%------------------------------------------------------------------------------ % File : Etableau---0.67 % Problem : SWX190+1 : TPTP v9.3.0. Released v9.3.0. % Transfm : none % Format : tptp:raw % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s % Computer : n003.cluster.edu % Model : x86_64 x86_64 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz % Memory : 8042.1875MB % OS : Linux 3.10.0-693.el7.x86_64 % CPULimit : 300s % WCLimit : 300s % DateTime : Tue May 5 07:00:41 PM UTC 2026 % Result : Theorem 0.20s 0.42s % Output : Assurance 0s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----No solution output by system %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : SWX190+1 : TPTP v9.3.0. Released v9.3.0. % 0.00/0.13 % Command : etableau --auto --tsmdo --quicksat=10000 --tableau=1 --tableau-saturation=1 -s -p --tableau-cores=8 --cpu-limit=%d %s % 0.17/0.34 % Computer : n003.cluster.edu % 0.17/0.34 % Model : x86_64 x86_64 % 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.34 % Memory : 8042.1875MB % 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.34 % CPULimit : 300 % 0.17/0.34 % WCLimit : 300 % 0.17/0.34 % DateTime : Tue May 5 09:52:56 EDT 2026 % 0.17/0.34 % CPUTime : % 0.20/0.37 # No SInE strategy applied % 0.20/0.37 # Auto-Mode selected heuristic G_E___208_C18_F1_SE_CS_SP_PS_S5PRR_RG_S04AN % 0.20/0.37 # and selection function SelectComplexExceptUniqMaxHorn. % 0.20/0.37 # % 0.20/0.37 # Presaturation interreduction done % 0.20/0.37 # Number of axioms: 53 Number of unprocessed: 53 % 0.20/0.37 # Tableaux proof search. % 0.20/0.37 # APR header successfully linked. % 0.20/0.37 # Hello from C++ % 0.20/0.38 # The folding up rule is enabled... % 0.20/0.38 # Local unification is enabled... % 0.20/0.38 # Any saturation attempts will use folding labels... % 0.20/0.38 # 53 beginning clauses after preprocessing and clausification % 0.20/0.38 # Creating start rules for all 1 conjectures. % 0.20/0.38 # There are 1 start rule candidates: % 0.20/0.38 # Found 40 unit axioms. % 0.20/0.38 # 1 start rule tableaux created. % 0.20/0.38 # 13 extension rule candidate clauses % 0.20/0.38 # 40 unit axiom clauses % 0.20/0.38 % 0.20/0.38 # Requested 8, 32 cores available to the main process. % 0.20/0.38 # There are not enough tableaux to fork, creating more from the initial 1 % 0.20/0.38 # Creating equality axioms % 0.20/0.38 # Ran out of tableaux, making start rules for all clauses % 0.20/0.38 # Returning from population with 87 new_tableaux and 0 remaining starting tableaux. % 0.20/0.38 # We now have 87 tableaux to operate on % 0.20/0.42 # There were 1 total branch saturation attempts. % 0.20/0.42 # There were 0 of these attempts blocked. % 0.20/0.42 # There were 0 deferred branch saturation attempts. % 0.20/0.42 # There were 0 free duplicated saturations. % 0.20/0.42 # There were 1 total successful branch saturations. % 0.20/0.42 # There were 0 successful branch saturations in interreduction. % 0.20/0.42 # There were 0 successful branch saturations on the branch. % 0.20/0.42 # There were 1 successful branch saturations after the branch. % 0.20/0.42 # There were 1 total branch saturation attempts. % 0.20/0.42 # There were 0 of these attempts blocked. % 0.20/0.42 # There were 0 deferred branch saturation attempts. % 0.20/0.42 # There were 0 free duplicated saturations. % 0.20/0.42 # There were 1 total successful branch saturations. % 0.20/0.42 # There were 0 successful branch saturations in interreduction. % 0.20/0.42 # There were 0 successful branch saturations on the branch. % 0.20/0.42 # There were 1 successful branch saturations after the branch. % 0.20/0.42 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # Begin clausification derivation % 0.20/0.42 % 0.20/0.42 # End clausification derivation % 0.20/0.42 # Begin listing active clauses obtained from FOF to CNF conversion % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X1)))=opt(d(X1)))). % 0.20/0.42 cnf(i_0_42, plain, (d(x2)=n(s(z)))). % 0.20/0.42 cnf(i_0_1, plain, (proj1S(s(X1))=X1)). % 0.20/0.42 cnf(i_0_3, plain, (proj1N(n(X1))=X1)). % 0.20/0.42 cnf(i_0_46, plain, (mulNat(z,X1)=z)). % 0.20/0.42 cnf(i_0_39, plain, (d(n(X1))=n(z))). % 0.20/0.42 cnf(i_0_44, plain, (addNat(z,X1)=X1)). % 0.20/0.42 cnf(i_0_22, plain, (fail(X1,n(z))=X1)). % 0.20/0.42 cnf(i_0_4, plain, (proj1(x(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_38, plain, (fail3(X1,n(z))=n(z))). % 0.20/0.42 cnf(i_0_5, plain, (proj2(x(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_6, plain, (proj12(y(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_7, plain, (proj22(y(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_30, plain, (fail22(X1,n(s(z)))=X1)). % 