%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM835+2 : 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 : n009.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 08:53:23 AM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : Proof 0.08s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM835+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ 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
% 0.08/0.36 % Computer : n009.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.37 % DateTime : Sat Sep 19 19:20:57 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.08/0.39 % SZS status Theorem for theBenchmark
% 0.08/0.39 % SZS output start Proof for theBenchmark
% 0.08/0.39 fof(dis(case_distinction(conseq(110))), conjecture,
% 0.08/0.39 ( ? [ Vd180 ] : vd165 = vplus(vd151, Vd180) | ? [ Vd170 ] : vd151 = vplus(vd165, Vd170) | vd151 = vd165 ),
% 0.08/0.39 file('theBenchmark.p', dis(case_distinction(conseq(110)))) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 2), 0), axiom,
% 0.08/0.39 ! [ Vd180 ] : ( vd165 = vplus(vd151, Vd180) => m(vsucc(vd165)) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 2), 0)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 2), 1), axiom,
% 0.08/0.39 ! [ Vd180 ] : ( vd165 = vplus(vd151, Vd180) => vsucc(vplus(vd151, Vd180)) = vplus(vd151, vsucc(Vd180)) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 2), 1)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 2), 2), axiom,
% 0.08/0.39 ! [ Vd180 ] : ( vd165 = vplus(vd151, Vd180) => vsucc(vd165) = vsucc(vplus(vd151, Vd180)) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 2), 2)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 1), 0), axiom,
% 0.08/0.39 ! [ Vd170 ] : ( vd151 = vplus(vd165, Vd170) => ( ~( Vd170 = v1 ) => m(vsucc(vd165)) ) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 1), 0)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 1), 1), axiom,
% 0.08/0.39 ! [ Vd170 ] : ( vd151 = vplus(vd165, Vd170) => ( ~( Vd170 = v1 ) => vplus(vplus(vd165, v1), vskolem3) = vplus(vsucc(vd165), vskolem3) ) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 1), 1)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 1), 2), axiom,
% 0.08/0.39 ! [ Vd170 ] : ( vd151 = vplus(vd165, Vd170) => ( ~( Vd170 = v1 ) => vplus(vd165, vplus(v1, vskolem3)) = vplus(vplus(vd165, v1), vskolem3) ) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 1), 2)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 1), 3), axiom,
% 0.08/0.39 ! [ Vd170 ] : ( vd151 = vplus(vd165, Vd170) => ( ~( Vd170 = v1 ) => vd151 = vplus(vd165, vplus(v1, vskolem3)) ) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 1), 3)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 1), 4), axiom,
% 0.08/0.39 ! [ Vd170 ] : ( vd151 = vplus(vd165, Vd170) => ( ~( Vd170 = v1 ) => vsucc(vskolem3) = vplus(v1, vskolem3) ) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 1), 4)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 1), 5), axiom,
% 0.08/0.39 ! [ Vd170 ] : ( vd151 = vplus(vd165, Vd170) => ( ~( Vd170 = v1 ) => Vd170 = vsucc(vskolem3) ) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 1), 5)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 1), 6), axiom,
% 0.08/0.39 ! [ Vd170 ] : ( vd151 = vplus(vd165, Vd170) => ( Vd170 = v1 => m(vsucc(vd165)) ) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 1), 6)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 1), 7), axiom,
% 0.08/0.39 ! [ Vd170 ] : ( vd151 = vplus(vd165, Vd170) => ( Vd170 = v1 => vplus(vd165, v1) = vsucc(vd165) ) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 1), 7)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 1), 8), axiom,
% 0.08/0.39 ! [ Vd170 ] : ( vd151 = vplus(vd165, Vd170) => ( Vd170 = v1 => vd151 = vplus(vd165, v1) ) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 1), 8)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 0), 0), axiom,
% 0.08/0.39 ( vd151 = vd165 => m(vsucc(vd165)) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 0), 0)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 0), 1), axiom,
% 0.08/0.39 ( vd151 = vd165 => vplus(vd165, v1) = vplus(vd151, v1) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 0), 1)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(conseq(110), 0), 2), axiom,
% 0.08/0.39 ( vd151 = vd165 => vsucc(vd165) = vplus(vd165, v1) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(conseq(110), 0), 2)) ).
