0.00/0.05 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.05 This is a problem 0.00/0.06 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 180 /export/starexec/sandbox/benchmark/theBenchmark.p 0.16/0.42 % Computer : n026.cluster.edu 0.16/0.42 % Model : x86_64 x86_64 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.16/0.42 % Memory : 8046.5625MB 0.16/0.42 % OS : Linux 6.8.0-71-generic 0.16/0.42 % CPULimit : 1440 0.16/0.42 % WCLimit : 180 0.16/0.42 % DateTime : Mon Jul 27 10:06:34 UTC 2026 0.16/0.42 % CPUTime : 117.27/117.70 % SZS status Theorem for theBenchmark 117.27/117.70 % SZS output start Proof for theBenchmark 117.27/117.70 fof(axiom_035, axiom, 117.27/117.70 ! [ X,Z,X3,Tx3 ] : ( just(Tx3) = index(X, X3) => ( tc(X, var(X3), Z) <=> Tx3 = Z ) ), 117.27/117.70 file('theBenchmark.p', axiom_035) ). 117.27/117.70 117.27/117.70 fof(axiom_026, axiom, 117.27/117.70 ! [ E ] : ( nf(E) <=> nf(lam(E)) ), 117.27/117.70 file('theBenchmark.p', axiom_026) ). 117.27/117.70 117.27/117.70 fof(axiom_027, axiom, 117.27/117.70 ! [ X4 ] : nf(var(X4)), 117.27/117.70 file('theBenchmark.p', axiom_027) ). 117.27/117.70 117.27/117.70 fof(axiom_033, axiom, 117.27/117.70 ! [ X,E,Tx2,T1 ] : ( tc(cons(Tx2, X), E, T1) <=> tc(X, lam(E), arr(Tx2, T1)) ), 117.27/117.70 file('theBenchmark.p', axiom_033) ). 117.27/117.70 117.27/117.70 fof(goal_036, conjecture, 117.27/117.70 ? [ E ] : ( nf(E) & tc(nil, E, arr(a, arr(b, b))) ), 117.27/117.70 file('theBenchmark.p', goal_036) ). 117.27/117.70 117.27/117.70 fof(axiom_029, axiom, 117.27/117.70 ! [ Z,Xs ] : just(Z) = index(cons(Z, Xs), zero), 117.27/117.70 file('theBenchmark.p', axiom_029) ). 117.27/117.70 117.27/117.70 fof(f_2_1, plain, 117.27/117.70 ! [ X,Z,X3,Tx3 ] : ( ~( just(Tx3) = index(X, X3) ) | ( ( ~( tc(X, var(X3), Z) ) | Tx3 = Z ) & ( ~( Tx3 = Z ) | tc(X, var(X3), Z) ) ) ), 117.27/117.70 inference(fof_nnf,[status(thm)],[axiom_035]) ). 117.27/117.70 117.27/117.70 fof(f_2_2, plain, 117.27/117.70 ! [ U_7,U_6,U_5,U_4 ] : ( ~( just(U_4) = index(U_7, U_5) ) | ( ( ~( tc(U_7, var(U_5), U_6) ) | U_4 = U_6 ) & ( ~( U_4 = U_6 ) | tc(U_7, var(U_5), U_6) ) ) ), 117.27/117.70 inference(variable_rename,[status(thm)],[f_2_1]) ). 117.27/117.70 117.27/117.70 cnf(f_2_4, plain, 117.27/117.70 ( just(U_4) != index(U_7, U_5) | U_4 != U_6 | tc(U_7, var(U_5), U_6) ), 117.27/117.70 inference(clausify,[status(thm)],[f_2_2]) ). 117.27/117.70 117.27/117.70 fof(f_9_1, plain, 117.27/117.70 ! [ E ] : ( ( ~( nf(E) ) | nf(lam(E)) ) & ( ~( nf(lam(E)) ) | nf(E) ) ), 117.27/117.70 inference(fof_nnf,[status(thm)],[axiom_026]) ). 117.27/117.70 117.27/117.70 fof(f_9_2, plain, 117.27/117.70 ! [ U_22 ] : ( ( ~( nf(U_22) ) | nf(lam(U_22)) ) & ( ~( nf(lam(U_22)) ) | nf(U_22) ) ), 117.27/117.70 inference(variable_rename,[status(thm)],[f_9_1]) ). 117.27/117.70 117.27/117.70 fof(f_9_3, plain, 117.27/117.70 ( ! [ U_23 ] : ( ~( nf(U_23) ) | nf(lam(U_23)) ) & ! [ U_24 ] : ( ~( nf(lam(U_24)) ) | nf(U_24) ) ), 117.27/117.70 inference(miniscope,[status(thm)],[f_9_2]) ). 117.27/117.70 117.27/117.70 cnf(f_9_4, plain, 117.27/117.70 ( ~nf(U_23) | nf(lam(U_23)) ), 117.27/117.70 inference(clausify,[status(thm)],[f_9_3]) ). 117.27/117.70 117.27/117.70 fof(f_11_1, plain, 117.27/117.70 ! [ X4 ] : nf(var(X4)), 117.27/117.70 inference(fof_nnf,[status(thm)],[axiom_027]) ). 