%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM851+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 : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:53:26 AM UTC 2026
% Result : Theorem 121.54s 131.82s
% Output : Proof 121.54s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM851+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/10.38 % Computer : n026.cluster.edu
% 0.12/10.38 % Model : x86_64 x86_64
% 0.12/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/10.38 % Memory : 8046.5625MB
% 0.12/10.38 % OS : Linux 6.8.0-71-generic
% 0.12/10.38 % CPULimit : 300
% 0.12/10.38 % WCLimit : 300
% 0.12/10.38 % DateTime : Sat Sep 19 19:24:32 UTC 2026
% 0.12/10.39 % CPUTime :
% 121.54/131.82 % SZS status Theorem for theBenchmark
% 121.54/131.82 % SZS output start Proof for theBenchmark
% 121.54/131.82 fof(holds(conseq_conjunct2(conseq(302)), 475, 1), conjecture,
% 121.54/131.82 vmul(vplus(vd471, vd473), vd469) = vplus(vmul(vd471, vd469), vmul(vd473, vd469)),
% 121.54/131.82 file('theBenchmark.p', holds(conseq_conjunct2(conseq(302)), 475, 1)) ).
% 121.54/131.82
% 121.54/131.82 fof(ass(cond(281, 0), 0), axiom,
% 121.54/131.82 ! [ Vd432,Vd433,Vd434 ] : vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)),
% 121.54/131.82 file('theBenchmark.p', ass(cond(281, 0), 0)) ).
% 121.54/131.82
% 121.54/131.82 fof(ass(cond(270, 0), 0), axiom,
% 121.54/131.82 ! [ Vd418,Vd419 ] : vmul(Vd418, Vd419) = vmul(Vd419, Vd418),
% 121.54/131.82 file('theBenchmark.p', ass(cond(270, 0), 0)) ).
% 121.54/131.82
% 121.54/131.82 fof(f_1_1, negated_conjecture,
% 121.54/131.82 ~( vmul(vplus(vd471, vd473), vd469) = vplus(vmul(vd471, vd469), vmul(vd473, vd469)) ),
% 121.54/131.82 inference(negate,[status(cth)],[holds(conseq_conjunct2(conseq(302)), 475, 1)]) ).
% 121.54/131.82
% 121.54/131.82 fof(f_1_2, negated_conjecture,
% 121.54/131.82 ( ( ( vmul(vplus(vd471, vd473), vd469) != vplus(vmul(vd471, vd469), vmul(vd473, vd469)) ) ) ),
% 121.54/131.82 inference(definitional_conversion,[status(esa)],[f_1_1]) ).
% 121.54/131.82
% 121.54/131.82 cnf(f_1_3, negated_conjecture,
% 121.54/131.82 ( vmul(vplus(vd471, vd473), vd469) != vplus(vmul(vd471, vd469), vmul(vd473, vd469)) ),
% 121.54/131.82 inference(clausify,[status(thm)],[f_1_2]) ).
% 121.54/131.82
% 121.54/131.82 fof(f_6_1, plain,
% 121.54/131.82 ! [ Vd432,Vd433,Vd434 ] : vmul(Vd432, vplus(Vd433, Vd434)) = vplus(vmul(Vd432, Vd433), vmul(Vd432, Vd434)),
% 121.54/131.82 inference(fof_nnf,[status(thm)],[ass(cond(281, 0), 0)]) ).
% 121.54/131.82
% 121.54/131.82 fof(f_6_2, plain,
% 121.54/131.82 ! [ U_5,U_4,U_3 ] : vmul(U_5, vplus(U_4, U_3)) = vplus(vmul(U_5, U_4), vmul(U_5, U_3)),
% 121.54/131.82 inference(variable_rename,[status(thm)],[f_6_1]) ).
% 121.54/131.82
% 121.54/131.82 cnf(f_6_3, plain,
% 121.54/131.82 ( vmul(U_5, vplus(U_4, U_3)) = vplus(vmul(U_5, U_4), vmul(U_5, U_3)) ),
% 121.54/131.82 inference(clausify,[status(thm)],[f_6_2]) ).
% 121.54/131.82
% 121.54/131.82 fof(f_7_1, plain,
% 121.54/131.82 ! [ Vd418,Vd419 ] : vmul(Vd418, Vd419) = vmul(Vd419, Vd418),
% 121.54/131.82 inference(fof_nnf,[status(thm)],[ass(cond(270, 0), 0)]) ).