% 0.08/0.39
% 0.08/0.39 fof(def(cond(conseq(105), 0), 1), axiom,
% 0.08/0.39 ! [ Vd151,Vd152 ] : ( m(Vd152) <=> ( Vd151 = Vd152 | ? [ Vd155 ] : Vd151 = vplus(Vd152, Vd155) | ? [ Vd157 ] : Vd152 = vplus(Vd151, Vd157) ) ),
% 0.08/0.39 file('theBenchmark.p', def(cond(conseq(105), 0), 1)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(61, 0), 0), axiom,
% 0.08/0.39 ! [ Vd78,Vd79 ] : vplus(Vd79, Vd78) = vplus(Vd78, Vd79),
% 0.08/0.39 file('theBenchmark.p', ass(cond(61, 0), 0)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(52, 0), 0), axiom,
% 0.08/0.39 ! [ Vd68,Vd69 ] : vplus(vsucc(Vd68), Vd69) = vsucc(vplus(Vd68, Vd69)),
% 0.08/0.39 file('theBenchmark.p', ass(cond(52, 0), 0)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(43, 0), 0), axiom,
% 0.08/0.39 ! [ Vd59 ] : vplus(v1, Vd59) = vsucc(Vd59),
% 0.08/0.39 file('theBenchmark.p', ass(cond(43, 0), 0)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(33, 0), 0), axiom,
% 0.08/0.39 ! [ Vd46,Vd47,Vd48 ] : vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)),
% 0.08/0.39 file('theBenchmark.p', ass(cond(33, 0), 0)) ).
% 0.08/0.39
% 0.08/0.39 fof(qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0))), axiom,
% 0.08/0.39 ! [ Vd42,Vd43 ] : ( vplus(Vd42, vsucc(Vd43)) = vsucc(vplus(Vd42, Vd43)) & vplus(Vd42, v1) = vsucc(Vd42) ),
% 0.08/0.39 file('theBenchmark.p', qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(20, 0), 0), axiom,
% 0.08/0.39 ! [ Vd24 ] : ( ~( Vd24 = v1 ) => Vd24 = vsucc(vskolem2(Vd24)) ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(20, 0), 0)) ).
% 0.08/0.39
% 0.08/0.39 fof(ass(cond(12, 0), 0), axiom,
% 0.08/0.39 ! [ Vd16 ] : ~( vsucc(Vd16) = Vd16 ),
% 0.08/0.39 file('theBenchmark.p', ass(cond(12, 0), 0)) ).
% 0.08/0.39
% 0.08/0.39 fof(f_1_1, negated_conjecture,
% 0.08/0.39 ~( ( ? [ Vd180 ] : vd165 = vplus(vd151, Vd180) | ? [ Vd170 ] : vd151 = vplus(vd165, Vd170) | vd151 = vd165 ) ),
% 0.08/0.39 inference(negate,[status(cth)],[dis(case_distinction(conseq(110)))]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_1_2, negated_conjecture,
% 0.08/0.39 ( ! [ Vd180 ] : ~( vd165 = vplus(vd151, Vd180) ) & ! [ Vd170 ] : ~( vd151 = vplus(vd165, Vd170) ) & ~( vd151 = vd165 ) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[f_1_1]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_1_3, negated_conjecture,
% 0.08/0.39 ( ! [ U_0 ] : ~( vd165 = vplus(vd151, U_0) ) & ! [ U_1 ] : ~( vd151 = vplus(vd165, U_1) ) & ~( vd151 = vd165 ) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_1_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_1_4, negated_conjecture,
% 0.08/0.39 ( ( ! [U_0] : ( vd165 != vplus(vd151, U_0) ) ) & ( ! [U_1] : ( vd151 != vplus(vd165, U_1) ) ) & ( ( vd151 != vd165 ) ) ),
% 0.08/0.39 inference(definitional_conversion,[status(esa)],[f_1_3]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_1_5, negated_conjecture,
% 0.08/0.39 ( vd165 != vplus(vd151, U_0) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_1_4]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_1_6, negated_conjecture,
% 0.08/0.39 ( vd151 != vplus(vd165, U_1) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_1_4]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_1_7, negated_conjecture,
% 0.08/0.39 ( vd151 != vd165 ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_1_4]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_2_1, plain,
% 0.08/0.39 ! [ Vd180 ] : ( ~( vd165 = vplus(vd151, Vd180) ) | m(vsucc(vd165)) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 2), 0)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_2_2, plain,
% 0.08/0.39 ! [ U_2 ] : ( ~( vd165 = vplus(vd151, U_2) ) | m(vsucc(vd165)) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_2_1]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_2_3, plain,
% 0.08/0.39 ( m(vsucc(vd165)) | ! [ U_2 ] : ~( vd165 = vplus(vd151, U_2) ) ),
% 0.08/0.39 inference(miniscope,[status(thm)],[f_2_2]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_2_4, plain,
