%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : NUM836+2 : 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 : n015.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 08:53:23 AM UTC 2026
% Result : Theorem 0.78s 1.03s
% Output : Proof 0.78s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM836+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.38 % Computer : n015.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 19:24:06 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.78/1.03 % SZS status Theorem for theBenchmark
% 0.78/1.03 % SZS output start Proof for theBenchmark
% 0.78/1.03 fof(dis(ex(cond(conseq(131), 0), 1)), conjecture,
% 0.78/1.03 ( ~( greater(vd203, vd204) ) | ~( less(vd203, vd204) ) ),
% 0.78/1.03 file('theBenchmark.p', dis(ex(cond(conseq(131), 0), 1))) ).
% 0.78/1.03
% 0.78/1.03 fof(dis(ex(cond(conseq(131), 0), 0)), axiom,
% 0.78/1.03 ( ~( vd203 = vd204 ) | ~( greater(vd203, vd204) ) ),
% 0.78/1.03 file('theBenchmark.p', dis(ex(cond(conseq(131), 0), 0))) ).
% 0.78/1.03
% 0.78/1.03 fof(def(cond(conseq(axiom(3)), 12), 1), axiom,
% 0.78/1.03 ! [ Vd198,Vd199 ] : ( less(Vd199, Vd198) <=> ? [ Vd201 ] : Vd198 = vplus(Vd199, Vd201) ),
% 0.78/1.03 file('theBenchmark.p', def(cond(conseq(axiom(3)), 12), 1)) ).
% 0.78/1.03
% 0.78/1.03 fof(def(cond(conseq(axiom(3)), 11), 1), axiom,
% 0.78/1.03 ! [ Vd193,Vd194 ] : ( greater(Vd194, Vd193) <=> ? [ Vd196 ] : Vd194 = vplus(Vd193, Vd196) ),
% 0.78/1.03 file('theBenchmark.p', def(cond(conseq(axiom(3)), 11), 1)) ).
% 0.78/1.03
% 0.78/1.03 fof(ass(cond(goal(88), 0), 0), axiom,
% 0.78/1.03 ! [ Vd120,Vd121 ] : ( Vd120 = Vd121 | ? [ Vd123 ] : Vd120 = vplus(Vd121, Vd123) | ? [ Vd125 ] : Vd121 = vplus(Vd120, Vd125) ),
% 0.78/1.03 file('theBenchmark.p', ass(cond(goal(88), 0), 0)) ).
% 0.78/1.03
% 0.78/1.03 fof(ass(cond(goal(88), 0), 2), axiom,
% 0.78/1.03 ! [ Vd120,Vd121 ] : ( ~( ? [ Vd123 ] : Vd120 = vplus(Vd121, Vd123) ) | ~( ? [ Vd125 ] : Vd121 = vplus(Vd120, Vd125) ) ),
% 0.78/1.03 file('theBenchmark.p', ass(cond(goal(88), 0), 2)) ).
% 0.78/1.03
% 0.78/1.03 fof(f_1_1, negated_conjecture,
% 0.78/1.03 ~( ( ~( greater(vd203, vd204) ) | ~( less(vd203, vd204) ) ) ),
% 0.78/1.03 inference(negate,[status(cth)],[dis(ex(cond(conseq(131), 0), 1))]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_1_2, negated_conjecture,
% 0.78/1.03 ( greater(vd203, vd204) & less(vd203, vd204) ),
% 0.78/1.03 inference(fof_nnf,[status(thm)],[f_1_1]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_1_3, negated_conjecture,
% 0.78/1.03 ( ( ( greater(vd203, vd204) ) ) & ( ( less(vd203, vd204) ) ) ),
% 0.78/1.03 inference(definitional_conversion,[status(esa)],[f_1_2]) ).
% 0.78/1.03
% 0.78/1.03 cnf(f_1_4, negated_conjecture,
% 0.78/1.03 ( greater(vd203, vd204) ),
% 0.78/1.03 inference(clausify,[status(thm)],[f_1_3]) ).
% 0.78/1.03
% 0.78/1.03 cnf(f_1_5, negated_conjecture,
% 0.78/1.03 ( less(vd203, vd204) ),
% 0.78/1.03 inference(clausify,[status(thm)],[f_1_3]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_2_1, plain,
% 0.78/1.03 ( ~( vd203 = vd204 ) | ~( greater(vd203, vd204) ) ),
% 0.78/1.03 inference(fof_nnf,[status(thm)],[dis(ex(cond(conseq(131), 0), 0))]) ).