0.20/0.42 cnf(i_0_34, plain, (fail12(n(s(z)),X1)=X1)). % 0.20/0.42 cnf(i_0_50, plain, (opt(x(n(z),X1))=X1)). % 0.20/0.42 cnf(i_0_40, plain, (x(d(X1),d(X2))=d(x(X1,X2)))). % 0.20/0.42 cnf(i_0_53, plain, (opt(y(n(z),X1))=n(z))). % 0.20/0.42 cnf(i_0_31, plain, (fail32(X1,n(z))=fail22(X1,n(z)))). % 0.20/0.42 cnf(i_0_35, plain, (fail12(n(z),X1)=fail22(n(z),X1))). % 0.20/0.42 cnf(i_0_43, plain, (addNat(s(X1),X2)=s(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_26, plain, (n(mulNat(X1,X2))=fail32(n(X1),n(X2)))). % 0.20/0.42 cnf(i_0_45, plain, (addNat(X1,mulNat(X2,X1))=mulNat(s(X2),X1))). % 0.20/0.42 cnf(i_0_19, plain, (fail1(n(X1),n(X2))=n(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_21, plain, (fail1(X1,n(s(X2)))=fail(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_37, plain, (fail3(X1,n(s(X2)))=fail12(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_49, plain, (fail(n(s(X1)),X2)=opt(x(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_52, plain, (fail3(n(s(X1)),X2)=opt(y(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_27, plain, (opt(y(X1,y(X2,X3)))=fail32(y(X1,X2),X3))). % 0.20/0.42 cnf(i_0_29, plain, (fail32(X1,n(s(s(X2))))=fail22(X1,n(s(s(X2)))))). % 0.20/0.42 cnf(i_0_41, plain, (x(y(d(X1),X2),y(X1,d(X2)))=d(y(X1,X2)))). % 0.20/0.42 cnf(i_0_33, plain, (fail12(n(s(s(X1))),X2)=fail22(n(s(s(X1))),X2))). % 0.20/0.42 cnf(i_0_14, plain, (fail2(X1,X1)=y(n(s(s(z))),opt(X1)))). % 0.20/0.42 cnf(i_0_2, plain, (s(X1)!=z)). % 0.20/0.42 cnf(i_0_10, plain, (n(X1)!=x2)). % 0.20/0.42 cnf(i_0_12, plain, (x(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_13, plain, (y(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_8, plain, (n(X1)!=x(X2,X3))). % 0.20/0.42 cnf(i_0_9, plain, (n(X1)!=y(X2,X3))). % 0.20/0.42 cnf(i_0_11, plain, (y(X1,X2)!=x(X3,X4))). % 0.20/0.42 cnf(i_0_17, plain, (fail2(X1,X2)=fail1(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_20, plain, (fail1(X1,X2)=fail(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_28, plain, (fail32(X1,X2)=fail22(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_32, plain, (fail12(X1,X2)=fail22(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_36, plain, (fail3(X1,X2)=fail12(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_48, plain, (fail(X1,X2)=opt(x(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_51, plain, (fail3(X1,X2)=opt(y(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_18, plain, (fail2(n(X1),X2)=fail1(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_25, plain, (y(opt(n(X1)),opt(X2))=fail32(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_47, plain, (y(proj12(X1),proj22(X1))=X1|x(proj1(X1),proj2(X1))=X1|opt(X1)=X1)). % 0.20/0.42 cnf(i_0_16, plain, (fail2(x(X1,X2),X3)=opt(x(X1,x(X2,X3)))|x(X1,X2)=X3)). % 0.20/0.42 cnf(i_0_15, plain, (x(opt(X1),opt(X2))=fail2(X1,X2)|x(proj1(X1),proj2(X1))=X1|X1=X2)). % 0.20/0.42 cnf(i_0_24, plain, (y(opt(X1),opt(X2))=fail32(X1,X2)|y(proj12(X1),proj22(X1))=X1|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_86, plain, (X121=X121)). % 0.20/0.42 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.20/0.42 # Begin printing tableau % 0.20/0.42 # Found 6 steps % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X6)))=opt(d(X6))), inference(start_rule)). % 0.20/0.42 cnf(i_0_111, plain, (opt(d(opt(X6)))=opt(d(X6))), inference(extension_rule, [i_0_109])). % 0.20/0.42 cnf(i_0_267, plain, (opt(d(opt(X1)))!=opt(d(X1))), inference(closure_rule, [i_0_54])). % 0.20/0.42 cnf(i_0_265, plain, (fail3(opt(d(opt(X6))),opt(d(opt(X1))))=fail3(opt(d(X6)),opt(d(X1)))), inference(extension_rule, [i_0_89])). % 0.20/0.42 cnf(i_0_305, plain, (fail3(opt(d(X6)),opt(d(X1)))!=proj2(x(X1,fail3(opt(d(X6)),opt(d(X1)))))), inference(closure_rule, [i_0_5])). % 0.20/0.42 cnf(i_0_303, plain, (fail3(opt(d(opt(X6))),opt(d(opt(X1))))=proj2(x(X1,fail3(opt(d(X6)),opt(d(X1)))))), inference(etableau_closure_rule, [i_0_303, ...])). % 0.20/0.42 # End printing tableau % 0.20/0.42 # SZS output end % 0.20/0.42 # Branches closed# There were 1 total branch saturation attempts. % 0.20/0.42 # There were 0 of these attempts blocked. % 0.20/0.42 # There were 0 deferred branch saturation attempts. % 0.20/0.42 # There were 0 free duplicated saturations. % 0.20/0.42 # There were 1 total successful branch saturations. % 0.20/0.42 # There were 0 successful branch saturations in interreduction. % 0.20/0.42 # There were 0 successful branch saturations on the