%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU089+1 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % Computer : n029.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 : Mon Jun 24 15:01:01 EDT 2024 % Result : Theorem 0.55s 0.67s % Output : CNFRefutation 0.55s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.11/0.12 % Problem : SEU089+1 : TPTP v8.2.0. Released v3.2.0. % 0.11/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.12/0.33 % Computer : n029.cluster.edu % 0.12/0.33 % Model : x86_64 x86_64 % 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.12/0.33 % Memory : 8042.1875MB % 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.12/0.33 % CPULimit : 300 % 0.12/0.33 % WCLimit : 300 % 0.12/0.33 % DateTime : Fri Jun 21 12:19:24 EDT 2024 % 0.12/0.33 % CPUTime : % 0.19/0.56 start to proof:theBenchmark % 0.55/0.66 %------------------------------------------- % 0.55/0.66 % File :CSE---1.7 % 0.55/0.66 % Problem :theBenchmark % 0.55/0.66 % Transform :cnf % 0.55/0.66 % Format :tptp:raw % 0.55/0.66 % Command :java -jar mcs_scs.jar %d %s % 0.55/0.66 % 0.55/0.66 % Result :Theorem 0.010000s % 0.55/0.66 % Output :CNFRefutation 0.010000s % 0.55/0.66 %------------------------------------------- % 0.55/0.66 %------------------------------------------------------------------------------ % 0.55/0.66 % File : SEU089+1 : TPTP v8.2.0. Released v3.2.0. % 0.55/0.66 % Domain : Set theory % 0.55/0.66 % Problem : Finite sets, theorem 20 % 0.55/0.66 % Version : [Urb06] axioms : Especial. % 0.55/0.66 % English : % 0.55/0.66 % 0.55/0.66 % Refs : [Dar90] Darmochwal (1990), Finite Sets % 0.55/0.66 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.55/0.66 % Source : [Urb06] % 0.55/0.66 % Names : finset_1__t20_finset_1 [Urb06] % 0.55/0.66 % 0.55/0.66 % Status : Theorem % 0.55/0.66 % Rating : 0.06 v8.1.0, 0.00 v7.3.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.07 v6.4.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.13 v5.5.0, 0.07 v5.4.0, 0.14 v5.3.0, 0.19 v5.2.0, 0.05 v5.1.0, 0.10 v5.0.0, 0.17 v4.1.0, 0.22 v4.0.0, 0.21 v3.7.0, 0.15 v3.5.0, 0.11 v3.4.0, 0.16 v3.3.0, 0.00 v3.2.0 % 0.55/0.66 % Syntax : Number of formulae : 60 ( 8 unt; 0 def) % 0.55/0.66 % Number of atoms : 189 ( 3 equ) % 0.55/0.66 % Maximal formula atoms : 10 ( 3 avg) % 0.55/0.66 % Number of connectives : 153 ( 24 ~; 1 |; 100 &) % 0.55/0.66 % ( 1 <=>; 27 =>; 0 <=; 0 <~>) % 0.55/0.66 % Maximal formula depth : 12 ( 5 avg) % 0.55/0.66 % Maximal term depth : 3 ( 1 avg) % 0.55/0.66 % Number of predicates : 19 ( 18 usr; 0 prp; 1-2 aty) % 0.55/0.66 % Number of functors : 5 ( 5 usr; 2 con; 0-3 aty) % 0.55/0.66 % Number of variables : 84 ( 58 !; 26 ?) % 0.55/0.66 % SPC : FOF_THM_RFO_SEQ % 0.55/0.66 % 0.55/0.66 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.55/0.66 % library, www.mizar.org % 0.55/0.66 %------------------------------------------------------------------------------ % 0.55/0.66 fof(antisymmetry_r2_hidden,axiom, % 0.55/0.66 ! [A,B] : % 0.55/0.66 ( in(A,B) % 0.55/0.66 => ~ in(B,A) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc1_arytm_3,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( ordinal(A) % 0.55/0.66 => ! [B] : % 0.55/0.66 ( element(B,A) % 0.55/0.66 => ( epsilon_transitive(B) % 