117.27/117.70 117.27/117.70 fof(f_11_2, plain, 117.27/117.70 ! [ U_40 ] : nf(var(U_40)), 117.27/117.70 inference(variable_rename,[status(thm)],[f_11_1]) ). 117.27/117.70 117.27/117.70 cnf(f_11_3, plain, 117.27/117.70 ( nf(var(U_40)) ), 117.27/117.70 inference(clausify,[status(thm)],[f_11_2]) ). 117.27/117.70 117.27/117.70 fof(f_23_1, plain, 117.27/117.70 ! [ X,E,Tx2,T1 ] : ( ( ~( tc(cons(Tx2, X), E, T1) ) | tc(X, lam(E), arr(Tx2, T1)) ) & ( ~( tc(X, lam(E), arr(Tx2, T1)) ) | tc(cons(Tx2, X), E, T1) ) ), 117.27/117.70 inference(fof_nnf,[status(thm)],[axiom_033]) ). 117.27/117.70 117.27/117.70 fof(f_23_2, plain, 117.27/117.70 ! [ U_64,U_63,U_62,U_61 ] : ( ( ~( tc(cons(U_62, U_64), U_63, U_61) ) | tc(U_64, lam(U_63), arr(U_62, U_61)) ) & ( ~( tc(U_64, lam(U_63), arr(U_62, U_61)) ) | tc(cons(U_62, U_64), U_63, U_61) ) ), 117.27/117.70 inference(variable_rename,[status(thm)],[f_23_1]) ). 117.27/117.70 117.27/117.70 fof(f_23_3, plain, 117.27/117.70 ( ! [ U_71,U_69,U_67,U_65 ] : ( ~( tc(cons(U_67, U_71), U_69, U_65) ) | tc(U_71, lam(U_69), arr(U_67, U_65)) ) & ! [ U_72,U_70,U_68,U_66 ] : ( ~( tc(U_72, lam(U_70), arr(U_68, U_66)) ) | tc(cons(U_68, U_72), U_70, U_66) ) ), 117.27/117.70 inference(miniscope,[status(thm)],[f_23_2]) ). 117.27/117.70 117.27/117.70 cnf(f_23_4, plain, 117.27/117.70 ( ~tc(cons(U_67, U_71), U_69, U_65) | tc(U_71, lam(U_69), arr(U_67, U_65)) ), 117.27/117.70 inference(clausify,[status(thm)],[f_23_3]) ). 117.27/117.70 117.27/117.70 fof(f_25_1, negated_conjecture, 117.27/117.70 ~( ? [ E ] : ( nf(E) & tc(nil, E, arr(a, arr(b, b))) ) ), 117.27/117.70 inference(negate,[status(cth)],[goal_036]) ). 117.27/117.70 117.27/117.70 fof(f_25_2, negated_conjecture, 117.27/117.70 ! [ E ] : ( ~( nf(E) ) | ~( tc(nil, E, arr(a, arr(b, b))) ) ), 117.27/117.70 inference(fof_nnf,[status(thm)],[f_25_1]) ). 117.27/117.70 117.27/117.70 fof(f_25_3, negated_conjecture, 117.27/117.70 ! [ U_76 ] : ( ~( nf(U_76) ) | ~( tc(nil, U_76, arr(a, arr(b, b))) ) ), 117.27/117.70 inference(variable_rename,[status(thm)],[f_25_2]) ). 117.27/117.70 117.27/117.70 cnf(f_25_4, negated_conjecture, 117.27/117.70 ( ~nf(U_76) | ~tc(nil, U_76, arr(a, arr(b, b))) ), 117.27/117.70 inference(clausify,[status(thm)],[f_25_3]) ). 117.27/117.70 117.27/117.70 fof(f_33_1, plain, 117.27/117.70 ! [ Z,Xs ] : just(Z) = index(cons(Z, Xs), zero), 117.27/117.70 inference(fof_nnf,[status(thm)],[axiom_029]) ). 117.27/117.70 117.27/117.70 fof(f_33_2, plain, 117.27/117.70 ! [ U_89,U_88 ] : just(U_89) = index(cons(U_89, U_88), zero), 117.27/117.70 inference(variable_rename,[status(thm)],[f_33_1]) ). 117.27/117.70 117.27/117.70 cnf(f_33_3, plain, 117.27/117.70 ( just(U_89) = index(cons(U_89, U_88), zero) ), 117.27/117.70 inference(clausify,[status(thm)],[f_33_2]) ). 117.27/117.70 117.27/117.70 cnf(equality_1, axiom, 117.27/117.70 ( Eq_x_0 = Eq_x_0 ), 117.27/117.70 theory(equality,[reflexivity]) ). 117.27/117.70 117.27/117.70 cnf(equality_24, axiom, 117.27/117.70 ( Eq_x_0 != Eq_y_0 | ~nf(Eq_x_0) | nf(Eq_y_0) ), 117.27/117.70 theory(equality,[substitution_predicates]) ). 117.27/117.70 117.27/117.70 cnf(t1, plain, ( ~tc(nil, lam(lam(var(zero))), arr(a, arr(b, b))) | ~nf(lam(lam(var(zero)))) ), 117.27/117.70 inference(start, [status(thm), parent(0:0)], [f_25_4]) ). 