branch. % 0.20/0.42 # There were 1 successful branch saturations after the branch. % 0.20/0.42 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # Begin clausification derivation % 0.20/0.42 % 0.20/0.42 # End clausification derivation % 0.20/0.42 # Begin listing active clauses obtained from FOF to CNF conversion % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X1)))=opt(d(X1)))). % 0.20/0.42 cnf(i_0_42, plain, (d(x2)=n(s(z)))). % 0.20/0.42 cnf(i_0_1, plain, (proj1S(s(X1))=X1)). % 0.20/0.42 cnf(i_0_3, plain, (proj1N(n(X1))=X1)). % 0.20/0.42 cnf(i_0_46, plain, (mulNat(z,X1)=z)). % 0.20/0.42 cnf(i_0_39, plain, (d(n(X1))=n(z))). % 0.20/0.42 cnf(i_0_44, plain, (addNat(z,X1)=X1)). % 0.20/0.42 cnf(i_0_22, plain, (fail(X1,n(z))=X1)). % 0.20/0.42 cnf(i_0_4, plain, (proj1(x(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_38, plain, (fail3(X1,n(z))=n(z))). % 0.20/0.42 cnf(i_0_5, plain, (proj2(x(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_6, plain, (proj12(y(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_7, plain, (proj22(y(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_30, plain, (fail22(X1,n(s(z)))=X1)). % 0.20/0.42 cnf(i_0_34, plain, (fail12(n(s(z)),X1)=X1)). % 0.20/0.42 cnf(i_0_50, plain, (opt(x(n(z),X1))=X1)). % 0.20/0.42 cnf(i_0_40, plain, (x(d(X1),d(X2))=d(x(X1,X2)))). % 0.20/0.42 cnf(i_0_53, plain, (opt(y(n(z),X1))=n(z))). % 0.20/0.42 cnf(i_0_31, plain, (fail32(X1,n(z))=fail22(X1,n(z)))). % 0.20/0.42 cnf(i_0_35, plain, (fail12(n(z),X1)=fail22(n(z),X1))). % 0.20/0.42 cnf(i_0_43, plain, (addNat(s(X1),X2)=s(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_26, plain, (n(mulNat(X1,X2))=fail32(n(X1),n(X2)))). % 0.20/0.42 cnf(i_0_45, plain, (addNat(X1,mulNat(X2,X1))=mulNat(s(X2),X1))). % 0.20/0.42 cnf(i_0_19, plain, (fail1(n(X1),n(X2))=n(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_21, plain, (fail1(X1,n(s(X2)))=fail(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_37, plain, (fail3(X1,n(s(X2)))=fail12(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_49, plain, (fail(n(s(X1)),X2)=opt(x(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_52, plain, (fail3(n(s(X1)),X2)=opt(y(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_27, plain, (opt(y(X1,y(X2,X3)))=fail32(y(X1,X2),X3))). % 0.20/0.42 cnf(i_0_29, plain, (fail32(X1,n(s(s(X2))))=fail22(X1,n(s(s(X2)))))). % 0.20/0.42 cnf(i_0_41, plain, (x(y(d(X1),X2),y(X1,d(X2)))=d(y(X1,X2)))). % 0.20/0.42 cnf(i_0_33, plain, (fail12(n(s(s(X1))),X2)=fail22(n(s(s(X1))),X2))). % 0.20/0.42 cnf(i_0_14, plain, (fail2(X1,X1)=y(n(s(s(z))),opt(X1)))). % 0.20/0.42 cnf(i_0_2, plain, (s(X1)!=z)). % 0.20/0.42 cnf(i_0_10, plain, (n(X1)!=x2)). % 0.20/0.42 cnf(i_0_12, plain, (x(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_13, plain, (y(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_8, plain, (n(X1)!=x(X2,X3))). % 0.20/0.42 cnf(i_0_9, plain, (n(X1)!=y(X2,X3))). % 0.20/0.42 cnf(i_0_11, plain, (y(X1,X2)!=x(X3,X4))). % 0.20/0.42 cnf(i_0_17, plain, (fail2(X1,X2)=fail1(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_20, plain, (fail1(X1,X2)=fail(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_28, plain, (fail32(X1,X2)=fail22(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_32, plain, (fail12(X1,X2)=fail22(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_36, plain, (fail3(X1,X2)=fail12(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_48, plain, (fail(X1,X2)=opt(x(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_51, plain, (fail3(X1,X2)=opt(y(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_18, plain, (fail2(n(X1),X2)=fail1(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_25, plain, (y(opt(n(X1)),opt(X2))=fail32(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_47, plain, (y(proj12(X1),proj22(X1))=X1|x(proj1(X1),proj2(X1))=X1|opt(X1)=X1)). % 0.20/0.42 cnf(i_0_16, plain, (fail2(x(X1,X2),X3)=opt(x(X1,x(X2,X3)))|x(X1,X2)=X3)). % 0.20/0.42 cnf(i_0_15, plain, (x(opt(X1),opt(X2))=fail2(X1,X2)|x(proj1(X1),proj2(X1))=X1|X1=X2)). % 0.20/0.42 cnf(i_0_24, plain, (y(opt(X1),opt(X2))=fail32(X1,X2)|y(proj12(X1),proj22(X1))=X1|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_86, plain, (X121=X121)). % 0.20/0.42 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.20/0.42 # Begin printing tableau % 0.20/0.42 # Found 5 steps % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X4)))=opt(d(X4))), inference(start_rule)). % 0.20/0.42 cnf(i_0_111, plain, (opt(d(opt(X4)))=opt(d(X4))), inference(extension_rule, [i_0_110])). % 0.20/0.42 cnf(i_0_268, plain, (d(opt(d(opt(X4))))=d(opt(d(X4)))), inference(extension_rule, [i_0_89])). % 0.20/0.42 cnf(i_0_305, plain, (d(opt(d(X4)))!