%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM852+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 : n010.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 08:53:27 AM UTC 2026
% Result : Theorem 126.85s 127.38s
% Output : Proof 126.85s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : NUM852+1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.03 This is a FOF_THM_RFO_SEQ problem
% 0.00/0.03 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.56 % Computer : n010.cluster.edu
% 0.08/0.56 % Model : x86_64 x86_64
% 0.08/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.56 % Memory : 8046.5625MB
% 0.08/0.56 % OS : Linux 6.8.0-71-generic
% 0.08/0.56 % CPULimit : 300
% 0.08/0.56 % WCLimit : 300
% 0.08/0.56 % DateTime : Sat Sep 19 19:21:57 UTC 2026
% 0.08/0.56 % CPUTime :
% 126.85/127.38 % SZS status Theorem for theBenchmark
% 126.85/127.38 % SZS output start Proof for theBenchmark
% 126.85/127.38 fof(holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0), conjecture,
% 126.85/127.38 greater(vmul(vd481, vd469), vmul(vd480, vd469)),
% 126.85/127.38 file('theBenchmark.p', holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)) ).
% 126.85/127.38
% 126.85/127.38 fof(holds(conseq_conjunct1(conseq(304)), 483, 0), axiom,
% 126.85/127.38 greater(vd481, vd480),
% 126.85/127.38 file('theBenchmark.p', holds(conseq_conjunct1(conseq(304)), 483, 0)) ).
% 126.85/127.38
% 126.85/127.38 fof(ass(cond(302, 0), 1), axiom,
% 126.85/127.38 ! [ Vd470,Vd471 ] : ( greater(Vd470, Vd471) => vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469)) ),
% 126.85/127.38 file('theBenchmark.p', ass(cond(302, 0), 1)) ).
% 126.85/127.38
% 126.85/127.38 fof(ass(cond(302, 0), 2), axiom,
% 126.85/127.38 ! [ Vd470,Vd471 ] : ( greater(Vd470, Vd471) => vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) ),
% 126.85/127.38 file('theBenchmark.p', ass(cond(302, 0), 2)) ).
% 126.85/127.38
% 126.85/127.38 fof(def(cond(conseq(axiom(3)), 11), 1), axiom,
% 126.85/127.38 ! [ Vd193,Vd194 ] : ( greater(Vd194, Vd193) <=> ? [ Vd196 ] : Vd194 = vplus(Vd193, Vd196) ),
% 126.85/127.38 file('theBenchmark.p', def(cond(conseq(axiom(3)), 11), 1)) ).
% 126.85/127.38
% 126.85/127.38 fof(f_1_1, negated_conjecture,
% 126.85/127.38 ~( greater(vmul(vd481, vd469), vmul(vd480, vd469)) ),
% 126.85/127.38 inference(negate,[status(cth)],[holds(conseq_conjunct1(conseq_conjunct2(conseq(304))), 484, 0)]) ).
% 126.85/127.38
% 126.85/127.38 fof(f_1_2, negated_conjecture,
% 126.85/127.38 ( ( ( ~greater(vmul(vd481, vd469), vmul(vd480, vd469)) ) ) ),
% 126.85/127.38 inference(definitional_conversion,[status(esa)],[f_1_1]) ).
% 126.85/127.38
% 126.85/127.38 cnf(f_1_3, negated_conjecture,
% 126.85/127.38 ( ~greater(vmul(vd481, vd469), vmul(vd480, vd469)) ),
% 126.85/127.38 inference(clausify,[status(thm)],[f_1_2]) ).
% 126.85/127.38
% 126.85/127.38 fof(f_2_1, plain,
% 126.85/127.38 greater(vd481, vd480),
% 126.85/127.38 inference(fof_nnf,[status(thm)],[holds(conseq_conjunct1(conseq(304)), 483, 0)]) ).
% 126.85/127.38
% 126.85/127.38 cnf(f_2_2, plain,
% 126.85/127.38 ( greater(vd481, vd480) ),
% 126.85/127.38 inference(clausify,[status(thm)],[f_2_1]) ).
