%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM846+1 : 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 08:53:25 AM UTC 2026
% Result : Theorem 0.15s 0.66s
% Output : Proof 0.15s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM846+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/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.57 % Computer : n001.cluster.edu
% 0.12/0.57 % Model : x86_64 x86_64
% 0.12/0.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.57 % Memory : 8046.5625MB
% 0.12/0.57 % OS : Linux 6.8.0-71-generic
% 0.12/0.57 % CPULimit : 300
% 0.12/0.57 % WCLimit : 300
% 0.12/0.57 % DateTime : Sat Sep 19 19:26:55 UTC 2026
% 0.12/0.58 % CPUTime :
% 0.15/0.66 % SZS status Theorem for theBenchmark
% 0.15/0.66 % SZS output start Proof for theBenchmark
% 0.15/0.66 fof(holds(286, 441, 2), conjecture,
% 0.15/0.66 vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436),
% 0.15/0.66 file('theBenchmark.p', holds(286, 441, 2)) ).
% 0.15/0.66
% 0.15/0.66 fof(holds(285, 440, 0), axiom,
% 0.15/0.66 vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439)),
% 0.15/0.66 file('theBenchmark.p', holds(285, 440, 0)) ).
% 0.15/0.66
% 0.15/0.66 fof(ass(cond(goal(193), 0), 1), axiom,
% 0.15/0.66 ! [ Vd301,Vd302,Vd303 ] : ( Vd301 = Vd302 => vplus(Vd301, Vd303) = vplus(Vd302, Vd303) ),
% 0.15/0.66 file('theBenchmark.p', ass(cond(goal(193), 0), 1)) ).
% 0.15/0.66
% 0.15/0.66 fof(f_1_1, negated_conjecture,
% 0.15/0.66 ~( vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) ),
% 0.15/0.66 inference(negate,[status(cth)],[holds(286, 441, 2)]) ).
% 0.15/0.66
% 0.15/0.66 fof(f_1_2, negated_conjecture,
% 0.15/0.66 ( ( ( vplus(vmul(vd436, vplus(vd437, vd439)), vd436) != vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) ) ) ),
% 0.15/0.66 inference(definitional_conversion,[status(esa)],[f_1_1]) ).
% 0.15/0.66
% 0.15/0.66 cnf(f_1_3, negated_conjecture,
% 0.15/0.66 ( vplus(vmul(vd436, vplus(vd437, vd439)), vd436) != vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) ),
% 0.15/0.66 inference(clausify,[status(thm)],[f_1_2]) ).
% 0.15/0.66
% 0.15/0.66 fof(f_4_1, plain,
% 0.15/0.66 vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439)),
% 0.15/0.66 inference(fof_nnf,[status(thm)],[holds(285, 440, 0)]) ).
% 0.15/0.66
% 0.15/0.66 cnf(f_4_2, plain,
% 0.15/0.66 ( vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439)) ),
% 0.15/0.66 inference(clausify,[status(thm)],[f_4_1]) ).
% 0.15/0.66
% 0.15/0.66 fof(f_22_1, plain,
% 0.15/0.66 ! [ Vd301,Vd302,Vd303 ] : ( ~( Vd301 = Vd302 ) | vplus(Vd301, Vd303) = vplus(Vd302, Vd303) ),
% 0.15/0.66 inference(fof_nnf,[status(thm)],[ass(cond(goal(193), 0), 1)]) ).
% 0.15/0.66
% 0.15/0.66 fof(f_22_2, plain,
% 0.15/0.66 ! [ U_40,U_39,U_38 ] : ( ~( U_40 = U_39 ) | vplus(U_40, U_38) = vplus(U_39, U_38) ),
% 0.15/0.66 inference(variable_rename,[status(thm)],[f_22_1]) ).
% 0.15/0.66
% 0.15/0.66 fof(f_22_3, plain,
% 0.15/0.66 ! [ U_40,U_39 ] : ( ~( U_40 = U_39 ) | ! [ U_38 ] : vplus(U_40, U_38) = vplus(U_39, U_38) ),
% 0.15/0.66 inference(miniscope,[status(thm)],[f_22_2]) ).
% 0.15/0.66
% 0.15/0.66 cnf(f_22_4, plain,
% 0.15/0.66 ( U_40 != U_39 | vplus(U_40, U_38) = vplus(U_39, U_38) ),
% 0.15/0.66 inference(clausify,[status(thm)],[f_22_3]) ).
% 0.15/0.66
% 0.15/0.66 cnf(t1, plain, ( vplus(vmul(vd436, vplus(vd437, vd439)), vd436) != vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) ),
% 0.15/0.66 inference(start, [status(thm), parent(0:0)], [f_1_3]) ).
% 0.15/0.66
% 0.15/0.66 cnf(t2, plain, ( vplus(vmul(vd436, vplus(vd437, vd439)), vd436) = vplus(vplus(vmul(vd436, vd437), vmul(vd436, vd439)), vd436) | vmul(vd436, vplus(vd437, vd439)) != vplus(vmul(vd436, vd437), vmul(vd436, vd439)) ),
% 0.15/0.66 inference(extension, [status(thm), parent(t1:1)], [f_22_4]) ).
% 0.15/0.66
% 0.15/0.66 cnf(t3, plain, $false,
% 0.15/0.66 inference(connection, [status(thm), parent(t2:1)], [t2:1,t1:1]) ).
% 0.15/0.66
% 0.15/0.66 cnf(t4, plain, ( vmul(vd436, vplus(vd437, vd439)) = vplus(vmul(vd436, vd437), vmul(vd436, vd439)) ),
% 0.15/0.66 inference(extension, [status(thm), parent(t2:2)], [f_4_2]) ).
% 0.15/0.66
% 0.15/0.66 cnf(t5, plain, $false,
% 0.15/0.66 inference(connection, [status(thm), parent(t4:1)], [t4:1,t2:2]) ).
% 0.15/0.66
% 0.15/0.66 % SZS output end Proof for theBenchmark
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