=proj1S(s(d(opt(d(X4)))))), inference(closure_rule, [i_0_1])). % 0.20/0.42 cnf(i_0_303, plain, (d(opt(d(opt(X4))))=proj1S(s(d(opt(d(X4)))))), inference(etableau_closure_rule, [i_0_303, ...])). % 0.20/0.42 # End printing tableau % 0.20/0.42 # SZS output end % 0.20/0.42 # Branches closed with saturation will be marked with an "s" % 0.20/0.42 # There were 1 total branch saturation attempts. % 0.20/0.42 # There were 0 of these attempts blocked. % 0.20/0.42 # There were 0 deferred branch saturation attempts. % 0.20/0.42 # There were 0 free duplicated saturations. % 0.20/0.42 # There were 1 total successful branch saturations. % 0.20/0.42 # There were 0 successful branch saturations in interreduction. % 0.20/0.42 # There were 0 successful branch saturations on the branch. % 0.20/0.42 # There were 1 successful branch saturations after the branch. % 0.20/0.42 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # Begin clausification derivation % 0.20/0.42 % 0.20/0.42 # End clausification derivation % 0.20/0.42 # Begin listing active clauses obtained from FOF to CNF conversion % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X1)))=opt(d(X1)))). % 0.20/0.42 cnf(i_0_42, plain, (d(x2)=n(s(z)))). % 0.20/0.42 cnf(i_0_1, plain, (proj1S(s(X1))=X1)). % 0.20/0.42 cnf(i_0_3, plain, (proj1N(n(X1))=X1)). % 0.20/0.42 cnf(i_0_46, plain, (mulNat(z,X1)=z)). % 0.20/0.42 cnf(i_0_39, plain, (d(n(X1))=n(z))). % 0.20/0.42 cnf(i_0_44, plain, (addNat(z,X1)=X1)). % 0.20/0.42 cnf(i_0_22, plain, (fail(X1,n(z))=X1)). % 0.20/0.42 cnf(i_0_4, plain, (proj1(x(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_38, plain, (fail3(X1,n(z))=n(z))). % 0.20/0.42 cnf(i_0_5, plain, (proj2(x(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_6, plain, (proj12(y(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_7, plain, (proj22(y(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_30, plain, (fail22(X1,n(s(z)))=X1)). % 0.20/0.42 cnf(i_0_34, plain, (fail12(n(s(z)),X1)=X1)). % 0.20/0.42 cnf(i_0_50, plain, (opt(x(n(z),X1))=X1)). % 0.20/0.42 cnf(i_0_40, plain, (x(d(X1),d(X2))=d(x(X1,X2)))). % 0.20/0.42 cnf(i_0_53, plain, (opt(y(n(z),X1))=n(z))). % 0.20/0.42 cnf(i_0_31, plain, (fail32(X1,n(z))=fail22(X1,n(z)))). % 0.20/0.42 cnf(i_0_35, plain, (fail12(n(z),X1)=fail22(n(z),X1))). % 0.20/0.42 cnf(i_0_43, plain, (addNat(s(X1),X2)=s(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_26, plain, (n(mulNat(X1,X2))=fail32(n(X1),n(X2)))). % 0.20/0.42 cnf(i_0_45, plain, (addNat(X1,mulNat(X2,X1))=mulNat(s(X2),X1))). % 0.20/0.42 cnf(i_0_19, plain, (fail1(n(X1),n(X2))=n(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_21, plain, (fail1(X1,n(s(X2)))=fail(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_37, plain, (fail3(X1,n(s(X2)))=fail12(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_49, plain, (fail(n(s(X1)),X2)=opt(x(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_52, plain, (fail3(n(s(X1)),X2)=opt(y(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_27, plain, (opt(y(X1,y(X2,X3)))=fail32(y(X1,X2),X3))). % 0.20/0.42 cnf(i_0_29, plain, (fail32(X1,n(s(s(X2))))=fail22(X1,n(s(s(X2)))))). % 0.20/0.42 cnf(i_0_41, plain, (x(y(d(X1),X2),y(X1,d(X2)))=d(y(X1,X2)))). % 0.20/0.42 cnf(i_0_33, plain, (fail12(n(s(s(X1))),X2)=fail22(n(s(s(X1))),X2))). % 0.20/0.42 cnf(i_0_14, plain, (fail2(X1,X1)=y(n(s(s(z))),opt(X1)))). % 0.20/0.42 cnf(i_0_2, plain, (s(X1)!=z)). % 0.20/0.42 cnf(i_0_10, plain, (n(X1)!=x2)). % 0.20/0.42 cnf(i_0_12, plain, (x(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_13, plain, (y(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_8, plain, (n(X1)!=x(X2,X3))). % 0.20/0.42 cnf(i_0_9, plain, (n(X1)!=y(X2,X3))). % 0.20/0.42 cnf(i_0_11, plain, (y(X1,X2)!=x(X3,X4))). % 0.20/0.42 cnf(i_0_17, plain, (fail2(X1,X2)=fail1(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_20, plain, (fail1(X1,X2)=fail(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_28, plain, (fail32(X1,X2)=fail22(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_32, plain, (fail12(X1,X2)=fail22(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_36, plain, (fail3(X1,X2)=fail12(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_48, plain, (fail(X1,X2)=opt(x(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_51, plain, (fail3(X1,X2)=opt(y(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_18, plain, (fail2(n(X1),X2)=fail1(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_25, plain, (y(opt(n(X1)),opt(X2))=fail32(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_47, plain, (y(proj12(X1),proj22(X1))=X1|x(proj1(X1),proj2(X1))=X1|opt(X1)=X1)). % 