% 0.78/1.03
% 0.78/1.03 cnf(f_2_2, plain,
% 0.78/1.03 ( vd203 != vd204 | ~greater(vd203, vd204) ),
% 0.78/1.03 inference(clausify,[status(thm)],[f_2_1]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_3_1, plain,
% 0.78/1.03 ! [ Vd198,Vd199 ] : ( ( ~( less(Vd199, Vd198) ) | ? [ Vd201 ] : Vd198 = vplus(Vd199, Vd201) ) & ( ! [ Vd201 ] : ~( Vd198 = vplus(Vd199, Vd201) ) | less(Vd199, Vd198) ) ),
% 0.78/1.03 inference(fof_nnf,[status(thm)],[def(cond(conseq(axiom(3)), 12), 1)]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_3_2, plain,
% 0.78/1.03 ! [ U_3,U_2 ] : ( ( ~( less(U_2, U_3) ) | ? [ U_0 ] : U_3 = vplus(U_2, U_0) ) & ( ! [ U_1 ] : ~( U_3 = vplus(U_2, U_1) ) | less(U_2, U_3) ) ),
% 0.78/1.03 inference(variable_rename,[status(thm)],[f_3_1]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_3_3, plain,
% 0.78/1.03 ( ! [ U_6,U_4 ] : ( ~( less(U_4, U_6) ) | ? [ U_0 ] : U_6 = vplus(U_4, U_0) ) & ! [ U_7,U_5 ] : ( ! [ U_1 ] : ~( U_7 = vplus(U_5, U_1) ) | less(U_5, U_7) ) ),
% 0.78/1.03 inference(miniscope,[status(thm)],[f_3_2]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_3_4, plain,
% 0.78/1.03 ( ! [ U_6,U_4 ] : ( ~( less(U_4, U_6) ) | U_6 = vplus(U_4, sK1(U_6, U_4)) ) & ! [ U_7,U_5 ] : ( ! [ U_1 ] : ~( U_7 = vplus(U_5, U_1) ) | less(U_5, U_7) ) ),
% 0.78/1.03 inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_0,sK1(U_6, U_4))],[f_3_3]) ).
% 0.78/1.03
% 0.78/1.03 cnf(f_3_5, plain,
% 0.78/1.03 ( ~less(U_4, U_6) | U_6 = vplus(U_4, sK1(U_6, U_4)) ),
% 0.78/1.03 inference(clausify,[status(thm)],[f_3_4]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_4_1, plain,
% 0.78/1.03 ! [ Vd193,Vd194 ] : ( ( ~( greater(Vd194, Vd193) ) | ? [ Vd196 ] : Vd194 = vplus(Vd193, Vd196) ) & ( ! [ Vd196 ] : ~( Vd194 = vplus(Vd193, Vd196) ) | greater(Vd194, Vd193) ) ),
% 0.78/1.03 inference(fof_nnf,[status(thm)],[def(cond(conseq(axiom(3)), 11), 1)]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_4_2, plain,
% 0.78/1.03 ! [ U_11,U_10 ] : ( ( ~( greater(U_10, U_11) ) | ? [ U_8 ] : U_10 = vplus(U_11, U_8) ) & ( ! [ U_9 ] : ~( U_10 = vplus(U_11, U_9) ) | greater(U_10, U_11) ) ),
% 0.78/1.03 inference(variable_rename,[status(thm)],[f_4_1]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_4_3, plain,
% 0.78/1.03 ( ! [ U_14,U_12 ] : ( ~( greater(U_12, U_14) ) | ? [ U_8 ] : U_12 = vplus(U_14, U_8) ) & ! [ U_15,U_13 ] : ( ! [ U_9 ] : ~( U_13 = vplus(U_15, U_9) ) | greater(U_13, U_15) ) ),
% 0.78/1.03 inference(miniscope,[status(thm)],[f_4_2]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_4_4, plain,
% 0.78/1.03 ( ! [ U_14,U_12 ] : ( ~( greater(U_12, U_14) ) | U_12 = vplus(U_14, sK2(U_14, U_12)) ) & ! [ U_15,U_13 ] : ( ! [ U_9 ] : ~( U_13 = vplus(U_15, U_9) ) | greater(U_13, U_15) ) ),
% 0.78/1.03 inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_8,sK2(U_14, U_12))],[f_4_3]) ).
% 0.78/1.03
% 0.78/1.03 cnf(f_4_5, plain,
% 0.78/1.03 ( ~greater(U_12, U_14) | U_12 = vplus(U_14, sK2(U_14, U_12)) ),
% 0.78/1.03 inference(clausify,[status(thm)],[f_4_4]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_5_1, plain,
% 0.78/1.03 ! [ Vd120,Vd121 ] : ( Vd120 = Vd121 | ? [ Vd123 ] : Vd120 = vplus(Vd121, Vd123) | ? [ Vd125 ] : Vd121 = vplus(Vd120, Vd125) ),
% 0.78/1.03 inference(fof_nnf,[status(thm)],[ass(cond(goal(88), 0), 0)]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_5_2, plain,
% 0.78/1.03 ! [ U_19,U_18 ] : ( U_19 = U_18 | ? [ U_16 ] : U_19 = vplus(U_18, U_16) | ? [ U_17 ] : U_18 = vplus(U_19, U_17) ),
% 0.78/1.03 inference(variable_rename,[status(thm)],[f_5_1]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_5_3, plain,
% 0.78/1.03 ! [ U_19,U_18 ] : ( U_19 = U_18 | U_19 = vplus(U_18, sK3(U_19, U_18)) | ? [ U_17 ] : U_18 = vplus(U_19, U_17) ),
% 0.78/1.03 inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_16,sK3(U_19, U_18))],[f_5_2]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_5_4, plain,
% 0.78/1.03 ! [ U_19,U_18 ] : ( U_19 = U_18 | U_19 = vplus(U_18, sK3(U_19, U_18)) | U_18 = vplus(U_19, sK4(U_19, U_18)) ),
% 0.78/1.03 inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_17,sK4(U_19, U_18))],[f_5_3]) ).
