%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM849+2 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /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 : Thu Sep 24 08:53:26 AM UTC 2026
% Result : Theorem 1.16s 1.47s
% Output : Proof 1.16s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM849+2 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a FOF_THM_RFO_PEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n001.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 19 19:27:11 UTC 2026
% 0.09/0.37 % CPUTime :
% 1.16/1.47 % SZS status Theorem for theBenchmark
% 1.16/1.47 % SZS output start Proof for theBenchmark
% 1.16/1.47 fof(qu(ind(296), imp(296)), conjecture,
% 1.16/1.47 ! [ Vd454 ] : ( vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)) => vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454))) ),
% 1.16/1.47 file('theBenchmark.p', qu(ind(296), imp(296))) ).
% 1.16/1.47
% 1.16/1.47 fof(ass(cond(conseq(292), 1), 0), axiom,
% 1.16/1.47 ! [ Vd451 ] : ( vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)) => vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451))) ),
% 1.16/1.47 file('theBenchmark.p', ass(cond(conseq(292), 1), 0)) ).
% 1.16/1.47
% 1.16/1.47 fof(ass(cond(conseq(292), 1), 1), axiom,
% 1.16/1.47 ! [ Vd451 ] : ( vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)) => vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) ),
% 1.16/1.47 file('theBenchmark.p', ass(cond(conseq(292), 1), 1)) ).
% 1.16/1.47
% 1.16/1.47 fof(ass(cond(conseq(292), 1), 2), axiom,
% 1.16/1.47 ! [ Vd451 ] : ( vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)) => vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) ),
% 1.16/1.47 file('theBenchmark.p', ass(cond(conseq(292), 1), 2)) ).
% 1.16/1.47
% 1.16/1.47 fof(qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), axiom,
% 1.16/1.47 ! [ Vd396,Vd397 ] : ( vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396) & vmul(Vd396, v1) = Vd396 ),
% 1.16/1.47 file('theBenchmark.p', qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) ).
% 1.16/1.47
% 1.16/1.47 fof(f_1_1, negated_conjecture,
% 1.16/1.47 ~( ! [ Vd454 ] : ( vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)) => vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454))) ) ),
% 1.16/1.47 inference(negate,[status(cth)],[qu(ind(296), imp(296))]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_1_2, negated_conjecture,
% 1.16/1.47 ? [ Vd454 ] : ( vmul(vmul(vd448, vd449), Vd454) = vmul(vd448, vmul(vd449, Vd454)) & ~( vmul(vmul(vd448, vd449), vsucc(Vd454)) = vmul(vd448, vmul(vd449, vsucc(Vd454))) ) ),
% 1.16/1.47 inference(fof_nnf,[status(thm)],[f_1_1]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_1_3, negated_conjecture,
% 1.16/1.47 ? [ U_0 ] : ( vmul(vmul(vd448, vd449), U_0) = vmul(vd448, vmul(vd449, U_0)) & ~( vmul(vmul(vd448, vd449), vsucc(U_0)) = vmul(vd448, vmul(vd449, vsucc(U_0))) ) ),
% 1.16/1.47 inference(variable_rename,[status(thm)],[f_1_2]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_1_4, negated_conjecture,
% 1.16/1.47 ( vmul(vmul(vd448, vd449), sK1) = vmul(vd448, vmul(vd449, sK1)) & ~( vmul(vmul(vd448, vd449), vsucc(sK1)) = vmul(vd448, vmul(vd449, vsucc(sK1))) ) ),
% 1.16/1.47 inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1)],[f_1_3]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_1_5, negated_conjecture,
% 1.16/1.47 ( ( ( vmul(vmul(vd448, vd449), sK1) = vmul(vd448, vmul(vd449, sK1)) ) ) & ( ( vmul(vmul(vd448, vd449), vsucc(sK1)) != vmul(vd448, vmul(vd449, vsucc(sK1))) ) ) ),
% 1.16/1.47 inference(definitional_conversion,[status(esa)],[f_1_4]) ).