0.20/0.42 cnf(i_0_16, plain, (fail2(x(X1,X2),X3)=opt(x(X1,x(X2,X3)))|x(X1,X2)=X3)). % 0.20/0.42 cnf(i_0_15, plain, (x(opt(X1),opt(X2))=fail2(X1,X2)|x(proj1(X1),proj2(X1))=X1|X1=X2)). % 0.20/0.42 cnf(i_0_24, plain, (y(opt(X1),opt(X2))=fail32(X1,X2)|y(proj12(X1),proj22(X1))=X1|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_86, plain, (X121=X121)). % 0.20/0.42 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.20/0.42 # Begin printing tableau % 0.20/0.42 # Found 6 steps % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X7)))=opt(d(X7))), inference(start_rule)). % 0.20/0.42 cnf(i_0_111, plain, (opt(d(opt(X7)))=opt(d(X7))), inference(extension_rule, [i_0_108])). % 0.20/0.42 cnf(i_0_263, plain, (opt(d(opt(X1)))!=opt(d(X1))), inference(closure_rule, [i_0_54])). % 0.20/0.42 cnf(i_0_262, plain, (fail12(opt(d(opt(X1))),opt(d(opt(X7))))=fail12(opt(d(X1)),opt(d(X7)))), inference(extension_rule, [i_0_89])). % 0.20/0.42 cnf(i_0_305, plain, (fail12(opt(d(X1)),opt(d(X7)))!=proj2(x(X1,fail12(opt(d(X1)),opt(d(X7)))))), inference(closure_rule, [i_0_5])). % 0.20/0.42 cnf(i_0_303, plain, (fail12(opt(d(opt(X1))),opt(d(opt(X7))))=proj2(x(X1,fail12(opt(d(X1)),opt(d(X7)))))), inference(etableau_closure_rule, [i_0_303, ...])). % 0.20/0.42 # End printing tableau % 0.20/0.42 # SZS output end % 0.20/0.42 # Branches closed with saturation will be marked with an "s" % 0.20/0.42 # There were 1 total branch saturation attempts. % 0.20/0.42 # There were 0 of these attempts blocked. % 0.20/0.42 # There were 0 deferred branch saturation attempts. % 0.20/0.42 # There were 0 free duplicated saturations. % 0.20/0.42 # There were 1 total successful branch saturations. % 0.20/0.42 # There were 0 successful branch saturations in interreduction. % 0.20/0.42 # There were 0 successful branch saturations on the branch. % 0.20/0.42 # There were 1 successful branch saturations after the branch. % 0.20/0.42 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # Begin clausification derivation % 0.20/0.42 % 0.20/0.42 # End clausification derivation % 0.20/0.42 # Begin listing active clauses obtained from FOF to CNF conversion % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X1)))=opt(d(X1)))). % 0.20/0.42 cnf(i_0_42, plain, (d(x2)=n(s(z)))). % 0.20/0.42 cnf(i_0_1, plain, (proj1S(s(X1))=X1)). % 0.20/0.42 cnf(i_0_3, plain, (proj1N(n(X1))=X1)). % 0.20/0.42 cnf(i_0_46, plain, (mulNat(z,X1)=z)). % 0.20/0.42 cnf(i_0_39, plain, (d(n(X1))=n(z))). % 0.20/0.42 cnf(i_0_44, plain, (addNat(z,X1)=X1)). % 0.20/0.42 cnf(i_0_22, plain, (fail(X1,n(z))=X1)). % 0.20/0.42 cnf(i_0_4, plain, (proj1(x(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_38, plain, (fail3(X1,n(z))=n(z))). % 0.20/0.42 cnf(i_0_5, plain, (proj2(x(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_6, plain, (proj12(y(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_7, plain, (proj22(y(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_30, plain, (fail22(X1,n(s(z)))=X1)). % 0.20/0.42 cnf(i_0_34, plain, (fail12(n(s(z)),X1)=X1)). % 0.20/0.42 cnf(i_0_50, plain, (opt(x(n(z),X1))=X1)). % 0.20/0.42 cnf(i_0_40, plain, (x(d(X1),d(X2))=d(x(X1,X2)))). % 0.20/0.42 cnf(i_0_53, plain, (opt(y(n(z),X1))=n(z))). % 0.20/0.42 cnf(i_0_31, plain, (fail32(X1,n(z))=fail22(X1,n(z)))). % 0.20/0.42 cnf(i_0_35, plain, (fail12(n(z),X1)=fail22(n(z),X1))). % 0.20/0.42 cnf(i_0_43, plain, (addNat(s(X1),X2)=s(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_26, plain, (n(mulNat(X1,X2))=fail32(n(X1),n(X2)))). % 0.20/0.42 cnf(i_0_45, plain, (addNat(X1,mulNat(X2,X1))=mulNat(s(X2),X1))). % 0.20/0.42 cnf(i_0_19, plain, (fail1(n(X1),n(X2))=n(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_21, plain, (fail1(X1,n(s(X2)))=fail(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_37, plain, (fail3(X1,n(s(X2)))=fail12(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_49, plain, (fail(n(s(X1)),X2)=opt(x(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_52, plain, (fail3(n(s(X1)),X2)=opt(y(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_27, plain, (opt(y(X1,y(X2,X3)))=fail32(y(X1,X2),X3))). % 0.20/0.42 cnf(i_0_29, plain, (fail32(X1,n(s(s(X2))))=fail22(X1,n(s(s(X2)))))). % 0.20/0.42 cnf(i_0_41, plain, (x(y(d(X1),X2),y(X1,d(X2)))=d(y(X1,X2)))). % 0.20/0.42 cnf(i_0_33, plain, (fail12(n(s(s(X1))),X2)=fail22(n(s(s(X1))),X2))). % 0.20/0.42 cnf(i_0_14, plain, (fail2(X1,X1)=y(n(s(s(z))),opt(X1)))). % 0.20/0.42 cnf(i_0_2, plain, (s(X1)!