% 0.08/0.39 ( m(vsucc(vd165)) | vd165 != vplus(vd151, U_2) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_2_3]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_3_1, plain,
% 0.08/0.39 ! [ Vd180 ] : ( ~( vd165 = vplus(vd151, Vd180) ) | vsucc(vplus(vd151, Vd180)) = vplus(vd151, vsucc(Vd180)) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 2), 1)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_3_2, plain,
% 0.08/0.39 ! [ U_3 ] : ( ~( vd165 = vplus(vd151, U_3) ) | vsucc(vplus(vd151, U_3)) = vplus(vd151, vsucc(U_3)) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_3_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_3_3, plain,
% 0.08/0.39 ( vd165 != vplus(vd151, U_3) | vsucc(vplus(vd151, U_3)) = vplus(vd151, vsucc(U_3)) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_3_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_4_1, plain,
% 0.08/0.39 ! [ Vd180 ] : ( ~( vd165 = vplus(vd151, Vd180) ) | vsucc(vd165) = vsucc(vplus(vd151, Vd180)) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 2), 2)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_4_2, plain,
% 0.08/0.39 ! [ U_4 ] : ( ~( vd165 = vplus(vd151, U_4) ) | vsucc(vd165) = vsucc(vplus(vd151, U_4)) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_4_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_4_3, plain,
% 0.08/0.39 ( vd165 != vplus(vd151, U_4) | vsucc(vd165) = vsucc(vplus(vd151, U_4)) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_4_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_5_1, plain,
% 0.08/0.39 ! [ Vd170 ] : ( ~( vd151 = vplus(vd165, Vd170) ) | ( Vd170 = v1 | m(vsucc(vd165)) ) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 1), 0)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_5_2, plain,
% 0.08/0.39 ! [ U_5 ] : ( ~( vd151 = vplus(vd165, U_5) ) | ( U_5 = v1 | m(vsucc(vd165)) ) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_5_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_5_3, plain,
% 0.08/0.39 ( vd151 != vplus(vd165, U_5) | U_5 = v1 | m(vsucc(vd165)) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_5_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_6_1, plain,
% 0.08/0.39 ! [ Vd170 ] : ( ~( vd151 = vplus(vd165, Vd170) ) | ( Vd170 = v1 | vplus(vplus(vd165, v1), vskolem3) = vplus(vsucc(vd165), vskolem3) ) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 1), 1)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_6_2, plain,
% 0.08/0.39 ! [ U_6 ] : ( ~( vd151 = vplus(vd165, U_6) ) | ( U_6 = v1 | vplus(vplus(vd165, v1), vskolem3) = vplus(vsucc(vd165), vskolem3) ) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_6_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_6_3, plain,
% 0.08/0.39 ( vd151 != vplus(vd165, U_6) | U_6 = v1 | vplus(vplus(vd165, v1), vskolem3) = vplus(vsucc(vd165), vskolem3) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_6_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_7_1, plain,
% 0.08/0.39 ! [ Vd170 ] : ( ~( vd151 = vplus(vd165, Vd170) ) | ( Vd170 = v1 | vplus(vd165, vplus(v1, vskolem3)) = vplus(vplus(vd165, v1), vskolem3) ) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 1), 2)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_7_2, plain,
% 0.08/0.39 ! [ U_7 ] : ( ~( vd151 = vplus(vd165, U_7) ) | ( U_7 = v1 | vplus(vd165, vplus(v1, vskolem3)) = vplus(vplus(vd165, v1), vskolem3) ) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_7_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_7_3, plain,
% 0.08/0.39 ( vd151 != vplus(vd165, U_7) | U_7 = v1 | vplus(vd165, vplus(v1, vskolem3)) = vplus(vplus(vd165, v1), vskolem3) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_7_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_8_1, plain,
% 0.08/0.39 ! [ Vd170 ] : ( ~( vd151 = vplus(vd165, Vd170) ) | ( Vd170 = v1 | vd151 = vplus(vd165, vplus(v1, vskolem3)) ) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 1), 3)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_8_2, plain,
