%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM835+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 : 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 : Thu Sep 24 08:53:23 AM UTC 2026
% Result : Theorem 0.14s 15.44s
% Output : Proof 0.14s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM835+1 : 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
% 0.10/15.37 % Computer : n002.cluster.edu
% 0.10/15.37 % Model : x86_64 x86_64
% 0.10/15.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/15.37 % Memory : 8046.5625MB
% 0.10/15.37 % OS : Linux 6.8.0-71-generic
% 0.10/15.37 % CPULimit : 300
% 0.10/15.37 % WCLimit : 300
% 0.10/15.37 % DateTime : Sat Sep 19 19:23:47 UTC 2026
% 0.10/15.38 % CPUTime :
% 0.14/15.44 % SZS status Theorem for theBenchmark
% 0.14/15.44 % SZS output start Proof for theBenchmark
% 0.14/15.44 fof(dis(case_distinction(conseq(110))), conjecture,
% 0.14/15.44 ( ? [ Vd180 ] : vd165 = vplus(vd151, Vd180) | ? [ Vd170 ] : vd151 = vplus(vd165, Vd170) | vd151 = vd165 ),
% 0.14/15.44 file('theBenchmark.p', dis(case_distinction(conseq(110)))) ).
% 0.14/15.44
% 0.14/15.44 fof(holds(110, 166, 0), axiom,
% 0.14/15.44 m(vd165),
% 0.14/15.44 file('theBenchmark.p', holds(110, 166, 0)) ).
% 0.14/15.44
% 0.14/15.44 fof(def(cond(conseq(105), 0), 1), axiom,
% 0.14/15.44 ! [ Vd151,Vd152 ] : ( m(Vd152) <=> ( Vd151 = Vd152 | ? [ Vd155 ] : Vd151 = vplus(Vd152, Vd155) | ? [ Vd157 ] : Vd152 = vplus(Vd151, Vd157) ) ),
% 0.14/15.44 file('theBenchmark.p', def(cond(conseq(105), 0), 1)) ).
% 0.14/15.44
% 0.14/15.44 fof(f_1_1, negated_conjecture,
% 0.14/15.44 ~( ( ? [ Vd180 ] : vd165 = vplus(vd151, Vd180) | ? [ Vd170 ] : vd151 = vplus(vd165, Vd170) | vd151 = vd165 ) ),
% 0.14/15.44 inference(negate,[status(cth)],[dis(case_distinction(conseq(110)))]) ).
% 0.14/15.44
% 0.14/15.44 fof(f_1_2, negated_conjecture,
% 0.14/15.44 ( ! [ Vd180 ] : ~( vd165 = vplus(vd151, Vd180) ) & ! [ Vd170 ] : ~( vd151 = vplus(vd165, Vd170) ) & ~( vd151 = vd165 ) ),
% 0.14/15.44 inference(fof_nnf,[status(thm)],[f_1_1]) ).
% 0.14/15.44
% 0.14/15.44 fof(f_1_3, negated_conjecture,
% 0.14/15.44 ( ! [ U_0 ] : ~( vd165 = vplus(vd151, U_0) ) & ! [ U_1 ] : ~( vd151 = vplus(vd165, U_1) ) & ~( vd151 = vd165 ) ),
% 0.14/15.44 inference(variable_rename,[status(thm)],[f_1_2]) ).
% 0.14/15.44
% 0.14/15.44 fof(f_1_4, negated_conjecture,
% 0.14/15.44 ( ( ! [U_0] : ( vd165 != vplus(vd151, U_0) ) ) & ( ! [U_1] : ( vd151 != vplus(vd165, U_1) ) ) & ( ( vd151 != vd165 ) ) ),
% 0.14/15.44 inference(definitional_conversion,[status(esa)],[f_1_3]) ).
% 0.14/15.44
% 0.14/15.44 cnf(f_1_5, negated_conjecture,
% 0.14/15.44 ( vd165 != vplus(vd151, U_0) ),
% 0.14/15.44 inference(clausify,[status(thm)],[f_1_4]) ).
% 0.14/15.44
% 0.14/15.44 cnf(f_1_6, negated_conjecture,
% 0.14/15.44 ( vd151 != vplus(vd165, U_1) ),
% 0.14/15.44 inference(clausify,[status(thm)],[f_1_4]) ).
% 0.14/15.44
% 0.14/15.44 cnf(f_1_7, negated_conjecture,
% 0.14/15.44 ( vd151 != vd165 ),
% 0.14/15.44 inference(clausify,[status(thm)],[f_1_4]) ).
% 0.14/15.44
% 0.14/15.44 fof(f_17_1, plain,
% 0.14/15.44 m(vd165),
% 0.14/15.44 inference(fof_nnf,[status(thm)],[holds(110, 166, 0)]) ).
% 0.14/15.44
% 0.14/15.44 cnf(f_17_2, plain,
% 0.14/15.44 ( m(vd165) ),
% 0.14/15.44 inference(clausify,[status(thm)],[f_17_1]) ).
% 0.14/15.44
% 0.14/15.44 fof(f_20_1, plain,
% 0.14/15.44 ! [ 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) ) ),
% 0.14/15.44 inference(fof_nnf,[status(thm)],[def(cond(conseq(105), 0), 1)]) ).