% 121.54/131.82
% 121.54/131.82 fof(f_7_2, plain,
% 121.54/131.82 ! [ U_7,U_6 ] : vmul(U_7, U_6) = vmul(U_6, U_7),
% 121.54/131.82 inference(variable_rename,[status(thm)],[f_7_1]) ).
% 121.54/131.82
% 121.54/131.82 cnf(f_7_3, plain,
% 121.54/131.82 ( vmul(U_7, U_6) = vmul(U_6, U_7) ),
% 121.54/131.82 inference(clausify,[status(thm)],[f_7_2]) ).
% 121.54/131.82
% 121.54/131.82 cnf(equality_3, axiom,
% 121.54/131.82 ( Eq_x_0 != Eq_x_1 | Eq_x_1 != Eq_x_2 | Eq_x_0 = Eq_x_2 ),
% 121.54/131.82 theory(equality,[transitivity]) ).
% 121.54/131.82
% 121.54/131.82 cnf(equality_4, axiom,
% 121.54/131.82 ( 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) ),
% 121.54/131.82 theory(equality,[substitution_functions]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t1, plain, ( vmul(vplus(vd471, vd473), vd469) != vplus(vmul(vd471, vd469), vmul(vd473, vd469)) ),
% 121.54/131.82 inference(start, [status(thm), parent(0:0)], [f_1_3]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t2, plain, ( vmul(vplus(vd471, vd473), vd469) = vplus(vmul(vd471, vd469), vmul(vd473, vd469)) | vmul(vplus(vd471, vd473), vd469) != vplus(vmul(vd469, vd471), vmul(vd469, vd473)) | vplus(vmul(vd469, vd471), vmul(vd469, vd473)) != vplus(vmul(vd471, vd469), vmul(vd473, vd469)) ),
% 121.54/131.82 inference(extension, [status(thm), parent(t1:1)], [equality_3]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t3, plain, $false,
% 121.54/131.82 inference(connection, [status(thm), parent(t2:1)], [t2:1,t1:1]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t4, plain, ( vmul(vplus(vd471, vd473), vd469) = vplus(vmul(vd469, vd471), vmul(vd469, vd473)) | vmul(vplus(vd471, vd473), vd469) != vmul(vd469, vplus(vd471, vd473)) | vmul(vd469, vplus(vd471, vd473)) != vplus(vmul(vd469, vd471), vmul(vd469, vd473)) ),
% 121.54/131.82 inference(extension, [status(thm), parent(t2:2)], [equality_3]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t5, plain, $false,
% 121.54/131.82 inference(connection, [status(thm), parent(t4:1)], [t4:1,t2:2]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t6, plain, ( vmul(vplus(vd471, vd473), vd469) = vmul(vd469, vplus(vd471, vd473)) ),
% 121.54/131.82 inference(extension, [status(thm), parent(t4:2)], [f_7_3]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t7, plain, $false,
% 121.54/131.82 inference(connection, [status(thm), parent(t6:1)], [t6:1,t4:2]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t8, plain, ( vmul(vd469, vplus(vd471, vd473)) = vplus(vmul(vd469, vd471), vmul(vd469, vd473)) ),
% 121.54/131.82 inference(extension, [status(thm), parent(t4:3)], [f_6_3]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t9, plain, $false,
% 121.54/131.82 inference(connection, [status(thm), parent(t8:1)], [t8:1,t4:3]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t10, plain, ( vplus(vmul(vd469, vd471), vmul(vd469, vd473)) = vplus(vmul(vd471, vd469), vmul(vd473, vd469)) | vmul(vd469, vd471) != vmul(vd471, vd469) | vmul(vd469, vd473) != vmul(vd473, vd469) ),
% 121.54/131.82 inference(extension, [status(thm), parent(t2:3)], [equality_4]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t11, plain, $false,
% 121.54/131.82 inference(connection, [status(thm), parent(t10:1)], [t10:1,t2:3]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t12, plain, ( vmul(vd469, vd471) = vmul(vd471, vd469) ),
% 121.54/131.82 inference(extension, [status(thm), parent(t10:2)], [f_7_3]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t13, plain, $false,
% 121.54/131.82 inference(connection, [status(thm), parent(t12:1)], [t12:1,t10:2]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t14, plain, ( vmul(vd469, vd473) = vmul(vd473, vd469) ),
% 121.54/131.82 inference(extension, [status(thm), parent(t10:3)], [f_7_3]) ).
% 121.54/131.82
% 121.54/131.82 cnf(t15, plain, $false,
% 121.54/131.82 inference(connection, [status(thm), parent(t14:1)], [t14:1,t10:3]) ).
% 121.54/131.82
% 121.54/131.82 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------