% 0.08/0.39 ! [ U_8 ] : ( ~( vd151 = vplus(vd165, U_8) ) | ( U_8 = v1 | vd151 = vplus(vd165, vplus(v1, vskolem3)) ) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_8_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_8_3, plain,
% 0.08/0.39 ( vd151 != vplus(vd165, U_8) | U_8 = v1 | vd151 = vplus(vd165, vplus(v1, vskolem3)) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_8_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_9_1, plain,
% 0.08/0.39 ! [ Vd170 ] : ( ~( vd151 = vplus(vd165, Vd170) ) | ( Vd170 = v1 | vsucc(vskolem3) = vplus(v1, vskolem3) ) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 1), 4)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_9_2, plain,
% 0.08/0.39 ! [ U_9 ] : ( ~( vd151 = vplus(vd165, U_9) ) | ( U_9 = v1 | vsucc(vskolem3) = vplus(v1, vskolem3) ) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_9_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_9_3, plain,
% 0.08/0.39 ( vd151 != vplus(vd165, U_9) | U_9 = v1 | vsucc(vskolem3) = vplus(v1, vskolem3) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_9_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_10_1, plain,
% 0.08/0.39 ! [ Vd170 ] : ( ~( vd151 = vplus(vd165, Vd170) ) | ( Vd170 = v1 | Vd170 = vsucc(vskolem3) ) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 1), 5)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_10_2, plain,
% 0.08/0.39 ! [ U_10 ] : ( ~( vd151 = vplus(vd165, U_10) ) | ( U_10 = v1 | U_10 = vsucc(vskolem3) ) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_10_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_10_3, plain,
% 0.08/0.39 ( vd151 != vplus(vd165, U_10) | U_10 = v1 | U_10 = vsucc(vskolem3) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_10_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_11_1, plain,
% 0.08/0.39 ! [ Vd170 ] : ( ~( vd151 = vplus(vd165, Vd170) ) | ( ~( Vd170 = v1 ) | m(vsucc(vd165)) ) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 1), 6)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_11_2, plain,
% 0.08/0.39 ! [ U_11 ] : ( ~( vd151 = vplus(vd165, U_11) ) | ( ~( U_11 = v1 ) | m(vsucc(vd165)) ) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_11_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_11_3, plain,
% 0.08/0.39 ( vd151 != vplus(vd165, U_11) | U_11 != v1 | m(vsucc(vd165)) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_11_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_12_1, plain,
% 0.08/0.39 ! [ Vd170 ] : ( ~( vd151 = vplus(vd165, Vd170) ) | ( ~( Vd170 = v1 ) | vplus(vd165, v1) = vsucc(vd165) ) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 1), 7)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_12_2, plain,
% 0.08/0.39 ! [ U_12 ] : ( ~( vd151 = vplus(vd165, U_12) ) | ( ~( U_12 = v1 ) | vplus(vd165, v1) = vsucc(vd165) ) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_12_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_12_3, plain,
% 0.08/0.39 ( vd151 != vplus(vd165, U_12) | U_12 != v1 | vplus(vd165, v1) = vsucc(vd165) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_12_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_13_1, plain,
% 0.08/0.39 ! [ Vd170 ] : ( ~( vd151 = vplus(vd165, Vd170) ) | ( ~( Vd170 = v1 ) | vd151 = vplus(vd165, v1) ) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 1), 8)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_13_2, plain,
% 0.08/0.39 ! [ U_13 ] : ( ~( vd151 = vplus(vd165, U_13) ) | ( ~( U_13 = v1 ) | vd151 = vplus(vd165, v1) ) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_13_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_13_3, plain,
% 0.08/0.39 ( vd151 != vplus(vd165, U_13) | U_13 != v1 | vd151 = vplus(vd165, v1) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_13_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_14_1, plain,
% 0.08/0.39 ( ~( vd151 = vd165 ) | m(vsucc(vd165)) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 0), 0)]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_14_2, plain,