% 0.78/1.03
% 0.78/1.03 cnf(f_5_5, plain,
% 0.78/1.03 ( U_19 = U_18 | U_19 = vplus(U_18, sK3(U_19, U_18)) | U_18 = vplus(U_19, sK4(U_19, U_18)) ),
% 0.78/1.03 inference(clausify,[status(thm)],[f_5_4]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_7_1, plain,
% 0.78/1.03 ! [ Vd120,Vd121 ] : ( ! [ Vd123 ] : ~( Vd120 = vplus(Vd121, Vd123) ) | ! [ Vd125 ] : ~( Vd121 = vplus(Vd120, Vd125) ) ),
% 0.78/1.03 inference(fof_nnf,[status(thm)],[ass(cond(goal(88), 0), 2)]) ).
% 0.78/1.03
% 0.78/1.03 fof(f_7_2, plain,
% 0.78/1.03 ! [ U_26,U_25 ] : ( ! [ U_23 ] : ~( U_26 = vplus(U_25, U_23) ) | ! [ U_24 ] : ~( U_25 = vplus(U_26, U_24) ) ),
% 0.78/1.03 inference(variable_rename,[status(thm)],[f_7_1]) ).
% 0.78/1.03
% 0.78/1.03 cnf(f_7_3, plain,
% 0.78/1.03 ( U_26 != vplus(U_25, U_23) | U_25 != vplus(U_26, U_24) ),
% 0.78/1.03 inference(clausify,[status(thm)],[f_7_2]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t1, plain, ( vd203 != vd204 | ~greater(vd203, vd204) ),
% 0.78/1.03 inference(start, [status(thm), parent(0:0)], [f_2_2]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t2, plain, ( vd203 = vd204 | vd204 = vplus(vd203, sK4(vd203, vd204)) | vd203 = vplus(vd204, sK3(vd203, vd204)) ),
% 0.78/1.03 inference(extension, [status(thm), parent(t1:1)], [f_5_5]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t3, plain, $false,
% 0.78/1.03 inference(connection, [status(thm), parent(t2:1)], [t2:1,t1:1]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t4, plain, ( vd204 != vplus(vd203, sK4(vd203, vd204)) | vd203 != vplus(vd204, sK2(vd204, vd203)) ),
% 0.78/1.03 inference(extension, [status(thm), parent(t2:2)], [f_7_3]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t5, plain, $false,
% 0.78/1.03 inference(connection, [status(thm), parent(t4:1)], [t4:1,t2:2]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t6, plain, ( vd203 = vplus(vd204, sK2(vd204, vd203)) | ~greater(vd203, vd204) ),
% 0.78/1.03 inference(extension, [status(thm), parent(t4:2)], [f_4_5]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t7, plain, $false,
% 0.78/1.03 inference(connection, [status(thm), parent(t6:1)], [t6:1,t4:2]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t8, plain, ( greater(vd203, vd204) ),
% 0.78/1.03 inference(extension, [status(thm), parent(t6:2)], [f_1_4]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t9, plain, $false,
% 0.78/1.03 inference(connection, [status(thm), parent(t8:1)], [t8:1,t6:2]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t10, plain, ( vd203 != vplus(vd204, sK3(vd203, vd204)) | vd204 != vplus(vd203, sK1(vd204, vd203)) ),
% 0.78/1.03 inference(extension, [status(thm), parent(t2:3)], [f_7_3]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t11, plain, $false,
% 0.78/1.03 inference(connection, [status(thm), parent(t10:1)], [t10:1,t2:3]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t12, plain, ( vd204 = vplus(vd203, sK1(vd204, vd203)) | ~less(vd203, vd204) ),
% 0.78/1.03 inference(extension, [status(thm), parent(t10:2)], [f_3_5]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t13, plain, $false,
% 0.78/1.03 inference(connection, [status(thm), parent(t12:1)], [t12:1,t10:2]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t14, plain, ( less(vd203, vd204) ),
% 0.78/1.03 inference(extension, [status(thm), parent(t12:2)], [f_1_5]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t15, plain, $false,
% 0.78/1.03 inference(connection, [status(thm), parent(t14:1)], [t14:1,t12:2]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t16, plain, ( greater(vd203, vd204) ),
% 0.78/1.03 inference(extension, [status(thm), parent(t1:2)], [f_1_4]) ).
% 0.78/1.03
% 0.78/1.03 cnf(t17, plain, $false,
% 0.78/1.03 inference(connection, [status(thm), parent(t16:1)], [t16:1,t1:2]) ).
% 0.78/1.03
% 0.78/1.03 % SZS output end Proof for theBenchmark
%------------------------------------------------------------------------------