0.55/0.66 & epsilon_connected(B) % 0.55/0.66 & ordinal(B) ) ) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc1_finset_1,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( empty(A) % 0.55/0.66 => finite(A) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc1_funct_1,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( empty(A) % 0.55/0.66 => function(A) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc1_ordinal1,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( ordinal(A) % 0.55/0.66 => ( epsilon_transitive(A) % 0.55/0.66 & epsilon_connected(A) ) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc1_relat_1,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( empty(A) % 0.55/0.66 => relation(A) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc1_relset_1,axiom, % 0.55/0.66 ! [A,B,C] : % 0.55/0.66 ( element(C,powerset(cartesian_product2(A,B))) % 0.55/0.66 => relation(C) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc2_arytm_3,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( ( empty(A) % 0.55/0.66 & ordinal(A) ) % 0.55/0.66 => ( epsilon_transitive(A) % 0.55/0.66 & epsilon_connected(A) % 0.55/0.66 & ordinal(A) % 0.55/0.66 & natural(A) ) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc2_finset_1,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( finite(A) % 0.55/0.66 => ! [B] : % 0.55/0.66 ( element(B,powerset(A)) % 0.55/0.66 => finite(B) ) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc2_funct_1,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( ( relation(A) % 0.55/0.66 & empty(A) % 0.55/0.66 & function(A) ) % 0.55/0.66 => ( relation(A) % 0.55/0.66 & function(A) % 0.55/0.66 & one_to_one(A) ) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc2_ordinal1,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( ( epsilon_transitive(A) % 0.55/0.66 & epsilon_connected(A) ) % 0.55/0.66 => ordinal(A) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc3_ordinal1,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( empty(A) % 0.55/0.66 => ( epsilon_transitive(A) % 0.55/0.66 & epsilon_connected(A) % 0.55/0.66 & ordinal(A) ) ) ). % 0.55/0.66 % 0.55/0.66 fof(cc4_arytm_3,axiom, % 0.55/0.66 ! [A] : % 0.55/0.66 ( element(A,positive_rationals) % 0.55/0.66 => ( ordinal(A) % 0.55/0.66 => ( epsilon_transitive(A) % 0.55/0.66 & epsilon_connected(A) % 0.55/0.66 & ordinal(A) % 0.55/0.66 & natural(A) ) ) ) ). % 0.55/0.66 % 0.55/0.66 fof(d3_zfmisc_1,axiom, % 0.55/0.66 ! [A,B,C] : cartesian_product3(A,B,C) = cartesian_product2(cartesian_product2(A,B),C) ). % 0.55/0.66 % 0.55/0.66 fof(existence_m1_subset_1,axiom, % 0.55/0.66 ! [A] : % 0.55/0.67 ? [B] : element(B,A) ). % 0.55/0.67 % 0.55/0.67 fof(fc12_relat_1,axiom, % 0.55/0.67 ( empty(empty_set) % 0.55/0.67 & relation(empty_set) % 0.55/0.67 & relation_empty_yielding(empty_set) ) ). % 0.55/0.67 % 0.55/0.67 fof(fc14_finset_1,axiom, % 0.55/0.67 ! [A,B] : % 0.55/0.67 ( ( finite(A) % 0.55/0.67 & finite(B) ) % 0.55/0.67 => finite(cartesian_product2(A,B)) ) ). % 0.55/0.67 % 0.55/0.67 fof(fc1_subset_1,axiom, % 0.55/0.67 ! [A] : ~ empty(powerset(A)) ). % 0.55/0.67 % 0.55/0.67 fof(fc1_xboole_0,axiom, % 0.55/0.67 empty(empty_set) ). % 0.55/0.67 % 0.55/0.67 fof(fc2_ordinal1,axiom, % 0.55/0.67 ( relation(empty_set) % 