_2E0)))) ) ) ). 0.57/0.74 0.57/0.74 fof(thm_2Ebool_2EEQ__CLAUSES,axiom, 0.57/0.74 ! [V0t_2E0] : 0.57/0.74 ( ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) 0.57/0.74 <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) 0.57/0.74 & ( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) 0.57/0.74 <=> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) ) 0.57/0.74 & ( ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) 0.57/0.74 <=> s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) ) 0.57/0.74 & ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) 0.57/0.74 <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) ). 0.57/0.74 0.57/0.74 fof(thm_2Ebool_2EIMP__CLAUSES,axiom, 0.57/0.74 ! [V0t_2E0] : 0.57/0.74 ( ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) 0.57/0.74 <=> ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) 0.57/0.74 <= p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) 0.57/0.74 & ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0)) 0.57/0.74 <= p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) 0.57/0.74 <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) 0.57/0.74 & ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) 0.57/0.74 <=> ( p(s(tyop_2Emin_2Ebool,V0t_2E0)) 0.57/0.74 <= p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) 0.57/0.74 & ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0)) 0.57/0.74 => p(s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0)) ) 0.57/0.74 <=> ~ p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) 0.57/0.74 & ( ( p(s(tyop_2Emin_2Ebool,V0t_2E0)) 0.57/0.74 <= p(s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0)) ) 0.57/0.74 <=> p(s(tyop_2Emin_2Ebool,V0t_2E0)) ) ) ). 0.57/0.74 0.57/0.74 fof(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom, 0.57/0.74 ! [X0_2E0,X1_2E0] : 0.57/0.74 ( ( p(s(tyop_2Emin_2Ebool,X0_2E0)) 0.57/0.74 | p(s(tyop_2Emin_2Ebool,X1_2E0)) ) 0.57/0.74 <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_5C_2F_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ). 0.57/0.74 0.57/0.74 fof(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom, 0.57/0.74 ! [X0_2E0,X1_2E0] : 0.57/0.74 ( ( p(s(tyop_2Emin_2Ebool,X1_2E0)) 0.57/0.74 <= p(s(tyop_2Emin_2Ebool,X0_2E0)) ) 0.57/0.74 <=> p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Emin_2E_3D_3D_3E_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) ) ). 0.57/0.74 0.57/0.74 fof(thm_2Eutil__prob_2ENUM__2D__BIJ,axiom, 0.57/0.74 ? [V0f_2E0] : p(s(tyop_2Emin_2Ebool,c_2Epred__set_2EBIJ_2E3(s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Enum_2Enum),V0f_2E0),s(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Ebool),c_2Epred__set_2ECROSS_2E2(s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0))),s(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2EUNIV_2E0)))) ). 0.57/0.74 0.57/0.74 fof(thm_2Esat_2Edc__conj,axiom, 0.57/0.74 ! [V0r_2E0,V1q_2E0,V2p_2E0] : 0.57/0.74 ( ( ( p(s(tyop_2Emin_2Ebool,V0r_2E0)) 0.57/0.74 & p(s(tyop_2Emin_2Ebool,V1q_2E0)) ) 0.57/0.74 <=> p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) 0.57/0.74 <=> ( ( ~ p(s(tyop_2Emin_2Ebool,V0r_2E0)) 0.57/0.74 | ~ p(s(tyop_2Emin_2Ebool,V1q_2E0)) 0.57/0.74 | p(s(tyop_2Emin_2Ebool,V2p_2E0)) ) 0.57/0.74 & ( ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.74 | p(s(tyop_2Emin_2Ebool,V0r_2E0)) ) 0.57/0.74 & ( ~ p(s(tyop_2Emin_2Ebool,V2p_2E0)) 0.57/0.74 | p(s(tyop_2Emin_2Ebool,V1q_2E0)) ) ) ) ). 