% 0.08/0.39 ( vd151 != vd165 | m(vsucc(vd165)) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_14_1]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_15_1, plain,
% 0.08/0.39 ( ~( vd151 = vd165 ) | vplus(vd165, v1) = vplus(vd151, v1) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 0), 1)]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_15_2, plain,
% 0.08/0.39 ( vd151 != vd165 | vplus(vd165, v1) = vplus(vd151, v1) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_15_1]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_16_1, plain,
% 0.08/0.39 ( ~( vd151 = vd165 ) | vsucc(vd165) = vplus(vd165, v1) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(conseq(110), 0), 2)]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_16_2, plain,
% 0.08/0.39 ( vd151 != vd165 | vsucc(vd165) = vplus(vd165, v1) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_16_1]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_17_1, plain,
% 0.08/0.39 ! [ Vd151,Vd152 ] : ( ( ~( m(Vd152) ) | ( Vd151 = Vd152 | ? [ Vd155 ] : Vd151 = vplus(Vd152, Vd155) | ? [ Vd157 ] : Vd152 = vplus(Vd151, Vd157) ) ) & ( ( ~( Vd151 = Vd152 ) & ! [ Vd155 ] : ~( Vd151 = vplus(Vd152, Vd155) ) & ! [ Vd157 ] : ~( Vd152 = vplus(Vd151, Vd157) ) ) | m(Vd152) ) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[def(cond(conseq(105), 0), 1)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_17_2, plain,
% 0.08/0.39 ! [ U_19,U_18 ] : ( ( ~( m(U_18) ) | ( U_19 = U_18 | ? [ U_14 ] : U_19 = vplus(U_18, U_14) | ? [ U_15 ] : U_18 = vplus(U_19, U_15) ) ) & ( ( ~( U_19 = U_18 ) & ! [ U_16 ] : ~( U_19 = vplus(U_18, U_16) ) & ! [ U_17 ] : ~( U_18 = vplus(U_19, U_17) ) ) | m(U_18) ) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_17_1]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_17_3, plain,
% 0.08/0.39 ( ! [ U_22,U_20 ] : ( ~( m(U_20) ) | ( U_22 = U_20 | ? [ U_14 ] : U_22 = vplus(U_20, U_14) | ? [ U_15 ] : U_20 = vplus(U_22, U_15) ) ) & ! [ U_23,U_21 ] : ( ( ~( U_23 = U_21 ) & ! [ U_16 ] : ~( U_23 = vplus(U_21, U_16) ) & ! [ U_17 ] : ~( U_21 = vplus(U_23, U_17) ) ) | m(U_21) ) ),
% 0.08/0.39 inference(miniscope,[status(thm)],[f_17_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_17_4, plain,
% 0.08/0.39 ( ! [ U_22,U_20 ] : ( ~( m(U_20) ) | ( U_22 = U_20 | U_22 = vplus(U_20, sK1(U_22, U_20)) | ? [ U_15 ] : U_20 = vplus(U_22, U_15) ) ) & ! [ U_23,U_21 ] : ( ( ~( U_23 = U_21 ) & ! [ U_16 ] : ~( U_23 = vplus(U_21, U_16) ) & ! [ U_17 ] : ~( U_21 = vplus(U_23, U_17) ) ) | m(U_21) ) ),
% 0.08/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_14,sK1(U_22, U_20))],[f_17_3]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_17_5, plain,
% 0.08/0.39 ( ! [ U_22,U_20 ] : ( ~( m(U_20) ) | ( U_22 = U_20 | U_22 = vplus(U_20, sK1(U_22, U_20)) | U_20 = vplus(U_22, sK2(U_22, U_20)) ) ) & ! [ U_23,U_21 ] : ( ( ~( U_23 = U_21 ) & ! [ U_16 ] : ~( U_23 = vplus(U_21, U_16) ) & ! [ U_17 ] : ~( U_21 = vplus(U_23, U_17) ) ) | m(U_21) ) ),
% 0.08/0.39 inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_15,sK2(U_22, U_20))],[f_17_4]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_17_6, plain,
% 0.08/0.39 ( ~m(U_20) | U_22 = U_20 | U_22 = vplus(U_20, sK1(U_22, U_20)) | U_20 = vplus(U_22, sK2(U_22, U_20)) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_17_5]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_17_7, plain,
% 0.08/0.39 ( m(U_21) | U_23 != U_21 ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_17_5]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_17_8, plain,
% 0.08/0.39 ( m(U_21) | U_23 != vplus(U_21, U_16) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_17_5]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_17_9, plain,
% 0.08/0.39 ( m(U_21) | U_21 != vplus(U_23, U_17) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_17_5]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_18_1, plain,
% 0.08/0.39 ! [ Vd78,Vd79 ] : vplus(Vd79, Vd78) = vplus(Vd78, Vd79),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(61, 0), 0)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_18_2, plain,