% 1.16/1.47
% 1.16/1.47 cnf(f_1_6, negated_conjecture,
% 1.16/1.47 ( vmul(vmul(vd448, vd449), sK1) = vmul(vd448, vmul(vd449, sK1)) ),
% 1.16/1.47 inference(clausify,[status(thm)],[f_1_5]) ).
% 1.16/1.47
% 1.16/1.47 cnf(f_1_7, negated_conjecture,
% 1.16/1.47 ( vmul(vmul(vd448, vd449), vsucc(sK1)) != vmul(vd448, vmul(vd449, vsucc(sK1))) ),
% 1.16/1.47 inference(clausify,[status(thm)],[f_1_5]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_2_1, plain,
% 1.16/1.47 ! [ Vd451 ] : ( ~( vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)) ) | vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) = vmul(vd448, vmul(vd449, vsucc(Vd451))) ),
% 1.16/1.47 inference(fof_nnf,[status(thm)],[ass(cond(conseq(292), 1), 0)]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_2_2, plain,
% 1.16/1.47 ! [ U_1 ] : ( ~( vmul(vmul(vd448, vd449), U_1) = vmul(vd448, vmul(vd449, U_1)) ) | vmul(vd448, vplus(vmul(vd449, U_1), vd449)) = vmul(vd448, vmul(vd449, vsucc(U_1))) ),
% 1.16/1.47 inference(variable_rename,[status(thm)],[f_2_1]) ).
% 1.16/1.47
% 1.16/1.47 cnf(f_2_3, plain,
% 1.16/1.47 ( vmul(vmul(vd448, vd449), U_1) != vmul(vd448, vmul(vd449, U_1)) | vmul(vd448, vplus(vmul(vd449, U_1), vd449)) = vmul(vd448, vmul(vd449, vsucc(U_1))) ),
% 1.16/1.47 inference(clausify,[status(thm)],[f_2_2]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_3_1, plain,
% 1.16/1.47 ! [ Vd451 ] : ( ~( vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)) ) | vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, Vd451), vd449)) ),
% 1.16/1.47 inference(fof_nnf,[status(thm)],[ass(cond(conseq(292), 1), 1)]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_3_2, plain,
% 1.16/1.47 ! [ U_2 ] : ( ~( vmul(vmul(vd448, vd449), U_2) = vmul(vd448, vmul(vd449, U_2)) ) | vplus(vmul(vd448, vmul(vd449, U_2)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, U_2), vd449)) ),
% 1.16/1.47 inference(variable_rename,[status(thm)],[f_3_1]) ).
% 1.16/1.47
% 1.16/1.47 cnf(f_3_3, plain,
% 1.16/1.47 ( vmul(vmul(vd448, vd449), U_2) != vmul(vd448, vmul(vd449, U_2)) | vplus(vmul(vd448, vmul(vd449, U_2)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, U_2), vd449)) ),
% 1.16/1.47 inference(clausify,[status(thm)],[f_3_2]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_4_1, plain,
% 1.16/1.47 ! [ Vd451 ] : ( ~( vmul(vmul(vd448, vd449), Vd451) = vmul(vd448, vmul(vd449, Vd451)) ) | vplus(vmul(vmul(vd448, vd449), Vd451), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, Vd451)), vmul(vd448, vd449)) ),
% 1.16/1.47 inference(fof_nnf,[status(thm)],[ass(cond(conseq(292), 1), 2)]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_4_2, plain,
% 1.16/1.47 ! [ U_3 ] : ( ~( vmul(vmul(vd448, vd449), U_3) = vmul(vd448, vmul(vd449, U_3)) ) | vplus(vmul(vmul(vd448, vd449), U_3), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, U_3)), vmul(vd448, vd449)) ),
% 1.16/1.47 inference(variable_rename,[status(thm)],[f_4_1]) ).