0.57/0.74 0.57/0.74 fof(reserved_2Eho_2Eeq__ext,axiom, 0.57/0.74 ! [A_27a,A_27b,V0f_2E0,V1g_2E0] : 0.57/0.74 ( s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0) = s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0) 0.57/0.74 <= ! [V2x_2E0] : s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))) = s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0),s(A_27a,V2x_2E0))) ) ). 0.57/0.74 0.57/0.74 fof(thm_2Ebool_2ERIGHT__FORALL__OR__THM,axiom, 0.57/0.74 ! [A_27a,V0P_2E0,V1Q_2E0] : 0.57/0.74 ( ( p(s(tyop_2Emin_2Ebool,V0P_2E0)) 0.57/0.74 | ! [V3x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))) ) 0.57/0.74 <=> ! [V2x_2E0] : 0.57/0.74 ( p(s(tyop_2Emin_2Ebool,V0P_2E0)) 0.57/0.74 | p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))) ) ) ). 0.57/0.74 0.57/0.74 fof(reserved_2Eho_2Es__thm,axiom, 0.57/0.74 ! [A_27a,A_27b,A_27c,V0f_2E0,V1g_2E0,V2x_2E0] : s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27b,A_27c),app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0),s(A_27a,V2x_2E0))),s(A_27b,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0),s(A_27a,V2x_2E0))))) = s(A_27c,app_2E2(s(tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))),combin_s_2E0),s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V0f_2E0))),s(tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0))),s(A_27a,V2x_2E0))) ). 0.57/0.74 0.57/0.74 fof(thm_2Ebool_2ERIGHT__EXISTS__AND__THM,axiom, 0.57/0.74 ! [A_27a,V0P_2E0,V1Q_2E0] : 0.57/0.74 ( ( p(s(tyop_2Emin_2Ebool,V0P_2E0)) 0.57/0.74 & ? [V3x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))) ) 0.57/0.74 <=> ? [V2x_2E0] : 0.57/0.74 ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))) 0.57/0.74 & p(s(tyop_2Emin_2Ebool,V0P_2E0)) ) ) ). 0.57/0.74 0.57/0.74 fof(reserved_2Equant_2E_21,axiom, 0.57/0.74 ! [A_27a,V0f_2E0] : 0.57/0.74 ( p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E1(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0)))) 0.57/0.74 <=> ! [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0f_2E0),s(A_27a,V1x_2E0)))) ) ). 0.57/0.74 0.57/0.74 fof(thm_2Ebool_2ERIGHT__AND__FORALL__THM,axiom, 0.57/0.74 ! [A_27a,V0P_2E0,V1Q_2E0] : 0.57/0.74 ( ! [V3x_2E0] : 0.57/0.74 ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V3x_2E0)))) 0.57/0.74 & p(s(tyop_2Emin_2Ebool,V0P_2E0)) ) 0.57/0.74 <=> ( ! [V2x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V1Q_2E0),s(A_27a,V2x_2E0)))) 0.57/0.74 & p(s(tyop_2Emin_2Ebool,V0P_2E0)) ) ) ). 0.57/0.74 0.57/0.74 fof(reserved_2Elogic_2E_5C_2F,axiom, 0.57/0.74 ! [V0_2E0,V1_2E0] : 0.57/0.74 ( ( p(s(tyop_2Emin_2Ebool,V0_2E0)) 0.57/0.74 | p(s(tyop_2Emin_2Ebool,V1_2E0)) ) 0.57/0.74 <=> p(s(tyop_2Emin_2Ebool,c_2Ebool_2E_5C_2F_2E2(s(tyop_2Emin_2Ebool,V0_2E0),s(tyop_2Emin_2Ebool,V1_2E0)))) ) ). 0.57/0.74 0.57/0.74 fof(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom, 0.57/0.74 ! [X0_2E0,X1_2E0] : 0.57/0.75 ( p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(s(tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2E_2F_5C_2E0),s(tyop_2Emin_2Ebool,X0_2E0))),s(tyop_2Emin_2Ebool,X1_2E0)))) 0.57/0.75 <=> ( p(s(tyop_2Emin_2Ebool,X1_2E0)) 0.57/0.75 & p(s(tyop_2Emin_2Ebool,X0_2E0)) ) ) ). 