%----Output an unreadable proof % SZS output start Proof for theBenchmark thf(type_def_5, type, a: $tType). thf(type_def_6, type, sTfun: ($tType * $tType) > $tType). thf(func_def_1, type, sK0: (a > a > a)). thf(func_def_2, type, sK1: (a > a > a)). thf(func_def_3, type, sK2: a). thf(func_def_4, type, sK3: a). thf(func_def_5, type, sK4: (a > a)). thf(func_def_6, type, sK5: a). thf(func_def_7, type, sK6: a). thf(func_def_8, type, sK7: a). thf(f1,conjecture,( ! [X2 : a,X3 : a,X1 : (a > a > a),X0 : (a > a > a)] : ((! [X4 : a] : (((X0 @ X3 @ X4)) = X4) & ! [X5 : a,X4 : a] : (((X0 @ (X1 @ X4 @ X5) @ X5)) = X5) & ! [X5 : a,X4 : a,X6 : a] : (((X1 @ X4 @ (X0 @ X5 @ X6))) = ((X0 @ (X1 @ X4 @ X5) @ (X1 @ X4 @ X6)))) & ! [X5 : a,X4 : a] : (((X1 @ (X0 @ X4 @ X5) @ X5)) = X5) & ! [X5 : a,X4 : a,X6 : a] : (((X0 @ X4 @ (X1 @ X5 @ X6))) = ((X1 @ (X0 @ X4 @ X5) @ (X0 @ X4 @ X6)))) & ! [X4 : a] : ? [X5 : a] : ((((X0 @ X4 @ X5)) = X2) & (((X1 @ X4 @ X5)) = X3)) & ! [X5 : a,X4 : a,X6 : a] : (((X0 @ (X0 @ X4 @ X5) @ X6)) = ((X0 @ X4 @ (X0 @ X5 @ X6)))) & ! [X4 : a] : (((X0 @ X2 @ X4)) = X2) & ! [X4 : a] : (((X1 @ X2 @ X4)) = X4) & ! [X4 : a] : (((X0 @ X4 @ X4)) = X4) & ! [X5 : a,X4 : a] : (((X0 @ X4 @ X5)) = ((X0 @ X5 @ X4))) & ! [X6 : a,X5 : a,X4 : a] : (((X1 @ (X1 @ X4 @ X5) @ X6)) = ((X1 @ X4 @ (X1 @ X5 @ X6)))) & ! [X5 : a,X4 : a] : (((X1 @ X4 @ X5)) = ((X1 @ X5 @ X4))) & ! [X4 : a] : (((X1 @ X3 @ X4)) = X3) & ! [X4 : a] : (((X1 @ X4 @ X4)) = X4)) => ! [X5 : a,X4 : a,X6 : a] : (((((X1 @ X4 @ X6)) = X3) & (((X0 @ X4 @ X5)) = X2) & (((X0 @ X4 @ X6)) = X2) & (((X1 @ X4 @ X5)) = X3)) => (X5 = X6)))), file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCD_LATTICE_THM_pme)). thf(f2,negated_conjecture,( ~ ! [X2 : a,X3 : a,X1 : (a > a > a),X0 : (a > a > a)] : ((! [X4 : a] : (((X0 @ X3 @ X4)) = X4) & ! [X5 : a,X4 : a] : (((X0 @ (X1 @ X4 @ X5) @ X5)) = X5) & ! [X5 : a,X4 : a,X6 : a] : (((X1 @ X4 @ (X0 @ X5 @ X6))) = ((X0 @ (X1 @ X4 @ X5) @ (X1 @ X4 @ X6)))) & ! [X5 : a,X4 : a] : (((X1 @ (X0 @ X4 @ X5) @ X5)) = X5) & ! [X5 : a,X4 : a,X6 : a] : (((X0 @ X4 @ (X1 @ X5 @ X6))) = ((X1 @ (X0 @ X4 @ X5) @ (X0 @ X4 @ X6)))) & ! [X4 : a] : ? [X5 : a] : ((((X0 @ X4 @ X5)) = X2) & (((X1 @ X4 @ X5)) = X3)) & ! [X5 : a,X4 : a,X6 : a] : (((X0 @ (X0 @ X4 @ X5) @ X6)) = ((X0 @ X4 @ (X0 @ X5 @ X6)))) & ! [X4 : a] : (((X0 @ X2 @ X4)) = X2) & ! [X4 : a] : (((X1 @ X2 @ X4)) = X4) & ! [X4 : a] : (((X0 @ X4 @ X4)) = X4) & ! [X5 : a,X4 : a] : (((X0 @ X4 @ X5)) = ((X0 @ X5 @ X4))) & ! [X6 : a,X5 : a,X4 : a] : (((X1 @ (X1 @ X4 @ X5) @ X6)) = ((X1 @ X4 @ (X1 @ X5 @ X6)))) & ! [X5 : a,X4 : a] : (((X1 @ X4 @ X5)) = ((X1 @ X5 @ X4))) & ! [X4 : a] : (((X1 @ X3 @ X4)) = X3) & ! [X4 : a] : (((X1 @ X4 @ X4)) = X4)) => ! [X5 : a,X4 : a,X6 : a] : (((((X1 @ X4 @ X6)) = X3) & (((X0 @ X4 @ X5)) = X2) & (((X0 @ X4 @ X6)) = X2) & (((X1 @ X4 @ X5)) = X3)) => (X5 = X6)))), inference(negated_conjecture,[status(cth)],[f1])). thf(f3,plain,( ~ ! [X1 : a,X0 : a,X2 : (a > a > a),X3 : (a > a > a)] : ((! [X13 : a,X12 : a,X14 : a] : (((X2 @ (X3 @ X13 @ X12) @ (X3 @ X13 @ X14))) = ((X3 @ X13 @ (X2 @ X12 @ X14)))) & ! [X5 : a,X6 : a] : (((X3 @ (X2 @ X6 @ X5) @ X5)) = X5) & ! [X11 : a,X10 : a] : (((X2 @ (X3 @ X11 @ X10) @ X10)) = X10) & ! [X20 : a] : (((X3 @ X0 @ X20)) = X0) & ! [X23 : a,X24 : a] : (((X3 @ X24 @ X23)) = ((X3 @ X23 @ X24))) & ! [X4 : a] : (((X3 @ X1 @ X4)) = X4) & ! [X26 : a,X27 : a,X25 : a] : (((X2 @ (X2 @ X27 @ X26) @ X25)) = ((X2 @ X27 @ (X2 @ X26 @ X25)))) & ! [X30 : a] : (((X2 @ X1 @ X30)) = X1) & ! [X31 : a] : (((X2 @ X31 @ X31)) = X31) & ! [X15 : a] : ? [X16 : a] : ((((X2 @ X15 @ X16)) = X1) & (((X3 @ X15 @ X16)) = X0)) & ! [X21 : a] : (((X2 @ X0 @ X21)) = X21) & ! [X9 : a,X8 : a,X7 : a] : (((X2 @ X8 @ (X3 @ X7 @ X9))) = ((X3 @ (X2 @ X8 @ X7) @ (X2 @ X8 @ X9)))) & ! [X18 : a,X17 : a,X19 : a] : (((X3 @ X18 @ (X3 @ X17 @ X19))) = ((X3 @ (X3 @ X18 @ X17) @ X19))) & ! [X22 : a] : (((X3 @ X22 @ X22)) = X22) & ! [X28 : a,X29 : a] : (((X2 @ X29 @ X28)) = ((X2 @ X28 @ X29)))) => ! [X34 : a,X33 : a,X32 : a] : (((((X3 @ X33 @ X34)) = X0) & (((X2 @ X33 @ X32)) = X1) & (((X3 @ X33 @ X32)) = X0) & (((X2 @ X33 @ X34)) = X1)) => (X32 = X34)))), inference(rectify,[],[f2])). thf(f4,plain,( ? [X1 : a,X0 : a,X2 : (a > a > a),X3 : (a > a > a)] : (? [X34 : a,X33 : a,X32 : a] : ((X32 != X34) & ((((X3 @ X33 @ X34)) = X0) & (((X2 @ X33 @ X32)) = X1) & (((X3 @ X33 @ X32)) = X0) & (((X2 @ X33 @ X34)) = X1))) & (! [X13 : a,X12 : a,X14 : a] : (((X2 @ (X3 @ X13 @ X12) @ (X3 @ X13 @ X14))) = ((X3 @ X13 @ (X2 @ X12 @ X14)))) & ! [X5 : a,X6 : a] : (((X3 @ (X2 @ X6 @ X5) @ X5)) = X5) & ! [X11 : a,X10 : a] : (((X2 @ (X3 @ X11 @ X10) @ X10)) = X10) & ! [X20 : a] : (((X3 @ X0 @ X20)) = X0) & ! [X23 : a,X24 : a] : (((X3 @ X24 @ X23)) = ((X3 @ X23 @ X24))) & ! [X4 : a] : (((X3 @ X1 @ X4)) = X4) & ! [X26 : a,X27 : a,X25 : a] : (((X2 @ (X2 @ X27 @ X26) @ X25)) = ((X2 @ X27 @ (X2 @ X26 @ X25)))) & ! [X30 : a] : (((X2 @ X1 @ X30)) = X1) & ! [X31 : a] : (((X2 @ X31 @ X31)) = X31) & ! [X15 : a] : ? [X16 : a] : ((((X2 @ X15 @ X16)) = X1) & (((X3 @ X15 @ X16)) = X0)) & ! [X21 : a] : (((X2 @ X0 @ X21)) = X21) & ! [X9 : a,X8 : a,X7 : a] : (((X2 @ X8 @ (X3 @ X7 @ X9))) = ((X3 @ (X2 @ X8 @ X7) @ (X2 @ X8 @ X9)))) & ! [X18 : a,X17 : a,X19 : a] : (((X3 @ X18 @ (X3 @ X17 @ X19))) = ((X3 @ (X3 @ X18 @ X17) @ X19))) & ! [X22 : a] : (((X3 @ X22 @ X22)) = X22) & ! [X28 : a,X29 : a] : (((X2 @ X29 @ X28)) = ((X2 @ X28 @ X29)))))), inference(ennf_transformation,[],[f3])). thf(f5,plain,( ? [X2 : (a > a > a),X3 : (a > a > a),X1 : a,X0 : a] : (! [X9 : a,X8 : a,X7 : a] : (((X2 @ X8 @ (X3 @ X7 @ X9))) = ((X3 @ (X2 @ X8 @ X7) @ (X2 @ X8 @ X9)))) & ! [X22 : a] : (((X3 @ X22 @ X22)) = X22) & ! [X20 : a] : (((X3 @ X0 @ X20)) = X0) & ! [X26 : a,X27 : a,X25 : a] : (((X2 @ (X2 @ X27 @ X26) @ X25)) = ((X2 @ X27 @ (X2 @ X26 @ X25)))) & ! [X15 : a] : ? [X16 : a] : ((((X2 @ X15 @ X16)) = X1) & (((X3 @ X15 @ X16)) = X0)) & ! [X13 : a,X12 : a,X14 : a] : (((X2 @ (X3 @ X13 @ X12) @ (X3 @ X13 @ X14))) = ((X3 @ X13 @ (X2 @ X12 @ X14)))) & ! [X18 : a,X17 : a,X19 : a] : (((X3 @ X18 @ (X3 @ X17 @ X19))) = ((X3 @ (X3 @ X18 @ X17) @ X19))) & ? [X32 : a,X33 : a,X34 : a] : ((((X3 @ X33 @ X34)) = X0) & (((X3 @ X33 @ X32)) = X0) & (((X2 @ X33 @ X32)) = X1) & (((X2 @ X33 @ X34)) = X1) & (X32 != X34)) & ! [X31 : a] : (((X2 @ X31 @ X31)) = X31) & ! [X5 : a,X6 : a] : (((X3 @ (X2 @ X6 @ X5) @ X5)) = X5) & ! [X11 : a,X10 : a] : (((X2 @ (X3 @ X11 @ X10) @ X10)) = X10) & ! [X4 : a] : (((X3 @ X1 @ X4)) = X4) & ! [X21 : a] : (((X2 @ X0 @ X21)) = X21) & ! [X23 : a,X24 : a] : (((X3 @ X24 @ X23)) = ((X3 @ X23 @ X24))) & ! [X28 : a,X29 : a] : (((X2 @ X29 @ X28)) = ((X2 @ X28 @ X29))) & ! [X30 : a] : (((X2 @ X1 @ X30)) = X1))), inference(flattening,[],[f4])). thf(f6,plain,( ? [X0 : (a > a > a),X1 : (a > a > a),X2 : a,X3 : a] : (! [X4 : a,X5 : a,X6 : a] : (((X0 @ X5 @ (X1 @ X6 @ X4))) = ((X1 @ (X0 @ X5 @ X6) @ (X0 @ X5 @ X4)))) & ! [X7 : a] : (((X1 @ X7 @ X7)) = X7) & ! [X8 : a] : (((X1 @ X3 @ X8)) = X3) & ! [X9 : a,X10 : a,X11 : a] : (((X0 @ X10 @ (X0 @ X9 @ X11))) = ((X0 @ (X0 @ X10 @ X9) @ X11))) & ! [X12 : a] : ? [X13 : a] : ((((X0 @ X12 @ X13)) = X2) & (((X1 @ X12 @ X13)) = X3)) & ! [X14 : a,X15 : a,X16 : a] : (((X0 @ (X1 @ X14 @ X15) @ (X1 @ X14 @ X16))) = ((X1 @ X14 @ (X0 @ X15 @ X16)))) & ! [X17 : a,X18 : a,X19 : a] : (((X1 @ (X1 @ X17 @ X18) @ X19)) = ((X1 @ X17 @ (X1 @ X18 @ X19)))) & ? [X20 : a,X21 : a,X22 : a] : ((((X1 @ X21 @ X22)) = X3) & (((X1 @ X21 @ X20)) = X3) & (((X0 @ X21 @ X20)) = X2) & (((X0 @ X21 @ X22)) = X2) & (X20 != X22)) & ! [X23 : a] : (((X0 @ X23 @ X23)) = X23) & ! [X24 : a,X25 : a] : (((X1 @ (X0 @ X25 @ X24) @ X24)) = X24) & ! [X26 : a,X27 : a] : (((X0 @ (X1 @ X26 @ X27) @ X27)) = X27) & ! [X28 : a] : (((X1 @ X2 @ X28)) = X28) & ! [X29 : a] : (((X0 @ X3 @ X29)) = X29) & ! [X30 : a,X31 : a] : (((X1 @ X31 @ X30)) = ((X1 @ X30 @ X31))) & ! [X32 : a,X33 : a] : (((X0 @ X32 @ X33)) = ((X0 @ X33 @ X32))) & ! [X34 : a] : (((X0 @ X2 @ X34)) = X2))), inference(rectify,[],[f5])). thf(f7,plain,( ! [X4 : a,X5 : a,X6 : a] : (((sK0 @ X5 @ (sK1 @ X6 @ X4))) = ((sK1 @ (sK0 @ X5 @ X6) @ (sK0 @ X5 @ X4)))) & ! [X7 : a] : (((sK1 @ X7 @ X7)) = X7) & ! [X8 : a] : (((sK1 @ sK3 @ X8)) = sK3) & ! [X9 : a,X10 : a,X11 : a] : (((sK0 @ (sK0 @ X10 @ X9) @ X11)) = ((sK0 @ X10 @ (sK0 @ X9 @ X11)))) & ! [X12 : a] : ((((sK0 @ X12 @ (sK4 @ X12))) = sK2) & (sK3 = ((sK1 @ X12 @ (sK4 @ X12))))) & ! [X14 : a,X15 : a,X16 : a] : (((sK0 @ (sK1 @ X14 @ X15) @ (sK1 @ X14 @ X16))) = ((sK1 @ X14 @ (sK0 @ X15 @ X16)))) & ! [X17 : a,X18 : a,X19 : a] : (((sK1 @ (sK1 @ X17 @ X18) @ X19)) = ((sK1 @ X17 @ (sK1 @ X18 @ X19)))) & ((((sK1 @ sK6 @ sK7)) = sK3) & (sK3 = ((sK1 @ sK6 @ sK5))) & (((sK0 @ sK6 @ sK5)) = sK2) & (sK2 = ((sK0 @ sK6 @ sK7))) & (sK7 != sK5)) & ! [X23 : a] : (((sK0 @ X23 @ X23)) = X23) & ! [X24 : a,X25 : a] : (((sK1 @ (sK0 @ X25 @ X24) @ X24)) = X24) & ! [X26 : a,X27 : a] : (((sK0 @ (sK1 @ X26 @ X27) @ X27)) = X27) & ! [X28 : a] : (((sK1 @ sK2 @ X28)) = X28) & ! [X29 : a] : (((sK0 @ sK3 @ X29)) = X29) & ! [X30 : a,X31 : a] : (((sK1 @ X31 @ X30)) = ((sK1 @ X30 @ X31))) & ! [X32 : a,X33 : a] : (((sK0 @ X32 @ X33)) = ((sK0 @ X33 @ X32))) & ! [X34 : a] : (((sK0 @ sK2 @ X34)) = sK2)), inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,vAPP,sK5,sK6,sK7]),skolemize(X0,$thf(sK0)),skolemize(X1,$thf(sK1)),skolemize(X2,$thf(sK2)),skolemize(X3,$thf(sK3)),skolemize(X13,$thf(sK4 @ X12)),skolemize(X20,$thf(sK5)),skolemize(X21,$thf(sK6)),skolemize(X22,$thf(sK7))],[f6])). thf(f9,plain,( ( ! [X32 : a,X33 : a] : ((((sK0 @ X32 @ X33)) = ((sK0 @ X33 @ X32)))) )), inference(cnf_transformation,[],[f7])). thf(f10,plain,( ( ! [X31 : a,X30 : a] : ((((sK1 @ X31 @ X30)) = ((sK1 @ X30 @ X31)))) )), inference(cnf_transformation,[],[f7])). thf(f11,plain,( ( ! [X29 : a] : ((((sK0 @ sK3 @ X29)) = X29)) )), inference(cnf_transformation,[],[f7])). thf(f12,plain,( ( ! [X28 : a] : ((((sK1 @ sK2 @ X28)) = X28)) )), inference(cnf_transformation,[],[f7])). thf(f13,plain,( ( ! [X26 : a,X27 : a] : ((((sK0 @ (sK1 @ X26 @ X27) @ X27)) = X27)) )), inference(cnf_transformation,[],[f7])). thf(f14,plain,( ( ! [X24 : a,X25 : a] : ((((sK1 @ (sK0 @ X25 @ X24) @ X24)) = X24)) )), inference(cnf_transformation,[],[f7])). thf(f16,plain,( (sK7 != sK5)), inference(cnf_transformation,[],[f7])). thf(f17,plain,( (sK2 = ((sK0 @ sK6 @ sK7)))), inference(cnf_transformation,[],[f7])). thf(f18,plain,( (((sK0 @ sK6 @ sK5)) = sK2)), inference(cnf_transformation,[],[f7])). thf(f19,plain,( (sK3 = ((sK1 @ sK6 @ sK5)))), inference(cnf_transformation,[],[f7])). thf(f20,plain,( (((sK1 @ sK6 @ sK7)) = sK3)), inference(cnf_transformation,[],[f7])). thf(f22,plain,( ( ! [X16 : a,X14 : a,X15 : a] : ((((sK0 @ (sK1 @ X14 @ X15) @ (sK1 @ X14 @ X16))) = ((sK1 @ X14 @ (sK0 @ X15 @ X16))))) )), inference(cnf_transformation,[],[f7])). thf(f23,plain,( ( ! [X12 : a] : ((sK3 = ((sK1 @ X12 @ (sK4 @ X12))))) )), inference(cnf_transformation,[],[f7])). thf(f24,plain,( ( ! [X12 : a] : ((((sK0 @ X12 @ (sK4 @ X12))) = sK2)) )), inference(cnf_transformation,[],[f7])). thf(f28,plain,( ( ! [X6 : a,X4 : a,X5 : a] : ((((sK0 @ X5 @ (sK1 @ X6 @ X4))) = ((sK1 @ (sK0 @ X5 @ X6) @ (sK0 @ X5 @ X4))))) )), inference(cnf_transformation,[],[f7])). thf(f36,plain,( ( ! [X0 : a] : ((((sK0 @ X0 @ sK3)) = X0)) )), inference(superposition,[],[f9,f11])). thf(f45,plain,( ( ! [X0 : a] : ((((sK1 @ X0 @ sK2)) = X0)) )), inference(superposition,[],[f10,f12])). thf(f53,plain,( ( ! [X26 : a,X27 : a] : ((((sK0 @ X27 @ (sK1 @ X26 @ X27))) = X27)) )), inference(forward_demodulation,[],[f13,f9])). thf(f58,plain,( ( ! [X24 : a,X25 : a] : ((((sK1 @ X24 @ (sK0 @ X25 @ X24))) = X24)) )), inference(forward_demodulation,[],[f14,f10])). thf(f171,plain,( ( ! [X0 : a,X1 : a] : ((((sK0 @ sK3 @ (sK1 @ X0 @ X1))) = ((sK1 @ X0 @ (sK0 @ (sK4 @ X0) @ X1))))) )), inference(superposition,[],[f22,f23])). thf(f173,plain,( ( ! [X0 : a] : ((((sK0 @ sK3 @ (sK1 @ sK6 @ X0))) = ((sK1 @ sK6 @ (sK0 @ sK5 @ X0))))) )), inference(superposition,[],[f22,f19])). thf(f174,plain,( ( ! [X0 : a] : ((((sK0 @ sK3 @ (sK1 @ sK6 @ X0))) = ((sK1 @ sK6 @ (sK0 @ sK7 @ X0))))) )), inference(superposition,[],[f22,f20])). thf(f186,plain,( ( ! [X0 : a] : ((((sK1 @ sK6 @ (sK0 @ sK7 @ X0))) = ((sK1 @ sK6 @ X0)))) )), inference(forward_demodulation,[],[f174,f11])). thf(f187,plain,( ( ! [X0 : a] : ((((sK1 @ sK6 @ (sK0 @ sK5 @ X0))) = ((sK1 @ sK6 @ X0)))) )), inference(forward_demodulation,[],[f173,f11])). thf(f192,plain,( ( ! [X0 : a,X1 : a] : ((((sK1 @ X0 @ X1)) = ((sK1 @ X0 @ (sK0 @ (sK4 @ X0) @ X1))))) )), inference(forward_demodulation,[],[f171,f11])). thf(f231,plain,( ( ! [X0 : a,X1 : a] : ((((sK0 @ X0 @ (sK1 @ (sK4 @ X0) @ X1))) = ((sK1 @ sK2 @ (sK0 @ X0 @ X1))))) )), inference(superposition,[],[f28,f24])). thf(f236,plain,( ( ! [X0 : a] : ((((sK0 @ sK6 @ (sK1 @ sK5 @ X0))) = ((sK1 @ sK2 @ (sK0 @ sK6 @ X0))))) )), inference(superposition,[],[f28,f18])). thf(f237,plain,( ( ! [X0 : a] : ((((sK1 @ sK2 @ (sK0 @ sK6 @ X0))) = ((sK0 @ sK6 @ (sK1 @ sK7 @ X0))))) )), inference(superposition,[],[f28,f17])). thf(f253,plain,( ( ! [X0 : a] : ((((sK0 @ sK6 @ (sK1 @ sK7 @ X0))) = ((sK0 @ sK6 @ X0)))) )), inference(forward_demodulation,[],[f237,f12])). thf(f255,plain,( ( ! [X0 : a] : ((((sK0 @ sK6 @ (sK1 @ sK5 @ X0))) = ((sK0 @ sK6 @ X0)))) )), inference(forward_demodulation,[],[f236,f12])). thf(f266,plain,( ( ! [X0 : a,X1 : a] : ((((sK0 @ X0 @ (sK1 @ (sK4 @ X0) @ X1))) = ((sK0 @ X0 @ X1)))) )), inference(forward_demodulation,[],[f231,f12])). thf(f893,plain,( (((sK1 @ sK6 @ (sK4 @ sK7))) = ((sK1 @ sK6 @ sK2)))), inference(superposition,[],[f186,f24])). thf(f917,plain,( (((sK1 @ sK6 @ (sK4 @ sK7))) = ((sK1 @ sK2 @ sK6)))), inference(forward_demodulation,[],[f893,f10])). thf(f926,plain,( (((sK1 @ sK6 @ (sK4 @ sK7))) = sK6)), inference(forward_demodulation,[],[f917,f12])). thf(f931,plain,( (((sK4 @ sK7)) = ((sK0 @ (sK4 @ sK7) @ sK6)))), inference(superposition,[],[f53,f926])). thf(f938,plain,( (((sK4 @ sK7)) = ((sK0 @ sK6 @ (sK4 @ sK7))))), inference(forward_demodulation,[],[f931,f9])). thf(f943,plain,( (((sK1 @ sK6 @ (sK4 @ sK5))) = ((sK1 @ sK6 @ sK2)))), inference(superposition,[],[f187,f24])). thf(f969,plain,( (((sK1 @ sK6 @ (sK4 @ sK5))) = ((sK1 @ sK2 @ sK6)))), inference(forward_demodulation,[],[f943,f10])). thf(f976,plain,( (((sK1 @ sK6 @ (sK4 @ sK5))) = sK6)), inference(forward_demodulation,[],[f969,f12])). thf(f980,plain,( (((sK0 @ (sK4 @ sK5) @ sK6)) = ((sK4 @ sK5)))), inference(superposition,[],[f53,f976])). thf(f986,plain,( (((sK4 @ sK5)) = ((sK0 @ sK6 @ (sK4 @ sK5))))), inference(forward_demodulation,[],[f980,f9])). thf(f1071,plain,( (((sK0 @ sK6 @ sK3)) = ((sK0 @ sK6 @ (sK4 @ sK7))))), inference(superposition,[],[f253,f23])). thf(f1095,plain,( (((sK4 @ sK7)) = ((sK0 @ sK6 @ sK3)))), inference(forward_demodulation,[],[f1071,f938])). thf(f1101,plain,( (((sK4 @ sK7)) = ((sK0 @ sK3 @ sK6)))), inference(forward_demodulation,[],[f1095,f9])). thf(f1103,plain,( (((sK4 @ sK7)) = sK6)), inference(forward_demodulation,[],[f1101,f11])). thf(f1114,plain,( (((sK0 @ sK6 @ sK3)) = ((sK0 @ sK6 @ (sK4 @ sK5))))), inference(superposition,[],[f255,f23])). thf(f1132,plain,( (((sK0 @ sK6 @ sK3)) = ((sK4 @ sK5)))), inference(forward_demodulation,[],[f1114,f986])). thf(f1143,plain,( (((sK4 @ sK5)) = ((sK0 @ sK3 @ sK6)))), inference(forward_demodulation,[],[f1132,f9])). thf(f1147,plain,( (((sK4 @ sK5)) = sK6)), inference(forward_demodulation,[],[f1143,f11])). thf(f1441,plain,( ( ! [X0 : a] : ((((sK1 @ X0 @ sK2)) = ((sK1 @ X0 @ (sK4 @ (sK4 @ X0)))))) )), inference(superposition,[],[f192,f24])). thf(f1489,plain,( ( ! [X0 : a] : ((((sK1 @ X0 @ (sK4 @ (sK4 @ X0)))) = X0)) )), inference(forward_demodulation,[],[f1441,f45])). thf(f1645,plain,( ( ! [X0 : a] : ((((sK0 @ X0 @ (sK4 @ (sK4 @ X0)))) = ((sK0 @ X0 @ sK3)))) )), inference(superposition,[],[f266,f23])). thf(f1695,plain,( ( ! [X0 : a] : ((((sK0 @ X0 @ (sK4 @ (sK4 @ X0)))) = X0)) )), inference(forward_demodulation,[],[f1645,f36])). thf(f1828,plain,( ( ! [X0 : a] : ((((sK1 @ (sK4 @ (sK4 @ X0)) @ X0)) = ((sK4 @ (sK4 @ X0))))) )), inference(superposition,[],[f58,f1695])). thf(f1844,plain,( ( ! [X0 : a] : ((((sK1 @ X0 @ (sK4 @ (sK4 @ X0)))) = ((sK4 @ (sK4 @ X0))))) )), inference(forward_demodulation,[],[f1828,f10])). thf(f1851,plain,( ( ! [X0 : a] : ((((sK4 @ (sK4 @ X0))) = X0)) )), inference(forward_demodulation,[],[f1844,f1489])). thf(f1999,plain,( (((sK4 @ sK6)) = sK5)), inference(superposition,[],[f1851,f1147])). thf(f2000,plain,( (((sK4 @ sK6)) = sK7)), inference(superposition,[],[f1851,f1103])). thf(f2175,plain,( (sK7 = sK5)), inference(forward_demodulation,[],[f2000,f1999])). thf(f2176,plain,( $false), inference(forward_subsumption_resolution,[],[f2175,f16])). % SZS output end Proof for theBenchmark