% 0.08/0.39 ! [ U_25,U_24 ] : vplus(U_24, U_25) = vplus(U_25, U_24),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_18_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_18_3, plain,
% 0.08/0.39 ( vplus(U_24, U_25) = vplus(U_25, U_24) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_18_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_19_1, plain,
% 0.08/0.39 ! [ Vd68,Vd69 ] : vplus(vsucc(Vd68), Vd69) = vsucc(vplus(Vd68, Vd69)),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(52, 0), 0)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_19_2, plain,
% 0.08/0.39 ! [ U_27,U_26 ] : vplus(vsucc(U_27), U_26) = vsucc(vplus(U_27, U_26)),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_19_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_19_3, plain,
% 0.08/0.39 ( vplus(vsucc(U_27), U_26) = vsucc(vplus(U_27, U_26)) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_19_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_20_1, plain,
% 0.08/0.39 ! [ Vd59 ] : vplus(v1, Vd59) = vsucc(Vd59),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(43, 0), 0)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_20_2, plain,
% 0.08/0.39 ! [ U_28 ] : vplus(v1, U_28) = vsucc(U_28),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_20_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_20_3, plain,
% 0.08/0.39 ( vplus(v1, U_28) = vsucc(U_28) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_20_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_21_1, plain,
% 0.08/0.39 ! [ Vd46,Vd47,Vd48 ] : vplus(vplus(Vd46, Vd47), Vd48) = vplus(Vd46, vplus(Vd47, Vd48)),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(33, 0), 0)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_21_2, plain,
% 0.08/0.39 ! [ U_31,U_30,U_29 ] : vplus(vplus(U_31, U_30), U_29) = vplus(U_31, vplus(U_30, U_29)),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_21_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_21_3, plain,
% 0.08/0.39 ( vplus(vplus(U_31, U_30), U_29) = vplus(U_31, vplus(U_30, U_29)) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_21_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_22_1, plain,
% 0.08/0.39 ! [ Vd42,Vd43 ] : ( vplus(Vd42, vsucc(Vd43)) = vsucc(vplus(Vd42, Vd43)) & vplus(Vd42, v1) = vsucc(Vd42) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_22_2, plain,
% 0.08/0.39 ! [ U_33,U_32 ] : ( vplus(U_33, vsucc(U_32)) = vsucc(vplus(U_33, U_32)) & vplus(U_33, v1) = vsucc(U_33) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_22_1]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_22_3, plain,
% 0.08/0.39 ( ! [ U_34 ] : vplus(U_34, v1) = vsucc(U_34) & ! [ U_35,U_32 ] : vplus(U_35, vsucc(U_32)) = vsucc(vplus(U_35, U_32)) ),
% 0.08/0.39 inference(miniscope,[status(thm)],[f_22_2]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_22_4, plain,
% 0.08/0.39 ( vplus(U_34, v1) = vsucc(U_34) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_22_3]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_22_5, plain,
% 0.08/0.39 ( vplus(U_35, vsucc(U_32)) = vsucc(vplus(U_35, U_32)) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_22_3]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_23_1, plain,
% 0.08/0.39 ! [ Vd24 ] : ( Vd24 = v1 | Vd24 = vsucc(vskolem2(Vd24)) ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(20, 0), 0)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_23_2, plain,
% 0.08/0.39 ! [ U_36 ] : ( U_36 = v1 | U_36 = vsucc(vskolem2(U_36)) ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_23_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_23_3, plain,
% 0.08/0.39 ( U_36 = v1 | U_36 = vsucc(vskolem2(U_36)) ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_23_2]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_24_1, plain,
% 0.08/0.39 ! [ Vd16 ] : ~( vsucc(Vd16) = Vd16 ),
% 0.08/0.39 inference(fof_nnf,[status(thm)],[ass(cond(12, 0), 0)]) ).