0.57/0.75 0.57/0.75 fof(thm_2Ebool_2ENOT__EXISTS__THM,axiom, 0.57/0.75 ! [A_27a,V0P_2E0] : 0.57/0.75 ( ~ ? [V1x_2E0] : p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V1x_2E0)))) 0.57/0.75 <=> ! [V2x_2E0] : ~ p(s(tyop_2Emin_2Ebool,app_2E2(s(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V0P_2E0),s(A_27a,V2x_2E0)))) ) ). 0.57/0.75 0.57/0.75 fof(reserved_2Eho_2Ebool__cases__ax,axiom, 0.57/0.75 ! [V0t_2E0] : 0.57/0.75 ( s(tyop_2Emin_2Ebool,c_2Ebool_2ET_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) 0.57/0.75 | s(tyop_2Emin_2Ebool,c_2Ebool_2EF_2E0) = s(tyop_2Emin_2Ebool,V0t_2E0) ) ). 0.57/0.75 0.57/0.75 %------------------------------------------- 0.57/0.75 % Proof found 0.57/0.75 % SZS status Theorem for theBenchmark 0.57/0.75 % SZS output start Proof 0.57/0.75 %ClaNum:228(EqnAxiom:113) 0.57/0.75 %VarNum:619(SingletonVarNum:225) 0.57/0.75 %MaxLitNum:4 0.57/0.75 %MaxfuncDepth:6 0.57/0.75 %SharedTerms:52 0.57/0.75 %goalClause: 129 0.57/0.75 %singleGoalClaCount:1 0.57/0.75 [116]P1(f5(a1,a2)) 0.57/0.75 [128]~P1(f5(a1,a4)) 0.57/0.75 [121]P1(f5(a1,f15(f5(f56(f58(a57,a57),a57),a27),f5(f56(f58(a57,a57),a1),f14(f5(f56(a57,a1),a13),f5(f56(a57,a1),a13))),f5(f56(a57,a1),a13)))) 0.57/0.75 [129]~P1(f5(a1,f15(f5(f56(a57,f58(a57,a57)),x1291),f5(f56(a57,a1),a13),f5(f56(f58(a57,a57),a1),f14(f5(f56(a57,a1),a13),f5(f56(a57,a1),a13)))))) 0.57/0.75 [117]E(f5(x1171,f3(f5(f56(x1171,x1171),a6),f5(x1171,x1172))),f5(x1171,x1172)) 0.57/0.75 [118]E(f5(a1,f3(f5(f56(f56(x1181,a1),a1),a7),f5(f56(x1181,a1),x1182))),f5(a1,f12(f5(f56(x1181,a1),x1182)))) 0.57/0.75 [119]E(f5(a1,f3(f5(f56(f56(x1191,a1),a1),a8),f5(f56(x1191,a1),x1192))),f5(a1,f9(f5(f56(x1191,a1),x1192)))) 0.57/0.75 [122]E(f5(f56(f58(a57,a57),a1),f3(f5(f56(f56(a57,a1),f56(f58(a57,a57),a1)),f3(f5(f56(f56(a57,a1),f56(f56(a57,a1),f56(f58(a57,a57),a1))),a25),f5(f56(a57,a1),x1221))),f5(f56(a57,a1),x1222))),f5(f56(f58(a57,a57),a1),f14(f5(f56(a57,a1),x1221),f5(f56(a57,a1),x1222)))) 0.57/0.75 [120]E(f5(x1201,f3(f5(f56(x1202,x1201),f3(f5(f56(x1201,f56(x1202,x1201)),a26),f5(x1201,x1203))),f5(x1202,x1204))),f5(x1201,x1203)) 0.57/0.75 [124]E(f5(a1,f3(f5(f56(f56(x1241,a1),a1),f3(f5(f56(f56(x1242,a1),f56(f56(x1241,a1),a1)),f3(f5(f56(f56(x1242,x1241),f56(f56(x1242,a1),f56(f56(x1241,a1),a1))),a16),f5(f56(x1242,x1241),x1243))),f5(f56(x1242,a1),x1244))),f5(f56(x1241,a1),x1245))),f5(a1,f15(f5(f56(x1242,x1241),x1243),f5(f56(x1242,a1),x1244),f5(f56(x1241,a1),x1245)))) 0.57/0.75 [125]E(f5(x1251,f3(f5(f56(x1252,x1251),f3(f5(f56(x1253,f56(x1252,x1251)),x1254),f5(x1253,x1255))),f5(x1252,f3(f5(f56(x1253,x1252),x1256),f5(x1253,x1255))))),f5(x1251,f3(f5(f56(x1253,x1251),f3(f5(f56(f56(x1253,x1252),f56(x1253,x1251)),f3(f5(f56(f56(x1253,f56(x1252,x1251)),f56(f56(x1253,x1252),f56(x1253,x1251))),a28),f5(f56(x1253,f56(x1252,x1251)),x1254))),f5(f56(x1253,x1252),x1256))),f5(x1253,x1255)))) 0.57/0.75 [130]E(f5(a1,a2),f5(a1,x1301))+E(f5(a1,a4),f5(a1,x1301)) 0.57/0.75 [135]E(f5(a1,a4),f5(a1,x1351))+P1(f5(a1,x1351)) 0.57/0.75 [139]~E(f5(a1,a2),f5(a1,x1391))+P1(f5(a1,x1391)) 0.57/0.75 [141]E(f5(a1,a2),f5(a1,x1411))+~P1(f5(a1,x1411)) 0.57/0.75 [148]~E(f5(a1,a4),f5(a1,x1481))+~P1(f5(a1,x1481)) 0.57/0.75 [166]P1(f5(a1,x1661))+P1(f5(a1,f17(f5(a1,x1661)))) 0.57/0.75 [177]~P1(f5(a1,x1771))+~P1(f5(a1,f17(f5(a1,x1771)))) 0.57/0.75 [186]P1(f5(a1,x1861))+P1(f5(a1,f3(f5(f56(a1,a1),a20),f5(a1,x1861)))) 0.57/0.75 [190]~P1(f5(a1,x1901))+~P1(f5(a1,f3(f5(f56(a1,a1),a20),f5(a1,x1901)))) 0.57/0.75 [178]P1(f5(a1,x1781))+P1(f5(a1,f21(f5(a1,x1781),f5(a1,x1782)))) 0.57/0.75 [179]~P1(f5(a1,x1792))+P1(f5(a1,f21(f5(a1,x1791),f5(a1,x1792)))) 0.57/0.75 [180]~P1(f5(a1,x1802))+P1(f5(a1,f18(f5(a1,x1801),f5(a1,x1802)))) 0.57/0.75 [181]~P1(f5(a1,x1811))+P1(f5(a1,f18(f5(a1,x1811),f5(a1,x1812)))) 0.57/0.75 [184]P1(f5(a1,x1841))+~P1(f5(a1,f10(f5(a1,x1842),f5(a1,x1841)))) 0.57/0.75 [185]P1(f5(a1,x1851))+~P1(f5(a1,f10(f5(a1,x1851),f5(a1,x1852)))) 0.57/0.75 [213]P1(f5(a1,x2131))+P1(f5(a1,f3(f5(f56(a1,a1),f3(f5(f56(a1,f56(a1,a1)),a24),f5(a1,x2131))),f5(a1,x2132)))) 0.57/0.75 [214]~P1(f5(a1,x2142))+P1(f5(a1,f3(f5(f56(a1,a1),f3(f5(f56(a1,f56(a1,a1)),a19),f5(a1,x2141))),f5(a1,x2142)))) 0.57/0.75 [215]~P1(f5(a1,x2151))+P1(f5(a1,f3(f5(f56(a1,a1),f3(f5(f56(a1,f56(a1,a1)),a19),f5(a1,x2151))),f5(a1,x2152)))) 0.57/0.75 [216]~P1(f5(a1,x2162))+P1(f5(a1,f3(f5(f56(a1,a1),f3(f5(f56(a1,f56(a1,a1)),a24),f5(a1,x2161))),f5(a1,x2162)))) 0.57/0.75 [219]P1(f5(a1,x2191))+~P1(f5(a1,f3(f5(f56(a1,a1),f3(f5(f56(a1,f56(a1,a1)),a11),f5(a1,x2192))),f5(a1,x2191)))) 0.57/0.75 [220]P1(f5(a1,x2201))+~P1(f5(a1,f3(f5(f56(a1,a1),f3(f5(f56(a1,f56(a1,a1)),a11),f5(a1,x2201))),f5(a1,x2202)))) 0.57/0.75 [193]P1(f5(a1,f3(f5(f56(x1931,a1),x1932),f5(x1931,f37(x1931,x1932)))))+~P1(f5(a1,f12(f5(f56(x1931,a1),x1932)))) 0.57/0.75 [194]~P1(f5(a1,f3(f5(f56(x1941,a1),x1942),f5(x1941,f39(x1941,x1942)))))+P1(f5(a1,f9(f5(f56(x1941,a1),x1942)))) 0.57/0.75 [182]~E(f5(x1821,x1823),f5(x1821,x1822))+P1(f5(a1,f22(f5(x1821,x1822),f5(x1821,x1823)))) 0.57/0.75 [188]E(f5(x1881,x1882),f5(x1881,x1883))+~P1(f5(a1,f22(f5(x1881,x1882),f5(x1881,x1883)))) 0.57/0.75 [218]~E(f5(x2181,x2183),f5(x2181,x2182))+P1(f5(a1,f3(f5(f56(x2181,a1),f3(f5(f56(x2181,f56(x2181,a1)),a23),f5(x2181,x2182))),f5(x2181,x2183)))) 0.57/0.75 [223]E(f5(x2231,x2232),f5(x2231,x2233))+~P1(f5(a1,f3(f5(f56(x2231,a1),f3(f5(f56(x2231,f56(x2231,a1)),a23),f5(x2231,x2232))),f5(x2231,x2233)))) 0.57/0.75 [191]P1(f5(a1,f3(f5(f56(x1911,a1),x1912),f5(x1911,x1913))))+~P1(f5(a1,f9(f5(f56(x1911,a1),x1912)))) 0.57/0.75 [192]~P1(f5(a1,f3(f5(f56(x1921,a1),x1922),f5(x1921,x1923))))+P1(f5(a1,f12(f5(f56(x1921,a1),x1922)))) 0.57/0.75 [195]~P1(f5(a1,f3(f5(f56(x1951,a1),x1952),f5(x1951,x1953))))+P1(f5(a1,f3(f5(f56(x1951,a1),x1952),f5(x1951,f44(x1951,x1952))))) 0.57/0.75 [196]~P1(f5(a1,f3(f5(f56(x1961,a1),x1962),f5(x1961,x1963))))+P1(f5(a1,f3(f5(f56(x1961,a1),x1962),f5(x1961,f47(x1961,x1962))))) 0.57/0.75 [226]E(f5(f56(x2261,x2262),x2263),f5(f56(x2261,x2262),x2264))+~E(f5(x2262,f3(f5(f56(x2261,x2262),x2263),f5(x2261,f38(x2261,x2262,x2264,x2263)))),f5(x2262,f3(f5(f56(x2261,x2262),x2264),f5(x2261,f38(x2261,x2262,x2264,x2263))))) 0.57/0.75 [224]~P1(f5(a1,f15(f5(f56(x2242,x2241),x2245),f5(f56(x2242,a1),x2243),f5(f56(x2241,a1),x2244))))+P1(f5(a1,f15(f5(f56(x2241,x2242),f49(x2242,x2241,x2243,x2244)),f5(f56(x2241,a1),x2244),f5(f56(x2242,a1),x2243)))) 0.57/0.75 [225]~P1(f5(a1,f15(f5(f56(x2252,x2251),x2255),f5(f56(x2252,a1),x2254),f5(f56(x2251,a1),x2253))))+P1(f5(a1,f15(f5(f56(x2251,x2252),f54(x2251,x2252,x2253,x2254)),f5(f56(x2251,a1),x2253),f5(f56(x2252,a1),x2254)))) 0.57/0.75 [227]~P1(f5(a1,f3(f5(f56(x2271,a1),f3(f5(f56(x2272,f56(x2271,a1)),x2273),f5(x2272,f51(x2272,x2271,x2273)))),f5(x2271,x2275))))+P1(f5(a1,f3(f5(f56(x2271,a1),f3(f5(f56(x2272,f56(x2271,a1)),x2273),f5(x2272,x2274))),f5(x2271,f3(f5(f56(x2272,x2271),f50(x2272,x2271,x2273)),f5(x2272,x2274)))))) 0.57/0.75 [228]P1(f5(a1,f3(f5(f56(x2281,a1),f3(f5(f56(x2282,f56(x2281,a1)),x2283),f5(x2282,x2284))),f5(x2281,f52(x2282,x2281,x2283,x2284)))))+~P1(f5(a1,f3(f5(f56(x2281,a1),f3(f5(f56(x2282,f56(x2281,a1)),x2283),f5(x2282,f53(x2282,x2281,x2283,x2285)))),f5(x2281,f3(f5(f56(x2282,x2281),x2285),f5(x2282,f53(x2282,x2281,x2283,x2285))))))) 0.57/0.75 [146]E(f5(a1,x1461),f5(a1,x1462))+P1(f5(a1,x1461))+P1(f5(a1,x1462)) 0.57/0.75 [154]E(f5(a1,x1541),f5(a1,x1542))+~P1(f5(a1,x1541))+~P1(f5(a1,x1542)) 0.57/0.75 [183]~P1(f5(a1,x1831))+~P1(f5(a1,x1832))+P1(f5(a1,f10(f5(a1,x1831),f5(a1,x1832)))) 0.57/0.75 [187]P1(f5(a1,x1871))+P1(f5(a1,x1872))+~P1(f5(a1,f18(f5(a1,x1872),f5(a1,x1871)))) 0.57/0.75 [189]P1(f5(a1,x1891))+~P1(f5(a1,x1892))+~P1(f5(a1,f21(f5(a1,x1892),f5(a1,x1891)))) 0.57/0.75 [217]~P1(f5(a1,x2171))+~P1(f5(a1,x2172))+P1(f5(a1,f3(f5(f56(a1,a1),f3(f5(f56(a1,f56(a1,a1)),a11),f5(a1,x2171))),f5(a1,x2172)))) 0.57/0.75 [221]P1(f5(a1,x2211))+P1(f5(a1,x2212))+~P1(f5(a1,f3(f5(f56(a1,a1),f3(f5(f56(a1,f56(a1,a1)),a19),f5(a1,x2212))),f5(a1,x2211)))) 0.57/0.75 [222]P1(f5(a1,x2221))+~P1(f5(a1,x2222))+~P1(f5(a1,f3(f5(f56(a1,a1),f3(f5(f56(a1,f56(a1,a1)),a24),f5(a1,x2222))),f5(a1,x2221)))) 0.57/0.75 [152]P2(x1521,x1522,x1523)+E(f5(a1,x1521),f5(a1,x1522))+P1(f5(a1,x1523)) 0.57/0.75 [157]P2(x1571,x1572,x1573)+P1(f5(a1,x1571))+~P1(f5(a1,x1573)) 0.57/0.75 [158]P2(x1581,x1582,x1583)+P1(f5(a1,x1581))+~P1(f5(a1,x1582)) 0.57/0.75 [159]P2(x1591,x1592,x1593)+~E(f5(a1,x1591),f5(a1,x1592))+~P1(f5(a1,x1593)) 0.57/0.75 [161]P2(x1611,x1612,x1613)+~P1(f5(a1,x1613))+~P1(f5(a1,x1612)) 0.57/0.75 [165]~P2(x1652,x1653,x1651)+~E(f5(a1,x1652),f5(a1,x1653))+P1(f5(a1,x1651)) 0.57/0.75 [197]P1(f5(a1,x1971))+~P1(f5(a1,f3(f5(f56(x1972,a1),x1973),f5(x1972,x1974))))+P1(f5(a1,f3(f5(f56(x1972,a1),x1973),f5(x1972,f48(x1972,x1973,x1971))))) 0.57/0.75 [198]P1(f5(a1,x1981))+~P1(f5(a1,f3(f5(f56(x1982,a1),x1983),f5(x1982,x1984))))+P1(f5(a1,f3(f5(f56(x1982,a1),x1983),f5(x1982,f55(x1982,x1983,x1981))))) 0.57/0.75 [199]P1(f5(a1,x1991))+~P1(f5(a1,f3(f5(f56(x1992,a1),x1993),f5(x1992,x1994))))+P1(f5(a1,f3(f5(f56(x1992,a1),x1993),f5(x1992,f29(x1992,x1991,x1993))))) 0.57/0.76 [200]P1(f5(a1,x2001))+~P1(f5(a1,f3(f5(f56(x2002,a1),x2003),f5(x2002,x2004))))+P1(f5(a1,f3(f5(f56(x2002,a1),x2003),f5(x2002,f30(x2002,x2001,x2003))))) 0.57/0.76 [201]~P1(f5(a1,x2013))+~P1(f5(a1,f3(f5(f56(x2011,a1),x2012),f5(x2011,x2014))))+P1(f5(a1,f3(f5(f56(x2011,a1),x2012),f5(x2011,f31(x2011,x2012,x2013))))) 0.57/0.76 [202]~P1(f5(a1,x2023))+~P1(f5(a1,f3(f5(f56(x2021,a1),x2022),f5(x2021,x2024))))+P1(f5(a1,f3(f5(f56(x2021,a1),x2022),f5(x2021,f36(x2021,x2022,x2023))))) 0.57/0.76 [203]~P1(f5(a1,x2033))+~P1(f5(a1,f3(f5(f56(x2031,a1),x2032),f5(x2031,x2034))))+P1(f5(a1,f3(f5(f56(x2031,a1),x2032),f5(x2031,f40(x2031,x2033,x2032))))) 0.57/0.76 [204]~P1(f5(a1,x2043))+~P1(f5(a1,f3(f5(f56(x2041,a1),x2042),f5(x2041,x2044))))+P1(f5(a1,f3(f5(f56(x2041,a1),x2042),f5(x2041,f43(x2041,x2043,x2042))))) 0.57/0.76 [205]P1(f5(a1,x2051))+P1(f5(a1,f3(f5(f56(x2052,a1),x2053),f5(x2052,x2054))))+~P1(f5(a1,f3(f5(f56(x2052,a1),x2053),f5(x2052,f32(x2052,x2051,x2053))))) 