% 126.85/127.38
% 126.85/127.38 fof(f_6_1, plain,
% 126.85/127.38 ! [ Vd470,Vd471 ] : ( ~( greater(Vd470, Vd471) ) | vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) = vplus(vmul(Vd471, vd469), vmul(vskolem9(Vd470, Vd471), vd469)) ),
% 126.85/127.38 inference(fof_nnf,[status(thm)],[ass(cond(302, 0), 1)]) ).
% 126.85/127.38
% 126.85/127.38 fof(f_6_2, plain,
% 126.85/127.38 ! [ U_5,U_4 ] : ( ~( greater(U_5, U_4) ) | vmul(vplus(U_4, vskolem9(U_5, U_4)), vd469) = vplus(vmul(U_4, vd469), vmul(vskolem9(U_5, U_4), vd469)) ),
% 126.85/127.38 inference(variable_rename,[status(thm)],[f_6_1]) ).
% 126.85/127.38
% 126.85/127.38 cnf(f_6_3, plain,
% 126.85/127.38 ( ~greater(U_5, U_4) | vmul(vplus(U_4, vskolem9(U_5, U_4)), vd469) = vplus(vmul(U_4, vd469), vmul(vskolem9(U_5, U_4), vd469)) ),
% 126.85/127.38 inference(clausify,[status(thm)],[f_6_2]) ).
% 126.85/127.38
% 126.85/127.38 fof(f_7_1, plain,
% 126.85/127.38 ! [ Vd470,Vd471 ] : ( ~( greater(Vd470, Vd471) ) | vmul(Vd470, vd469) = vmul(vplus(Vd471, vskolem9(Vd470, Vd471)), vd469) ),
% 126.85/127.38 inference(fof_nnf,[status(thm)],[ass(cond(302, 0), 2)]) ).
% 126.85/127.38
% 126.85/127.38 fof(f_7_2, plain,
% 126.85/127.38 ! [ U_7,U_6 ] : ( ~( greater(U_7, U_6) ) | vmul(U_7, vd469) = vmul(vplus(U_6, vskolem9(U_7, U_6)), vd469) ),
% 126.85/127.38 inference(variable_rename,[status(thm)],[f_7_1]) ).
% 126.85/127.38
% 126.85/127.38 cnf(f_7_3, plain,
% 126.85/127.38 ( ~greater(U_7, U_6) | vmul(U_7, vd469) = vmul(vplus(U_6, vskolem9(U_7, U_6)), vd469) ),
% 126.85/127.38 inference(clausify,[status(thm)],[f_7_2]) ).
% 126.85/127.38
% 126.85/127.38 fof(f_42_1, plain,
% 126.85/127.38 ! [ Vd193,Vd194 ] : ( ( ~( greater(Vd194, Vd193) ) | ? [ Vd196 ] : Vd194 = vplus(Vd193, Vd196) ) & ( ! [ Vd196 ] : ~( Vd194 = vplus(Vd193, Vd196) ) | greater(Vd194, Vd193) ) ),
% 126.85/127.38 inference(fof_nnf,[status(thm)],[def(cond(conseq(axiom(3)), 11), 1)]) ).
% 126.85/127.38
% 126.85/127.38 fof(f_42_2, plain,
% 126.85/127.38 ! [ U_110,U_109 ] : ( ( ~( greater(U_109, U_110) ) | ? [ U_107 ] : U_109 = vplus(U_110, U_107) ) & ( ! [ U_108 ] : ~( U_109 = vplus(U_110, U_108) ) | greater(U_109, U_110) ) ),
% 126.85/127.38 inference(variable_rename,[status(thm)],[f_42_1]) ).
% 126.85/127.38
% 126.85/127.38 fof(f_42_3, plain,
% 126.85/127.38 ( ! [ U_113,U_111 ] : ( ~( greater(U_111, U_113) ) | ? [ U_107 ] : U_111 = vplus(U_113, U_107) ) & ! [ U_114,U_112 ] : ( ! [ U_108 ] : ~( U_112 = vplus(U_114, U_108) ) | greater(U_112, U_114) ) ),
% 126.85/127.38 inference(miniscope,[status(thm)],[f_42_2]) ).
