%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM848+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 08:53:26 AM UTC 2026
% Result : Theorem 0.96s 1.21s
% Output : Proof 0.96s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM848+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
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 19:24:02 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.96/1.21 % SZS status Theorem for theBenchmark
% 0.96/1.21 % SZS output start Proof for theBenchmark
% 0.96/1.21 fof(holds(286, 441, 4), conjecture,
% 0.96/1.21 vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))),
% 0.96/1.21 file('theBenchmark.p', holds(286, 441, 4)) ).
% 0.96/1.21
% 0.96/1.21 fof(qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0))), axiom,
% 0.96/1.21 ! [ Vd396,Vd397 ] : ( vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396) & vmul(Vd396, v1) = Vd396 ),
% 0.96/1.21 file('theBenchmark.p', qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))) ).
% 0.96/1.21
% 0.96/1.21 fof(qu(antec(axiom(3)), imp(antec(axiom(3)))), axiom,
% 0.96/1.21 ! [ Vd3,Vd4 ] : ( vsucc(Vd3) = vsucc(Vd4) => Vd3 = Vd4 ),
% 0.96/1.21 file('theBenchmark.p', qu(antec(axiom(3)), imp(antec(axiom(3))))) ).
% 0.96/1.21
% 0.96/1.21 fof(f_1_1, negated_conjecture,
% 0.96/1.21 ~( vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))) ),
% 0.96/1.21 inference(negate,[status(cth)],[holds(286, 441, 4)]) ).
% 0.96/1.21
% 0.96/1.21 fof(f_1_2, negated_conjecture,
% 0.96/1.21 ( ( ( vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) != vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))) ) ) ),
% 0.96/1.21 inference(definitional_conversion,[status(esa)],[f_1_1]) ).
% 0.96/1.21
% 0.96/1.21 cnf(f_1_3, negated_conjecture,
% 0.96/1.21 ( vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) != vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))) ),
% 0.96/1.21 inference(clausify,[status(thm)],[f_1_2]) ).
% 0.96/1.21
% 0.96/1.21 fof(f_13_1, plain,
% 0.96/1.21 ! [ Vd396,Vd397 ] : ( vmul(Vd396, vsucc(Vd397)) = vplus(vmul(Vd396, Vd397), Vd396) & vmul(Vd396, v1) = Vd396 ),
% 0.96/1.21 inference(fof_nnf,[status(thm)],[qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))]) ).
% 0.96/1.21
% 0.96/1.21 fof(f_13_2, plain,
% 0.96/1.21 ! [ U_6,U_5 ] : ( vmul(U_6, vsucc(U_5)) = vplus(vmul(U_6, U_5), U_6) & vmul(U_6, v1) = U_6 ),
% 0.96/1.21 inference(variable_rename,[status(thm)],[f_13_1]) ).
% 0.96/1.21
% 0.96/1.21 fof(f_13_3, plain,
% 0.96/1.21 ( ! [ U_7 ] : vmul(U_7, v1) = U_7 & ! [ U_8,U_5 ] : vmul(U_8, vsucc(U_5)) = vplus(vmul(U_8, U_5), U_8) ),
% 0.96/1.21 inference(miniscope,[status(thm)],[f_13_2]) ).
% 0.96/1.21
% 0.96/1.21 cnf(f_13_5, plain,
% 0.96/1.21 ( vmul(U_8, vsucc(U_5)) = vplus(vmul(U_8, U_5), U_8) ),
% 0.96/1.21 inference(clausify,[status(thm)],[f_13_3]) ).
% 0.96/1.21
% 0.96/1.21 fof(f_56_1, plain,
% 0.96/1.21 ! [ Vd3,Vd4 ] : ( ~( vsucc(Vd3) = vsucc(Vd4) ) | Vd3 = Vd4 ),
% 0.96/1.21 inference(fof_nnf,[status(thm)],[qu(antec(axiom(3)), imp(antec(axiom(3))))]) ).
% 0.96/1.21
% 0.96/1.21 fof(f_56_2, plain,
% 0.96/1.21 ! [ U_135,U_134 ] : ( ~( vsucc(U_135) = vsucc(U_134) ) | U_135 = U_134 ),
% 0.96/1.21 inference(variable_rename,[status(thm)],[f_56_1]) ).