% 0.08/0.39
% 0.08/0.39 fof(f_24_2, plain,
% 0.08/0.39 ! [ U_37 ] : ~( vsucc(U_37) = U_37 ),
% 0.08/0.39 inference(variable_rename,[status(thm)],[f_24_1]) ).
% 0.08/0.39
% 0.08/0.39 cnf(f_24_3, plain,
% 0.08/0.39 ( vsucc(U_37) != U_37 ),
% 0.08/0.39 inference(clausify,[status(thm)],[f_24_2]) ).
% 0.08/0.39
% 0.08/0.39 cnf(equality_1, axiom,
% 0.08/0.39 ( Eq_x_0 = Eq_x_0 ),
% 0.08/0.39 theory(equality,[reflexivity]) ).
% 0.08/0.39
% 0.08/0.39 cnf(equality_2, axiom,
% 0.08/0.39 ( Eq_x_0 != Eq_x_1 | Eq_x_1 = Eq_x_0 ),
% 0.08/0.39 theory(equality,[symmetry]) ).
% 0.08/0.39
% 0.08/0.39 cnf(equality_3, axiom,
% 0.08/0.39 ( Eq_x_0 != Eq_x_1 | Eq_x_1 != Eq_x_2 | Eq_x_0 = Eq_x_2 ),
% 0.08/0.39 theory(equality,[transitivity]) ).
% 0.08/0.39
% 0.08/0.39 cnf(equality_4, axiom,
% 0.08/0.39 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | vplus(Eq_x_0, Eq_x_1) = vplus(Eq_y_0, Eq_y_1) ),
% 0.08/0.39 theory(equality,[substitution_functions]) ).
% 0.08/0.39
% 0.08/0.39 cnf(equality_5, axiom,
% 0.08/0.39 ( Eq_x_0 != Eq_y_0 | vsucc(Eq_x_0) = vsucc(Eq_y_0) ),
% 0.08/0.39 theory(equality,[substitution_functions]) ).
% 0.08/0.39
% 0.08/0.39 cnf(equality_6, axiom,
% 0.08/0.39 ( Eq_x_0 != Eq_y_0 | vskolem2(Eq_x_0) = vskolem2(Eq_y_0) ),
% 0.08/0.39 theory(equality,[substitution_functions]) ).
% 0.08/0.39
% 0.08/0.39 cnf(equality_7, axiom,
% 0.08/0.39 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | sK1(Eq_x_0, Eq_x_1) = sK1(Eq_y_0, Eq_y_1) ),
% 0.08/0.39 theory(equality,[substitution_functions]) ).
% 0.08/0.39
% 0.08/0.39 cnf(equality_8, axiom,
% 0.08/0.39 ( Eq_x_0 != Eq_y_0 | Eq_x_1 != Eq_y_1 | sK2(Eq_x_0, Eq_x_1) = sK2(Eq_y_0, Eq_y_1) ),
% 0.08/0.39 theory(equality,[substitution_functions]) ).
% 0.08/0.39
% 0.08/0.39 cnf(equality_9, axiom,
% 0.08/0.39 ( Eq_x_0 != Eq_y_0 | ~m(Eq_x_0) | m(Eq_y_0) ),
% 0.08/0.39 theory(equality,[substitution_predicates]) ).
% 0.08/0.39
% 0.08/0.39 cnf(sat_proved, plain, $false,
% 0.08/0.39 inference(cadical, [status(thm)], [
% 0.08/0.39 ]) ).
% 0.08/0.39 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------