% 1.16/1.47
% 1.16/1.47 cnf(f_4_3, plain,
% 1.16/1.47 ( vmul(vmul(vd448, vd449), U_3) != vmul(vd448, vmul(vd449, U_3)) | vplus(vmul(vmul(vd448, vd449), U_3), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, U_3)), vmul(vd448, vd449)) ),
% 1.16/1.47 inference(clausify,[status(thm)],[f_4_2]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_10_1, plain,
% 1.16/1.47 ! [ Vd396,Vd397 ] : ( vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396) & vmul(Vd396, v1) = Vd396 ),
% 1.16/1.47 inference(fof_nnf,[status(thm)],[qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_10_2, plain,
% 1.16/1.47 ! [ U_13,U_12 ] : ( vmul(U_13, vsucc(U_12)) = vplus(vmul(U_13, U_12), U_13) & vmul(U_13, v1) = U_13 ),
% 1.16/1.47 inference(variable_rename,[status(thm)],[f_10_1]) ).
% 1.16/1.47
% 1.16/1.47 fof(f_10_3, plain,
% 1.16/1.47 ( ! [ U_14 ] : vmul(U_14, v1) = U_14 & ! [ U_15,U_12 ] : vmul(U_15, vsucc(U_12)) = vplus(vmul(U_15, U_12), U_15) ),
% 1.16/1.47 inference(miniscope,[status(thm)],[f_10_2]) ).
% 1.16/1.47
% 1.16/1.47 cnf(f_10_5, plain,
% 1.16/1.47 ( vmul(U_15, vsucc(U_12)) = vplus(vmul(U_15, U_12), U_15) ),
% 1.16/1.47 inference(clausify,[status(thm)],[f_10_3]) ).
% 1.16/1.47
% 1.16/1.47 cnf(equality_3, axiom,
% 1.16/1.47 ( Eq_x_0 != Eq_x_1 | Eq_x_1 != Eq_x_2 | Eq_x_0 = Eq_x_2 ),
% 1.16/1.47 theory(equality,[transitivity]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t1, plain, ( vmul(vmul(vd448, vd449), vsucc(sK1)) != vmul(vd448, vmul(vd449, vsucc(sK1))) ),
% 1.16/1.47 inference(start, [status(thm), parent(0:0)], [f_1_7]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t2, plain, ( vmul(vmul(vd448, vd449), vsucc(sK1)) = vmul(vd448, vmul(vd449, vsucc(sK1))) | vmul(vmul(vd448, vd449), vsucc(sK1)) != vplus(vmul(vd448, vmul(vd449, sK1)), vmul(vd448, vd449)) | vplus(vmul(vd448, vmul(vd449, sK1)), vmul(vd448, vd449)) != vmul(vd448, vmul(vd449, vsucc(sK1))) ),
% 1.16/1.47 inference(extension, [status(thm), parent(t1:1)], [equality_3]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t3, plain, $false,
% 1.16/1.47 inference(connection, [status(thm), parent(t2:1)], [t2:1,t1:1]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t4, plain, ( vmul(vmul(vd448, vd449), vsucc(sK1)) = vplus(vmul(vd448, vmul(vd449, sK1)), vmul(vd448, vd449)) | vmul(vmul(vd448, vd449), vsucc(sK1)) != vplus(vmul(vmul(vd448, vd449), sK1), vmul(vd448, vd449)) | vplus(vmul(vmul(vd448, vd449), sK1), vmul(vd448, vd449)) != vplus(vmul(vd448, vmul(vd449, sK1)), vmul(vd448, vd449)) ),
% 1.16/1.47 inference(extension, [status(thm), parent(t2:2)], [equality_3]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t5, plain, $false,
% 1.16/1.47 inference(connection, [status(thm), parent(t4:1)], [t4:1,t2:2]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t6, plain, ( vmul(vmul(vd448, vd449), vsucc(sK1)) = vplus(vmul(vmul(vd448, vd449), sK1), vmul(vd448, vd449)) ),
% 1.16/1.47 inference(extension, [status(thm), parent(t4:2)], [f_10_5]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t7, plain, $false,