% 0.14/15.44
% 0.14/15.44 fof(f_20_2, plain,
% 0.14/15.44 ! [ U_21,U_20 ] : ( ( ~( m(U_20) ) | ( U_21 = U_20 | ? [ U_16 ] : U_21 = vplus(U_20, U_16) | ? [ U_17 ] : U_20 = vplus(U_21, U_17) ) ) & ( ( ~( U_21 = U_20 ) & ! [ U_18 ] : ~( U_21 = vplus(U_20, U_18) ) & ! [ U_19 ] : ~( U_20 = vplus(U_21, U_19) ) ) | m(U_20) ) ),
% 0.14/15.44 inference(variable_rename,[status(thm)],[f_20_1]) ).
% 0.14/15.44
% 0.14/15.44 fof(f_20_3, plain,
% 0.14/15.44 ( ! [ U_24,U_22 ] : ( ~( m(U_22) ) | ( U_24 = U_22 | ? [ U_16 ] : U_24 = vplus(U_22, U_16) | ? [ U_17 ] : U_22 = vplus(U_24, U_17) ) ) & ! [ U_25,U_23 ] : ( ( ~( U_25 = U_23 ) & ! [ U_18 ] : ~( U_25 = vplus(U_23, U_18) ) & ! [ U_19 ] : ~( U_23 = vplus(U_25, U_19) ) ) | m(U_23) ) ),
% 0.14/15.44 inference(miniscope,[status(thm)],[f_20_2]) ).
% 0.14/15.44
% 0.14/15.44 fof(f_20_4, plain,
% 0.14/15.44 ( ! [ U_24,U_22 ] : ( ~( m(U_22) ) | ( U_24 = U_22 | U_24 = vplus(U_22, sK2(U_24, U_22)) | ? [ U_17 ] : U_22 = vplus(U_24, U_17) ) ) & ! [ U_25,U_23 ] : ( ( ~( U_25 = U_23 ) & ! [ U_18 ] : ~( U_25 = vplus(U_23, U_18) ) & ! [ U_19 ] : ~( U_23 = vplus(U_25, U_19) ) ) | m(U_23) ) ),
% 0.14/15.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_16,sK2(U_24, U_22))],[f_20_3]) ).
% 0.14/15.44
% 0.14/15.44 fof(f_20_5, plain,
% 0.14/15.44 ( ! [ U_24,U_22 ] : ( ~( m(U_22) ) | ( U_24 = U_22 | U_24 = vplus(U_22, sK2(U_24, U_22)) | U_22 = vplus(U_24, sK3(U_24, U_22)) ) ) & ! [ U_25,U_23 ] : ( ( ~( U_25 = U_23 ) & ! [ U_18 ] : ~( U_25 = vplus(U_23, U_18) ) & ! [ U_19 ] : ~( U_23 = vplus(U_25, U_19) ) ) | m(U_23) ) ),
% 0.14/15.44 inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_17,sK3(U_24, U_22))],[f_20_4]) ).
% 0.14/15.44
% 0.14/15.44 cnf(f_20_6, plain,
% 0.14/15.44 ( ~m(U_22) | U_24 = U_22 | U_24 = vplus(U_22, sK2(U_24, U_22)) | U_22 = vplus(U_24, sK3(U_24, U_22)) ),
% 0.14/15.44 inference(clausify,[status(thm)],[f_20_5]) ).
% 0.14/15.44
% 0.14/15.44 cnf(t1, plain, ( vd165 != vplus(vd151, sK3(vd151, vd165)) ),
% 0.14/15.44 inference(start, [status(thm), parent(0:0)], [f_1_5]) ).
% 0.14/15.44
% 0.14/15.44 cnf(t2, plain, ( vd165 = vplus(vd151, sK3(vd151, vd165)) | ~m(vd165) | vd151 = vplus(vd165, sK2(vd151, vd165)) | vd151 = vd165 ),
% 0.14/15.44 inference(extension, [status(thm), parent(t1:1)], [f_20_6]) ).
% 0.14/15.44
% 0.14/15.44 cnf(t3, plain, $false,
% 0.14/15.44 inference(connection, [status(thm), parent(t2:1)], [t2:1,t1:1]) ).
% 0.14/15.44
% 0.14/15.44 cnf(t4, plain, ( m(vd165) ),
% 0.14/15.44 inference(extension, [status(thm), parent(t2:2)], [f_17_2]) ).
% 0.14/15.44
% 0.14/15.44 cnf(t5, plain, $false,
% 0.14/15.44 inference(connection, [status(thm), parent(t4:1)], [t4:1,t2:2]) ).
% 0.14/15.44
% 0.14/15.44 cnf(t6, plain, ( vd151 != vplus(vd165, sK2(vd151, vd165)) ),
% 0.14/15.44 inference(extension, [status(thm), parent(t2:3)], [f_1_6]) ).
% 0.14/15.44
% 0.14/15.44 cnf(t7, plain, $false,
% 0.14/15.44 inference(connection, [status(thm), parent(t6:1)], [t6:1,t2:3]) ).
% 0.14/15.44
% 0.14/15.44 cnf(t8, plain, ( vd151 != vd165 ),
% 0.14/15.44 inference(extension, [status(thm), parent(t2:4)], [f_1_7]) ).
% 0.14/15.44
% 0.14/15.44 cnf(t9, plain, $false,
% 0.14/15.44 inference(connection, [status(thm), parent(t8:1)], [t8:1,t2:4]) ).
% 0.14/15.44
% 0.14/15.44 % SZS output end Proof for theBenchmark
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