=z)). % 0.20/0.42 cnf(i_0_10, plain, (n(X1)!=x2)). % 0.20/0.42 cnf(i_0_12, plain, (x(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_13, plain, (y(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_8, plain, (n(X1)!=x(X2,X3))). % 0.20/0.42 cnf(i_0_9, plain, (n(X1)!=y(X2,X3))). % 0.20/0.42 cnf(i_0_11, plain, (y(X1,X2)!=x(X3,X4))). % 0.20/0.42 cnf(i_0_17, plain, (fail2(X1,X2)=fail1(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_20, plain, (fail1(X1,X2)=fail(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_28, plain, (fail32(X1,X2)=fail22(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_32, plain, (fail12(X1,X2)=fail22(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_36, plain, (fail3(X1,X2)=fail12(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_48, plain, (fail(X1,X2)=opt(x(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_51, plain, (fail3(X1,X2)=opt(y(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_18, plain, (fail2(n(X1),X2)=fail1(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_25, plain, (y(opt(n(X1)),opt(X2))=fail32(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_47, plain, (y(proj12(X1),proj22(X1))=X1|x(proj1(X1),proj2(X1))=X1|opt(X1)=X1)). % 0.20/0.42 cnf(i_0_16, plain, (fail2(x(X1,X2),X3)=opt(x(X1,x(X2,X3)))|x(X1,X2)=X3)). % 0.20/0.42 cnf(i_0_15, plain, (x(opt(X1),opt(X2))=fail2(X1,X2)|x(proj1(X1),proj2(X1))=X1|X1=X2)). % 0.20/0.42 cnf(i_0_24, plain, (y(opt(X1),opt(X2))=fail32(X1,X2)|y(proj12(X1),proj22(X1))=X1|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_86, plain, (X121=X121)). % 0.20/0.42 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.20/0.42 # Begin printing tableau % 0.20/0.42 # Found 6 steps % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X6)))=opt(d(X6))), inference(start_rule)). % 0.20/0.42 cnf(i_0_111, plain, (opt(d(opt(X6)))=opt(d(X6))), inference(extension_rule, [i_0_108])). % 0.20/0.42 cnf(i_0_264, plain, (opt(d(opt(X1)))!=opt(d(X1))), inference(closure_rule, [i_0_54])). % 0.20/0.42 cnf(i_0_262, plain, (fail12(opt(d(opt(X6))),opt(d(opt(X1))))=fail12(opt(d(X6)),opt(d(X1)))), inference(extension_rule, [i_0_89])). % 0.20/0.42 cnf(i_0_305, plain, (fail12(opt(d(X6)),opt(d(X1)))!=proj2(x(X1,fail12(opt(d(X6)),opt(d(X1)))))), inference(closure_rule, [i_0_5])). % 0.20/0.42 cnf(i_0_303, plain, (fail12(opt(d(opt(X6))),opt(d(opt(X1))))=proj2(x(X1,fail12(opt(d(X6)),opt(d(X1)))))), inference(etableau_closure_rule, [i_0_303, ...])). % 0.20/0.42 # End printing tableau % 0.20/0.42 # SZS output end % 0.20/0.42 # Branches closed with saturation will be marked with an "s" % 0.20/0.42 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # Begin clausification derivation % 0.20/0.42 % 0.20/0.42 # End clausification derivation % 0.20/0.42 # Begin listing active clauses obtained from FOF to CNF conversion % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X1)))=opt(d(X1)))). % 0.20/0.42 cnf(i_0_42, plain, (d(x2)=n(s(z)))). % 0.20/0.42 cnf(i_0_1, plain, (proj1S(s(X1))=X1)). % 0.20/0.42 cnf(i_0_3, plain, (proj1N(n(X1))=X1)). % 0.20/0.42 cnf(i_0_46, plain, (mulNat(z,X1)=z)). % 0.20/0.42 cnf(i_0_39, plain, (d(n(X1))=n(z))). % 0.20/0.42 cnf(i_0_44, plain, (addNat(z,X1)=X1)). % 0.20/0.42 cnf(i_0_22, plain, (fail(X1,n(z))=X1)). % 0.20/0.42 cnf(i_0_4, plain, (proj1(x(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_38, plain, (fail3(X1,n(z))=n(z))). % 0.20/0.42 cnf(i_0_5, plain, (proj2(x(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_6, plain, (proj12(y(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_7, plain, (proj22(y(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_30, plain, (fail22(X1,n(s(z)))=X1)). % 0.20/0.42 cnf(i_0_34, plain, (fail12(n(s(z)),X1)=X1)). % 0.20/0.42 cnf(i_0_50, plain, (opt(x(n(z),X1))=X1)). % 0.20/0.42 cnf(i_0_40, plain, (x(d(X1),d(X2))=d(x(X1,X2)))). % 0.20/0.42 cnf(i_0_53, plain, (opt(y(n(z),X1))=n(z))). % 0.20/0.42 cnf(i_0_31, plain, (fail32(X1,n(z))=fail22(X1,n(z)))). % 0.20/0.42 cnf(i_0_35, plain, (fail12(n(z),X1)=fail22(n(z),X1))). % 0.20/0.42 cnf(i_0_43, plain, (addNat(s(X1),X2)=s(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_26, plain, (n(mulNat(X1,X2))=fail32(n(X1),n(X2)))). % 0.20/0.42 cnf(i_0_45, plain, (addNat(X1,mulNat(X2,X1))=mulNat(s(X2),X1))). % 0.20/0.42 cnf(i_0_19, plain, (fail1(n(X1),n(X2))=n(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_21, plain, (fail1(X1,n(s(X2)))=fail(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_37, plain, (fail3(X1,n(s(X2)))=fail12(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_49, plain, (fail(n(s(X1)),X2)=opt(x(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_52, plain, (fail3(n(s(X1)),X2)=opt(y(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_27, plain, (opt(y(X1,y(X2,X3)))=fail32(y(X1,X2),X3))). % 0.20/0.42 cnf(i_0_29, plain, (fail32(X1,n(s(s(X2))))=fail22(X1,n(s(s(X2)))))). % 0.20/0.42 cnf(i_0_41, plain, (x(y(d(X1),X2),y(X1,d(X2)))=d(y(X1,X2)))). % 0.20/0.42 cnf(i_0_33, plain, (fail12(n(s(s(X1))),X2)=fail22(n(s(s(X1))),X2))). % 0.20/0.42 cnf(i_0_14, plain, (fail2(X1,X1)=y(n(s(s(z))),opt(X1)))). % 0.20/0.42 cnf(i_0_2, plain, (s(X1)!