% 1.16/1.47 inference(connection, [status(thm), parent(t6:1)], [t6:1,t4:2]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t8, plain, ( vplus(vmul(vmul(vd448, vd449), sK1), vmul(vd448, vd449)) = vplus(vmul(vd448, vmul(vd449, sK1)), vmul(vd448, vd449)) | vmul(vmul(vd448, vd449), sK1) != vmul(vd448, vmul(vd449, sK1)) ),
% 1.16/1.47 inference(extension, [status(thm), parent(t4:3)], [f_4_3]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t9, plain, $false,
% 1.16/1.47 inference(connection, [status(thm), parent(t8:1)], [t8:1,t4:3]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t10, plain, ( vmul(vmul(vd448, vd449), sK1) = vmul(vd448, vmul(vd449, sK1)) ),
% 1.16/1.47 inference(extension, [status(thm), parent(t8:2)], [f_1_6]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t11, plain, $false,
% 1.16/1.47 inference(connection, [status(thm), parent(t10:1)], [t10:1,t8:2]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t12, plain, ( vplus(vmul(vd448, vmul(vd449, sK1)), vmul(vd448, vd449)) = vmul(vd448, vmul(vd449, vsucc(sK1))) | vplus(vmul(vd448, vmul(vd449, sK1)), vmul(vd448, vd449)) != vmul(vd448, vplus(vmul(vd449, sK1), vd449)) | vmul(vd448, vplus(vmul(vd449, sK1), vd449)) != vmul(vd448, vmul(vd449, vsucc(sK1))) ),
% 1.16/1.47 inference(extension, [status(thm), parent(t2:3)], [equality_3]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t13, plain, $false,
% 1.16/1.47 inference(connection, [status(thm), parent(t12:1)], [t12:1,t2:3]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t14, plain, ( vplus(vmul(vd448, vmul(vd449, sK1)), vmul(vd448, vd449)) = vmul(vd448, vplus(vmul(vd449, sK1), vd449)) | vmul(vmul(vd448, vd449), sK1) != vmul(vd448, vmul(vd449, sK1)) ),
% 1.16/1.47 inference(extension, [status(thm), parent(t12:2)], [f_3_3]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t15, plain, $false,
% 1.16/1.47 inference(connection, [status(thm), parent(t14:1)], [t14:1,t12:2]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t16, plain, ( vmul(vmul(vd448, vd449), sK1) = vmul(vd448, vmul(vd449, sK1)) ),
% 1.16/1.47 inference(extension, [status(thm), parent(t14:2)], [f_1_6]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t17, plain, $false,
% 1.16/1.47 inference(connection, [status(thm), parent(t16:1)], [t16:1,t14:2]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t18, plain, ( vmul(vd448, vplus(vmul(vd449, sK1), vd449)) = vmul(vd448, vmul(vd449, vsucc(sK1))) | vmul(vmul(vd448, vd449), sK1) != vmul(vd448, vmul(vd449, sK1)) ),
% 1.16/1.47 inference(extension, [status(thm), parent(t12:3)], [f_2_3]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t19, plain, $false,
% 1.16/1.47 inference(connection, [status(thm), parent(t18:1)], [t18:1,t12:3]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t20, plain, ( vmul(vmul(vd448, vd449), sK1) = vmul(vd448, vmul(vd449, sK1)) ),
% 1.16/1.47 inference(extension, [status(thm), parent(t18:2)], [f_1_6]) ).
% 1.16/1.47
% 1.16/1.47 cnf(t21, plain, $false,
% 1.16/1.47 inference(connection, [status(thm), parent(t20:1)], [t20:1,t18:2]) ).
% 1.16/1.47
% 1.16/1.47 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------