% 126.85/127.38
% 126.85/127.38 fof(f_42_4, plain,
% 126.85/127.38 ( ! [ U_113,U_111 ] : ( ~( greater(U_111, U_113) ) | U_111 = vplus(U_113, sK2(U_113, U_111)) ) & ! [ U_114,U_112 ] : ( ! [ U_108 ] : ~( U_112 = vplus(U_114, U_108) ) | greater(U_112, U_114) ) ),
% 126.85/127.38 inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_107,sK2(U_113, U_111))],[f_42_3]) ).
% 126.85/127.38
% 126.85/127.38 cnf(f_42_6, plain,
% 126.85/127.38 ( U_112 != vplus(U_114, U_108) | greater(U_112, U_114) ),
% 126.85/127.38 inference(clausify,[status(thm)],[f_42_4]) ).
% 126.85/127.38
% 126.85/127.38 cnf(equality_3, axiom,
% 126.85/127.38 ( Eq_x_0 != Eq_x_1 | Eq_x_1 != Eq_x_2 | Eq_x_0 = Eq_x_2 ),
% 126.85/127.38 theory(equality,[transitivity]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t1, plain, ( ~greater(vmul(vd481, vd469), vmul(vd480, vd469)) ),
% 126.85/127.38 inference(start, [status(thm), parent(0:0)], [f_1_3]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t2, plain, ( greater(vmul(vd481, vd469), vmul(vd480, vd469)) | vmul(vd481, vd469) != vplus(vmul(vd480, vd469), vmul(vskolem9(vd481, vd480), vd469)) ),
% 126.85/127.38 inference(extension, [status(thm), parent(t1:1)], [f_42_6]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t3, plain, $false,
% 126.85/127.38 inference(connection, [status(thm), parent(t2:1)], [t2:1,t1:1]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t4, plain, ( vmul(vd481, vd469) = vplus(vmul(vd480, vd469), vmul(vskolem9(vd481, vd480), vd469)) | vmul(vd481, vd469) != vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469) | vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469) != vplus(vmul(vd480, vd469), vmul(vskolem9(vd481, vd480), vd469)) ),
% 126.85/127.38 inference(extension, [status(thm), parent(t2:2)], [equality_3]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t5, plain, $false,
% 126.85/127.38 inference(connection, [status(thm), parent(t4:1)], [t4:1,t2:2]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t6, plain, ( vmul(vd481, vd469) = vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469) | ~greater(vd481, vd480) ),
% 126.85/127.38 inference(extension, [status(thm), parent(t4:2)], [f_7_3]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t7, plain, $false,
% 126.85/127.38 inference(connection, [status(thm), parent(t6:1)], [t6:1,t4:2]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t8, plain, ( greater(vd481, vd480) ),
% 126.85/127.38 inference(extension, [status(thm), parent(t6:2)], [f_2_2]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t9, plain, $false,
% 126.85/127.38 inference(connection, [status(thm), parent(t8:1)], [t8:1,t6:2]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t10, plain, ( vmul(vplus(vd480, vskolem9(vd481, vd480)), vd469) = vplus(vmul(vd480, vd469), vmul(vskolem9(vd481, vd480), vd469)) | ~greater(vd481, vd480) ),
% 126.85/127.38 inference(extension, [status(thm), parent(t4:3)], [f_6_3]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t11, plain, $false,
% 126.85/127.38 inference(connection, [status(thm), parent(t10:1)], [t10:1,t4:3]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t12, plain, ( greater(vd481, vd480) ),
% 126.85/127.38 inference(extension, [status(thm), parent(t10:2)], [f_2_2]) ).
% 126.85/127.38
% 126.85/127.38 cnf(t13, plain, $false,
% 126.85/127.38 inference(connection, [status(thm), parent(t12:1)], [t12:1,t10:2]) ).
% 126.85/127.38
% 126.85/127.38 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------