% 0.96/1.21
% 0.96/1.21 cnf(f_56_3, plain,
% 0.96/1.21 ( vsucc(U_135) != vsucc(U_134) | U_135 = U_134 ),
% 0.96/1.21 inference(clausify,[status(thm)],[f_56_2]) ).
% 0.96/1.21
% 0.96/1.21 cnf(equality_1, axiom,
% 0.96/1.21 ( Eq_x_0 = Eq_x_0 ),
% 0.96/1.21 theory(equality,[reflexivity]) ).
% 0.96/1.21
% 0.96/1.21 cnf(equality_2, axiom,
% 0.96/1.21 ( Eq_x_0 != Eq_x_1 | Eq_x_1 = Eq_x_0 ),
% 0.96/1.21 theory(equality,[symmetry]) ).
% 0.96/1.21
% 0.96/1.21 cnf(equality_5, axiom,
% 0.96/1.21 ( 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) ),
% 0.96/1.21 theory(equality,[substitution_functions]) ).
% 0.96/1.21
% 0.96/1.21 cnf(t1, plain, ( vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) != vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))) ),
% 0.96/1.21 inference(start, [status(thm), parent(0:0)], [f_1_3]) ).
% 0.96/1.21
% 0.96/1.21 cnf(t2, plain, ( vplus(vmul(vd436, vd437), vplus(vmul(vd436, vd439), vd436)) = vplus(vmul(vd436, vd437), vmul(vd436, vsucc(vd439))) | vmul(vd436, vd437) != vmul(vd436, vd437) | vplus(vmul(vd436, vd439), vd436) != vmul(vd436, vsucc(vd439)) ),
% 0.96/1.21 inference(extension, [status(thm), parent(t1:1)], [equality_5]) ).
% 0.96/1.21
% 0.96/1.21 cnf(t3, plain, $false,
% 0.96/1.21 inference(connection, [status(thm), parent(t2:1)], [t2:1,t1:1]) ).
% 0.96/1.21
% 0.96/1.21 cnf(t4, plain, ( vmul(vd436, vd437) = vmul(vd436, vd437) | vsucc(vmul(vd436, vd437)) != vsucc(vmul(vd436, vd437)) ),
% 0.96/1.21 inference(extension, [status(thm), parent(t2:2)], [f_56_3]) ).
% 0.96/1.21
% 0.96/1.21 cnf(t5, plain, $false,
% 0.96/1.21 inference(connection, [status(thm), parent(t4:1)], [t4:1,t2:2]) ).
% 0.96/1.21
% 0.96/1.21 cnf(t6, plain, ( vsucc(vmul(vd436, vd437)) = vsucc(vmul(vd436, vd437)) ),
% 0.96/1.21 inference(extension, [status(thm), parent(t4:2)], [equality_1]) ).
% 0.96/1.21
% 0.96/1.21 cnf(t7, plain, $false,
% 0.96/1.21 inference(connection, [status(thm), parent(t6:1)], [t6:1,t4:2]) ).
% 0.96/1.21
% 0.96/1.21 cnf(t8, plain, ( vplus(vmul(vd436, vd439), vd436) = vmul(vd436, vsucc(vd439)) | vmul(vd436, vsucc(vd439)) != vplus(vmul(vd436, vd439), vd436) ),
% 0.96/1.21 inference(extension, [status(thm), parent(t2:3)], [equality_2]) ).
% 0.96/1.21
% 0.96/1.21 cnf(t9, plain, $false,
% 0.96/1.21 inference(connection, [status(thm), parent(t8:1)], [t8:1,t2:3]) ).
% 0.96/1.21
% 0.96/1.21 cnf(t10, plain, ( vmul(vd436, vsucc(vd439)) = vplus(vmul(vd436, vd439), vd436) ),
% 0.96/1.21 inference(extension, [status(thm), parent(t8:2)], [f_13_5]) ).
% 0.96/1.21
% 0.96/1.21 cnf(t11, plain, $false,
% 0.96/1.21 inference(connection, [status(thm), parent(t10:1)], [t10:1,t8:2]) ).
% 0.96/1.21
% 0.96/1.21 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------