=z)). % 0.20/0.42 cnf(i_0_10, plain, (n(X1)!=x2)). % 0.20/0.42 cnf(i_0_12, plain, (x(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_13, plain, (y(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_8, plain, (n(X1)!=x(X2,X3))). % 0.20/0.42 cnf(i_0_9, plain, (n(X1)!=y(X2,X3))). % 0.20/0.42 cnf(i_0_11, plain, (y(X1,X2)!=x(X3,X4))). % 0.20/0.42 cnf(i_0_17, plain, (fail2(X1,X2)=fail1(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_20, plain, (fail1(X1,X2)=fail(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_28, plain, (fail32(X1,X2)=fail22(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_32, plain, (fail12(X1,X2)=fail22(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_36, plain, (fail3(X1,X2)=fail12(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_48, plain, (fail(X1,X2)=opt(x(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_51, plain, (fail3(X1,X2)=opt(y(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_18, plain, (fail2(n(X1),X2)=fail1(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_25, plain, (y(opt(n(X1)),opt(X2))=fail32(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_47, plain, (y(proj12(X1),proj22(X1))=X1|x(proj1(X1),proj2(X1))=X1|opt(X1)=X1)). % 0.20/0.42 cnf(i_0_16, plain, (fail2(x(X1,X2),X3)=opt(x(X1,x(X2,X3)))|x(X1,X2)=X3)). % 0.20/0.42 cnf(i_0_15, plain, (x(opt(X1),opt(X2))=fail2(X1,X2)|x(proj1(X1),proj2(X1))=X1|X1=X2)). % 0.20/0.42 cnf(i_0_24, plain, (y(opt(X1),opt(X2))=fail32(X1,X2)|y(proj12(X1),proj22(X1))=X1|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_86, plain, (X121=X121)). % 0.20/0.42 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.20/0.42 # Begin printing tableau % 0.20/0.42 # Found 6 steps % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X7)))=opt(d(X7))), inference(start_rule)). % 0.20/0.42 cnf(i_0_111, plain, (opt(d(opt(X7)))=opt(d(X7))), inference(extension_rule, [i_0_107])). % 0.20/0.42 cnf(i_0_260, plain, (opt(d(opt(X1)))!=opt(d(X1))), inference(closure_rule, [i_0_54])). % 0.20/0.42 cnf(i_0_259, plain, (fail22(opt(d(opt(X1))),opt(d(opt(X7))))=fail22(opt(d(X1)),opt(d(X7)))), inference(extension_rule, [i_0_89])). % 0.20/0.42 cnf(i_0_305, plain, (fail22(opt(d(X1)),opt(d(X7)))!=proj2(x(X1,fail22(opt(d(X1)),opt(d(X7)))))), inference(closure_rule, [i_0_5])). % 0.20/0.42 cnf(i_0_303, plain, (fail22(opt(d(opt(X1))),opt(d(opt(X7))))=proj2(x(X1,fail22(opt(d(X1)),opt(d(X7)))))), inference(etableau_closure_rule, [i_0_303, ...])). % 0.20/0.42 # End printing tableau % 0.20/0.42 # SZS output end % 0.20/0.42 # Branches closed with saturation will be marked with an "s" % 0.20/0.42 # There were 1 total branch saturation attempts. % 0.20/0.42 # There were 0 of these attempts blocked. % 0.20/0.42 # There were 0 deferred branch saturation attempts. % 0.20/0.42 # There were 0 free duplicated saturations. % 0.20/0.42 # There were 1 total successful branch saturations. % 0.20/0.42 # There were 0 successful branch saturations in interreduction. % 0.20/0.42 # There were 0 successful branch saturations on the branch. % 0.20/0.42 # There were 1 successful branch saturations after the branch. % 0.20/0.42 # SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # SZS output start for /export/starexec/sandbox/benchmark/theBenchmark.p % 0.20/0.42 # Begin clausification derivation % 0.20/0.42 % 0.20/0.42 # End clausification derivation % 0.20/0.42 # Begin listing active clauses obtained from FOF to CNF conversion % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X1)))=opt(d(X1)))). % 0.20/0.42 cnf(i_0_42, plain, (d(x2)=n(s(z)))). % 0.20/0.42 cnf(i_0_1, plain, (proj1S(s(X1))=X1)). % 0.20/0.42 cnf(i_0_3, plain, (proj1N(n(X1))=X1)). % 0.20/0.42 cnf(i_0_46, plain, (mulNat(z,X1)=z)). % 0.20/0.42 cnf(i_0_39, plain, (d(n(X1))=n(z))). % 0.20/0.42 cnf(i_0_44, plain, (addNat(z,X1)=X1)). % 0.20/0.42 cnf(i_0_22, plain, (fail(X1,n(z))=X1)). % 0.20/0.42 cnf(i_0_4, plain, (proj1(x(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_38, plain, (fail3(X1,n(z))=n(z))). % 