117.27/117.70 117.27/117.70 cnf(t2, plain, ( tc(nil, lam(lam(var(zero))), arr(a, arr(b, b))) | ~tc(cons(a, nil), lam(var(zero)), arr(b, b)) ), 117.27/117.70 inference(extension, [status(thm), parent(t1:1)], [f_23_4]) ). 117.27/117.70 117.27/117.70 cnf(t3, plain, $false, 117.27/117.70 inference(connection, [status(thm), parent(t2:1)], [t2:1,t1:1]) ). 117.27/117.70 117.27/117.70 cnf(t4, plain, ( tc(cons(a, nil), lam(var(zero)), arr(b, b)) | ~tc(cons(b, cons(a, nil)), var(zero), b) ), 117.27/117.70 inference(extension, [status(thm), parent(t2:2)], [f_23_4]) ). 117.27/117.70 117.27/117.70 cnf(t5, plain, $false, 117.27/117.70 inference(connection, [status(thm), parent(t4:1)], [t4:1,t2:2]) ). 117.27/117.70 117.27/117.70 cnf(t6, plain, ( tc(cons(b, cons(a, nil)), var(zero), b) | just(b) != index(cons(b, cons(a, nil)), zero) | b != b ), 117.27/117.70 inference(extension, [status(thm), parent(t4:2)], [f_2_4]) ). 117.27/117.70 117.27/117.70 cnf(t7, plain, $false, 117.27/117.70 inference(connection, [status(thm), parent(t6:1)], [t6:1,t4:2]) ). 117.27/117.70 117.27/117.70 cnf(t8, plain, ( just(b) = index(cons(b, cons(a, nil)), zero) ), 117.27/117.70 inference(extension, [status(thm), parent(t6:2)], [f_33_3]) ). 117.27/117.70 117.27/117.70 cnf(t9, plain, $false, 117.27/117.70 inference(connection, [status(thm), parent(t8:1)], [t8:1,t6:2]) ). 117.27/117.70 117.27/117.70 cnf(t10, plain, ( b = b ), 117.27/117.70 inference(extension, [status(thm), parent(t6:3)], [equality_1]) ). 117.27/117.70 117.27/117.70 cnf(t11, plain, $false, 117.27/117.70 inference(connection, [status(thm), parent(t10:1)], [t10:1,t6:3]) ). 117.27/117.70 117.27/117.70 cnf(t12, plain, ( nf(lam(lam(var(zero)))) | ~nf(lam(var(zero))) ), 117.27/117.70 inference(extension, [status(thm), parent(t1:2)], [f_9_4]) ). 117.27/117.70 117.27/117.70 cnf(t13, plain, $false, 117.27/117.70 inference(connection, [status(thm), parent(t12:1)], [t12:1,t1:2]) ). 117.27/117.70 117.27/117.70 cnf(t14, plain, ( nf(lam(var(zero))) | ~nf(var(zero)) ), 117.27/117.70 inference(extension, [status(thm), parent(t12:2)], [f_9_4]) ). 117.27/117.70 117.27/117.70 cnf(t15, plain, $false, 117.27/117.70 inference(connection, [status(thm), parent(t14:1)], [t14:1,t12:2]) ). 117.27/117.70 117.27/117.70 cnf(t16, plain, ( nf(var(zero)) | ~nf(var(zero)) | var(zero) != var(zero) ), 117.27/117.70 inference(extension, [status(thm), parent(t14:2)], [equality_24]) ). 117.27/117.70 117.27/117.70 cnf(t17, plain, $false, 117.27/117.70 inference(connection, [status(thm), parent(t16:1)], [t16:1,t14:2]) ). 117.27/117.70 117.27/117.70 cnf(t18, plain, ( nf(var(zero)) ), 117.27/117.70 inference(extension, [status(thm), parent(t16:2)], [f_11_3]) ). 117.27/117.70 117.27/117.70 cnf(t19, plain, $false, 117.27/117.70 inference(connection, [status(thm), parent(t18:1)], [t18:1,t16:2]) ). 117.27/117.70 117.27/117.70 cnf(t20, plain, ( var(zero) = var(zero) ), 117.27/117.70 inference(extension, [status(thm), parent(t16:3)], [equality_1]) ). 117.27/117.70 117.27/117.70 cnf(t21, plain, $false, 117.27/117.70 inference(connection, [status(thm), parent(t20:1)], [t20:1,t16:3]) ). 117.27/117.70 117.27/117.70 % SZS output end Proof for theBenchmark 117.47/117.97 EOF