0.57/0.76 [206]P1(f5(a1,x2061))+P1(f5(a1,f3(f5(f56(x2062,a1),x2063),f5(x2062,x2064))))+~P1(f5(a1,f3(f5(f56(x2062,a1),x2063),f5(x2062,f35(x2062,x2061,x2063))))) 0.57/0.76 [207]P1(f5(a1,x2071))+P1(f5(a1,f3(f5(f56(x2072,a1),x2073),f5(x2072,x2074))))+~P1(f5(a1,f3(f5(f56(x2072,a1),x2073),f5(x2072,f41(x2072,x2071,x2073))))) 0.57/0.76 [208]P1(f5(a1,x2081))+P1(f5(a1,f3(f5(f56(x2082,a1),x2083),f5(x2082,x2084))))+~P1(f5(a1,f3(f5(f56(x2082,a1),x2083),f5(x2082,f42(x2082,x2081,x2083))))) 0.57/0.76 [209]~P1(f5(a1,x2094))+P1(f5(a1,f3(f5(f56(x2091,a1),x2092),f5(x2091,x2093))))+~P1(f5(a1,f3(f5(f56(x2091,a1),x2092),f5(x2091,f33(x2091,x2092,x2094))))) 0.57/0.76 [210]~P1(f5(a1,x2104))+P1(f5(a1,f3(f5(f56(x2101,a1),x2102),f5(x2101,x2103))))+~P1(f5(a1,f3(f5(f56(x2101,a1),x2102),f5(x2101,f34(x2101,x2102,x2104))))) 0.57/0.76 [211]~P1(f5(a1,x2114))+P1(f5(a1,f3(f5(f56(x2111,a1),x2112),f5(x2111,x2113))))+~P1(f5(a1,f3(f5(f56(x2111,a1),x2112),f5(x2111,f45(x2111,x2114,x2112))))) 0.57/0.76 [212]~P1(f5(a1,x2124))+P1(f5(a1,f3(f5(f56(x2121,a1),x2122),f5(x2121,x2123))))+~P1(f5(a1,f3(f5(f56(x2121,a1),x2122),f5(x2121,f46(x2121,x2124,x2122))))) 0.57/0.76 [162]P2(x1621,x1622,x1623)+P1(f5(a1,x1622))+P1(f5(a1,x1623))+~P1(f5(a1,x1621)) 0.57/0.76 [167]~P2(x1671,x1672,x1673)+P1(f5(a1,x1671))+P1(f5(a1,x1672))+P1(f5(a1,x1673)) 0.57/0.76 [171]~P2(x1711,x1712,x1713)+E(f5(a1,x1711),f5(a1,x1712))+P1(f5(a1,x1712))+~P1(f5(a1,x1713)) 0.57/0.76 [174]~P2(x1741,x1742,x1743)+E(f5(a1,x1741),f5(a1,x1742))+~P1(f5(a1,x1741))+~P1(f5(a1,x1743)) 0.57/0.76 [175]~P2(x1752,x1751,x1753)+~P1(f5(a1,x1752))+~P1(f5(a1,x1753))+P1(f5(a1,x1751)) 0.57/0.76 [176]~P2(x1762,x1763,x1761)+~P1(f5(a1,x1763))+~P1(f5(a1,x1762))+P1(f5(a1,x1761)) 0.57/0.76 %EqnAxiom 0.57/0.76 [1]E(x11,x11) 0.57/0.76 [2]E(x22,x21)+~E(x21,x22) 0.57/0.76 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) 0.57/0.76 [4]~E(x41,x42)+E(f5(x41,x43),f5(x42,x43)) 0.57/0.76 [5]~E(x51,x52)+E(f5(x53,x51),f5(x53,x52)) 0.57/0.76 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63)) 0.57/0.76 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72)) 0.57/0.76 [8]~E(x81,x82)+E(f17(x81),f17(x82)) 0.57/0.76 [9]~E(x91,x92)+E(f56(x91,x93),f56(x92,x93)) 0.57/0.76 [10]~E(x101,x102)+E(f56(x103,x101),f56(x103,x102)) 0.57/0.76 [11]~E(x111,x112)+E(f53(x111,x113,x114,x115),f53(x112,x113,x114,x115)) 0.57/0.76 [12]~E(x121,x122)+E(f53(x123,x121,x124,x125),f53(x123,x122,x124,x125)) 0.57/0.76 [13]~E(x131,x132)+E(f53(x133,x134,x131,x135),f53(x133,x134,x132,x135)) 0.57/0.76 [14]~E(x141,x142)+E(f53(x143,x144,x145,x141),f53(x143,x144,x145,x142)) 0.57/0.76 [15]~E(x151,x152)+E(f41(x151,x153,x154),f41(x152,x153,x154)) 0.57/0.76 [16]~E(x161,x162)+E(f41(x163,x161,x164),f41(x163,x162,x164)) 0.57/0.76 [17]~E(x171,x172)+E(f41(x173,x174,x171),f41(x173,x174,x172)) 0.57/0.76 [18]~E(x181,x182)+E(f21(x181,x183),f21(x182,x183)) 0.57/0.76 [19]~E(x191,x192)+E(f21(x193,x191),f21(x193,x192)) 0.57/0.76 [20]~E(x201,x202)+E(f14(x201,x203),f14(x202,x203)) 0.57/0.76 [21]~E(x211,x212)+E(f14(x213,x211),f14(x213,x212)) 0.57/0.76 [22]~E(x221,x222)+E(f15(x221,x223,x224),f15(x222,x223,x224)) 0.57/0.76 [23]~E(x231,x232)+E(f15(x233,x231,x234),f15(x233,x232,x234)) 0.57/0.76 [24]~E(x241,x242)+E(f15(x243,x244,x241),f15(x243,x244,x242)) 0.57/0.76 [25]~E(x251,x252)+E(f42(x251,x253,x254),f42(x252,x253,x254)) 0.57/0.76 [26]~E(x261,x262)+E(f42(x263,x261,x264),f42(x263,x262,x264)) 0.57/0.76 [27]~E(x271,x272)+E(f42(x273,x274,x271),f42(x273,x274,x272)) 0.57/0.76 [28]~E(x281,x282)+E(f33(x281,x283,x284),f33(x282,x283,x284)) 0.57/0.76 [29]~E(x291,x292)+E(f33(x293,x291,x294),f33(x293,x292,x294)) 0.57/0.76 [30]~E(x301,x302)+E(f33(x303,x304,x301),f33(x303,x304,x302)) 0.57/0.76 [31]~E(x311,x312)+E(f35(x311,x313,x314),f35(x312,x313,x314)) 0.57/0.76 [32]~E(x321,x322)+E(f35(x323,x321,x324),f35(x323,x322,x324)) 0.57/0.76 [33]~E(x331,x332)+E(f35(x333,x334,x331),f35(x333,x334,x332)) 0.57/0.76 [34]~E(x341,x342)+E(f34(x341,x343,x344),f34(x342,x343,x344)) 0.57/0.76 [35]~E(x351,x352)+E(f34(x353,x351,x354),f34(x353,x352,x354)) 0.57/0.76 [36]~E(x361,x362)+E(f34(x363,x364,x361),f34(x363,x364,x362)) 0.57/0.76 [37]~E(x371,x372)+E(f32(x371,x373,x374),f32(x372,x373,x374)) 0.57/0.76 [38]~E(x381,x382)+E(f32(x383,x381,x384),f32(x383,x382,x384)) 0.57/0.76 [39]~E(x391,x392)+E(f32(x393,x394,x391),f32(x393,x394,x392)) 0.57/0.76 [40]~E(x401,x402)+E(f18(x401,x403),f18(x402,x403)) 0.57/0.76 [41]~E(x411,x412)+E(f18(x413,x411),f18(x413,x412)) 0.78/0.76 [42]~E(x421,x422)+E(f45(x421,x423,x424),f45(x422,x423,x424)) 0.78/0.76 [43]~E(x431,x432)+E(f45(x433,x431,x434),f45(x433,x432,x434)) 0.78/0.76 [44]~E(x441,x442)+E(f45(x443,x444,x441),f45(x443,x444,x442)) 0.78/0.76 [45]~E(x451,x452)+E(f46(x451,x453,x454),f46(x452,x453,x454)) 0.78/0.76 [46]~E(x461,x462)+E(f46(x463,x461,x464),f46(x463,x462,x464)) 0.78/0.76 [47]~E(x471,x472)+E(f46(x473,x474,x471),f46(x473,x474,x472)) 0.78/0.76 [48]~E(x481,x482)+E(f49(x481,x483,x484,x485),f49(x482,x483,x484,x485)) 0.78/0.76 [49]~E(x491,x492)+E(f49(x493,x491,x494,x495),f49(x493,x492,x494,x495)) 0.78/0.76 [50]~E(x501,x502)+E(f49(x503,x504,x501,x505),f49(x503,x504,x502,x505)) 0.78/0.76 [51]~E(x511,x512)+E(f49(x513,x514,x515,x511),f49(x513,x514,x515,x512)) 0.78/0.76 [52]~E(x521,x522)+E(f12(x521),f12(x522)) 0.78/0.76 [53]~E(x531,x532)+E(f52(x531,x533,x534,x535),f52(x532,x533,x534,x535)) 0.78/0.76 [54]~E(x541,x542)+E(f52(x543,x541,x544,x545),f52(x543,x542,x544,x545)) 0.78/0.76 [55]~E(x551,x552)+E(f52(x553,x554,x551,x555),f52(x553,x554,x552,x555)) 0.78/0.76 [56]~E(x561,x562)+E(f52(x563,x564,x565,x561),f52(x563,x564,x565,x562)) 0.78/0.76 [57]~E(x571,x572)+E(f43(x571,x573,x574),f43(x572,x573,x574)) 0.78/0.76 [58]~E(x581,x582)+E(f43(x583,x581,x584),f43(x583,x582,x584)) 0.78/0.76 [59]~E(x591,x592)+E(f43(x593,x594,x591),f43(x593,x594,x592)) 0.78/0.76 [60]~E(x601,x602)+E(f40(x601,x603,x604),f40(x602,x603,x604)) 0.78/0.76 [61]~E(x611,x612)+E(f40(x613,x611,x614),f40(x613,x612,x614)) 0.78/0.76 [62]~E(x621,x622)+E(f40(x623,x624,x621),f40(x623,x624,x622)) 0.78/0.76 [63]~E(x631,x632)+E(f22(x631,x633),f22(x632,x633)) 0.78/0.76 [64]~E(x641,x642)+E(f22(x643,x641),f22(x643,x642)) 0.78/0.76 [65]~E(x651,x652)+E(f54(x651,x653,x654,x655),f54(x652,x653,x654,x655)) 0.78/0.76 [66]~E(x661,x662)+E(f54(x663,x661,x664,x665),f54(x663,x662,x664,x665)) 0.78/0.76 [67]~E(x671,x672)+E(f54(x673,x674,x671,x675),f54(x673,x674,x672,x675)) 0.78/0.76 [68]~E(x681,x682)+E(f54(x683,x684,x685,x681),f54(x683,x684,x685,x682)) 0.78/0.76 [69]~E(x691,x692)+E(f58(x691,x693),f58(x692,x693)) 0.78/0.76 [70]~E(x701,x702)+E(f58(x703,x701),f58(x703,x702)) 0.78/0.76 [71]~E(x711,x712)+E(f10(x711,x713),f10(x712,x713)) 0.78/0.76 [72]~E(x721,x722)+E(f10(x723,x721),f10(x723,x722)) 0.78/0.76 [73]~E(x731,x732)+E(f47(x731,x733),f47(x732,x733)) 0.78/0.76 [74]~E(x741,x742)+E(f47(x743,x741),f47(x743,x742)) 0.78/0.76 [75]~E(x751,x752)+E(f48(x751,x753,x754),f48(x752,x753,x754)) 0.78/0.76 [76]~E(x761,x762)+E(f48(x763,x761,x764),f48(x763,x762,x764)) 0.78/0.76 [77]~E(x771,x772)+E(f48(x773,x774,x771),f48(x773,x774,x772)) 0.78/0.76 [78]~E(x781,x782)+E(f9(x781),f9(x782)) 0.78/0.76 [79]~E(x791,x792)+E(f37(x791,x793),f37(x792,x793)) 0.78/0.76 [80]~E(x801,x802)+E(f37(x803,x801),f37(x803,x802)) 0.78/0.76 [81]~E(x811,x812)+E(f39(x811,x813),f39(x812,x813)) 0.78/0.76 [82]~E(x821,x822)+E(f39(x823,x821),f39(x823,x822)) 0.78/0.76 [83]~E(x831,x832)+E(f55(x831,x833,x834),f55(x832,x833,x834)) 0.78/0.76 [84]~E(x841,x842)+E(f55(x843,x841,x844),f55(x843,x842,x844)) 0.78/0.76 [85]~E(x851,x852)+E(f55(x853,x854,x851),f55(x853,x854,x852)) 0.78/0.76 [86]~E(x861,x862)+E(f36(x861,x863,x864),f36(x862,x863,x864)) 0.78/0.76 [87]~E(x871,x872)+E(f36(x873,x871,x874),f36(x873,x872,x874)) 0.78/0.76 [88]~E(x881,x882)+E(f36(x883,x884,x881),f36(x883,x884,x882)) 0.78/0.76 [89]~E(x891,x892)+E(f38(x891,x893,x894,x895),f38(x892,x893,x894,x895)) 0.78/0.76 [90]~E(x901,x902)+E(f38(x903,x901,x904,x905),f38(x903,x902,x904,x905)) 0.78/0.76 [91]~E(x911,x912)+E(f38(x913,x914,x911,x915),f38(x913,x914,x912,x915)) 0.78/0.76 [92]~E(x921,x922)+E(f38(x923,x924,x925,x921),f38(x923,x924,x925,x922)) 0.78/0.76 [93]~E(x931,x932)+E(f50(x931,x933,x934),f50(x932,x933,x934)) 0.78/0.76 [94]~E(x941,x942)+E(f50(x943,x941,x944),f50(x943,x942,x944)) 0.78/0.76 [95]~E(x951,x952)+E(f50(x953,x954,x951),f50(x953,x954,x952)) 0.78/0.76 [96]~E(x961,x962)+E(f51(x961,x963,x964),f51(x962,x963,x964)) 0.78/0.76 [97]~E(x971,x972)+E(f51(x973,x971,x974),f51(x973,x972,x974)) 0.78/0.76 [98]~E(x981,x982)+E(f51(x983,x984,x981),f51(x983,x984,x982)) 0.78/0.76 [99]~E(x991,x992)+E(f29(x991,x993,x994),f29(x992,x993,x994)) 0.78/0.76 [100]~E(x1001,x1002)+E(f29(x1003,x1001,x1004),f29(x1003,x1002,x1004)) 0.78/0.76 [101]~E(x1011,x1012)+E(f29(x1013,x1014,x1011),f29(x1013,x1014,x1012)) 0.78/0.76 [102]~E(x1021,x1022)+E(f31(x1021,x1023,x1024),f31(x1022,x1023,x1024)) 0.78/0.76 [103]~E(x1031,x1032)+E(f31(x1033,x1031,x1034),f31(x1033,x1032,x1034)) 0.78/0.76 [104]~E(x1041,x1042)+E(f31(x1043,x1044,x1041),f31(x1043,x1044,x1042)) 0.78/0.76 [105]~E(x1051,x1052)+E(f30(x1051,x1053,x1054),f30(x1052,x1053,x1054)) 0.78/0.76 [106]~E(x1061,x1062)+E(f30(x1063,x1061,x1064),f30(x1063,x1062,x1064)) 0.78/0.76 [107]~E(x1071,x1072)+E(f30(x1073,x1074,x1071),f30(x1073,x1074,x1072)) 0.78/0.76 [108]~E(x1081,x1082)+E(f44(x1081,x1083),f44(x1082,x1083)) 0.78/0.76 [109]~E(x1091,x1092)+E(f44(x1093,x1091),f44(x1093,x1092)) 0.78/0.76 [110]~P1(x1101)+P1(x1102)+~E(x1101,x1102) 0.78/0.76 [111]P2(x1112,x1113,x1114)+~E(x1111,x1112)+~P2(x1111,x1113,x1114) 0.78/0.76 [112]P2(x1123,x1122,x1124)+~E(x1121,x1122)+~P2(x1123,x1121,x1124) 0.78/0.76 [113]P2(x1133,x1134,x1132)+~E(x1131,x1132)+~P2(x1133,x1134,x1131) 0.78/0.76 0.78/0.76 %------------------------------------------- 0.78/0.76 cnf(229,plain, 0.78/0.76 ($false), 0.78/0.76 inference(scs_inference,[],[121,129,224]), 0.78/0.76 ['proof']). 0.78/0.76 % SZS output end Proof 0.78/0.76 % Total time :0.000000s 0.78/0.78 EOF