0.20/0.42 cnf(i_0_5, plain, (proj2(x(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_6, plain, (proj12(y(X1,X2))=X1)). % 0.20/0.42 cnf(i_0_7, plain, (proj22(y(X1,X2))=X2)). % 0.20/0.42 cnf(i_0_30, plain, (fail22(X1,n(s(z)))=X1)). % 0.20/0.42 cnf(i_0_34, plain, (fail12(n(s(z)),X1)=X1)). % 0.20/0.42 cnf(i_0_50, plain, (opt(x(n(z),X1))=X1)). % 0.20/0.42 cnf(i_0_40, plain, (x(d(X1),d(X2))=d(x(X1,X2)))). % 0.20/0.42 cnf(i_0_53, plain, (opt(y(n(z),X1))=n(z))). % 0.20/0.42 cnf(i_0_31, plain, (fail32(X1,n(z))=fail22(X1,n(z)))). % 0.20/0.42 cnf(i_0_35, plain, (fail12(n(z),X1)=fail22(n(z),X1))). % 0.20/0.42 cnf(i_0_43, plain, (addNat(s(X1),X2)=s(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_26, plain, (n(mulNat(X1,X2))=fail32(n(X1),n(X2)))). % 0.20/0.42 cnf(i_0_45, plain, (addNat(X1,mulNat(X2,X1))=mulNat(s(X2),X1))). % 0.20/0.42 cnf(i_0_19, plain, (fail1(n(X1),n(X2))=n(addNat(X1,X2)))). % 0.20/0.42 cnf(i_0_21, plain, (fail1(X1,n(s(X2)))=fail(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_37, plain, (fail3(X1,n(s(X2)))=fail12(X1,n(s(X2))))). % 0.20/0.42 cnf(i_0_49, plain, (fail(n(s(X1)),X2)=opt(x(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_52, plain, (fail3(n(s(X1)),X2)=opt(y(n(s(X1)),X2)))). % 0.20/0.42 cnf(i_0_27, plain, (opt(y(X1,y(X2,X3)))=fail32(y(X1,X2),X3))). % 0.20/0.42 cnf(i_0_29, plain, (fail32(X1,n(s(s(X2))))=fail22(X1,n(s(s(X2)))))). % 0.20/0.42 cnf(i_0_41, plain, (x(y(d(X1),X2),y(X1,d(X2)))=d(y(X1,X2)))). % 0.20/0.42 cnf(i_0_33, plain, (fail12(n(s(s(X1))),X2)=fail22(n(s(s(X1))),X2))). % 0.20/0.42 cnf(i_0_14, plain, (fail2(X1,X1)=y(n(s(s(z))),opt(X1)))). % 0.20/0.42 cnf(i_0_2, plain, (s(X1)!=z)). % 0.20/0.42 cnf(i_0_10, plain, (n(X1)!=x2)). % 0.20/0.42 cnf(i_0_12, plain, (x(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_13, plain, (y(X1,X2)!=x2)). % 0.20/0.42 cnf(i_0_8, plain, (n(X1)!=x(X2,X3))). % 0.20/0.42 cnf(i_0_9, plain, (n(X1)!=y(X2,X3))). % 0.20/0.42 cnf(i_0_11, plain, (y(X1,X2)!=x(X3,X4))). % 0.20/0.42 cnf(i_0_17, plain, (fail2(X1,X2)=fail1(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_20, plain, (fail1(X1,X2)=fail(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_28, plain, (fail32(X1,X2)=fail22(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_32, plain, (fail12(X1,X2)=fail22(X1,X2)|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_36, plain, (fail3(X1,X2)=fail12(X1,X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_48, plain, (fail(X1,X2)=opt(x(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_51, plain, (fail3(X1,X2)=opt(y(X1,X2))|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_18, plain, (fail2(n(X1),X2)=fail1(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_25, plain, (y(opt(n(X1)),opt(X2))=fail32(n(X1),X2)|n(proj1N(X2))=X2)). % 0.20/0.42 cnf(i_0_47, plain, (y(proj12(X1),proj22(X1))=X1|x(proj1(X1),proj2(X1))=X1|opt(X1)=X1)). % 0.20/0.42 cnf(i_0_16, plain, (fail2(x(X1,X2),X3)=opt(x(X1,x(X2,X3)))|x(X1,X2)=X3)). % 0.20/0.42 cnf(i_0_15, plain, (x(opt(X1),opt(X2))=fail2(X1,X2)|x(proj1(X1),proj2(X1))=X1|X1=X2)). % 0.20/0.42 cnf(i_0_24, plain, (y(opt(X1),opt(X2))=fail32(X1,X2)|y(proj12(X1),proj22(X1))=X1|n(proj1N(X1))=X1)). % 0.20/0.42 cnf(i_0_86, plain, (X121=X121)). % 0.20/0.42 # End listing active clauses. There is an equivalent clause to each of these in the clausification! % 0.20/0.42 # Begin printing tableau % 0.20/0.42 # Found 6 steps % 0.20/0.42 cnf(i_0_54, negated_conjecture, (opt(d(opt(X6)))=opt(d(X6))), inference(start_rule)). % 0.20/0.42 cnf(i_0_111, plain, (opt(d(opt(X6)))=opt(d(X6))), inference(extension_rule, [i_0_107])). % 0.20/0.42 cnf(i_0_261, plain, (opt(d(opt(X1)))!=opt(d(X1))), inference(closure_rule, [i_0_54])). % 0.20/0.42 cnf(i_0_259, plain, (fail22(opt(d(opt(X6))),opt(d(opt(X1))))=fail22(opt(d(X6)),opt(d(X1)))), inference(extension_rule, [i_0_89])). % 0.20/0.42 cnf(i_0_305, plain, (fail22(opt(d(X6)),opt(d(X1)))!=proj2(x(X1,fail22(opt(d(X6)),opt(d(X1)))))), inference(closure_rule, [i_0_5])). % 0.20/0.42 cnf(i_0_303, plain, (fail22(opt(d(opt(X6))),opt(d(opt(X1))))=proj2(x(X1,fail22(opt(d(X6)),opt(d(X1)))))), inference(etableau_closure_rule, [i_0_303, ...])). % 0.20/0.42 # End printing tableau % 0.20/0.42 # SZS output end % 0.20/0.42 # Branches closed with saturation will be marked with an "s" % 0.20/0.42 with saturation will be marked with an "s" % 0.20/0.42 # Child (21414) has found a proof. % 0.20/0.42 % 0.20/0.42 # Proof search is over... % 0.20/0.42 # Freeing feature tree %------------------------------------------------------------------------------