0.55/0.67 & relation_empty_yielding(empty_set) % 0.55/0.67 & function(empty_set) % 0.55/0.67 & one_to_one(empty_set) % 0.55/0.67 & empty(empty_set) % 0.55/0.67 & epsilon_transitive(empty_set) % 0.55/0.67 & epsilon_connected(empty_set) % 0.55/0.67 & ordinal(empty_set) ) ). % 0.55/0.67 % 0.55/0.67 fof(fc4_relat_1,axiom, % 0.55/0.67 ( empty(empty_set) % 0.55/0.67 & relation(empty_set) ) ). % 0.55/0.67 % 0.55/0.67 fof(fc4_subset_1,axiom, % 0.55/0.67 ! [A,B] : % 0.55/0.67 ( ( ~ empty(A) % 0.55/0.67 & ~ empty(B) ) % 0.55/0.67 => ~ empty(cartesian_product2(A,B)) ) ). % 0.55/0.67 % 0.55/0.67 fof(fc5_subset_1,axiom, % 0.55/0.67 ! [A,B,C] : % 0.55/0.67 ( ( ~ empty(A) % 0.55/0.67 & ~ empty(B) % 0.55/0.67 & ~ empty(C) ) % 0.55/0.67 => ~ empty(cartesian_product3(A,B,C)) ) ). % 0.55/0.67 % 0.55/0.67 fof(fc8_arytm_3,axiom, % 0.55/0.67 ~ empty(positive_rationals) ). % 0.55/0.67 % 0.55/0.67 fof(rc1_arytm_3,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( ~ empty(A) % 0.55/0.67 & epsilon_transitive(A) % 0.55/0.67 & epsilon_connected(A) % 0.55/0.67 & ordinal(A) % 0.55/0.67 & natural(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc1_finset_1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( ~ empty(A) % 0.55/0.67 & finite(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc1_funcop_1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( relation(A) % 0.55/0.67 & function(A) % 0.55/0.67 & function_yielding(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc1_funct_1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( relation(A) % 0.55/0.67 & function(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc1_ordinal1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( epsilon_transitive(A) % 0.55/0.67 & epsilon_connected(A) % 0.55/0.67 & ordinal(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc1_ordinal2,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( epsilon_transitive(A) % 0.55/0.67 & epsilon_connected(A) % 0.55/0.67 & ordinal(A) % 0.55/0.67 & being_limit_ordinal(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc1_relat_1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( empty(A) % 0.55/0.67 & relation(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc1_subset_1,axiom, % 0.55/0.67 ! [A] : % 0.55/0.67 ( ~ empty(A) % 0.55/0.67 => ? [B] : % 0.55/0.67 ( element(B,powerset(A)) % 0.55/0.67 & ~ empty(B) ) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc1_xboole_0,axiom, % 0.55/0.67 ? [A] : empty(A) ). % 0.55/0.67 % 0.55/0.67 fof(rc2_arytm_3,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( element(A,positive_rationals) % 0.55/0.67 & ~ empty(A) % 0.55/0.67 & epsilon_transitive(A) % 0.55/0.67 & epsilon_connected(A) % 0.55/0.67 & ordinal(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc2_finset_1,axiom, % 0.55/0.67 ! [A] : % 0.55/0.67 ? [B] : % 0.55/0.67 ( element(B,powerset(A)) % 0.55/0.67 & empty(B) % 0.55/0.67 & relation(B) % 0.55/0.67 & function(B) % 0.55/0.67 & one_to_one(B) % 0.55/0.67 & epsilon_transitive(B) % 0.55/0.67 & epsilon_connected(B) % 0.55/0.67 & ordinal(B) % 0.55/0.67 & natural(B) % 0.55/0.67 & finite(B) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc2_funct_1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( relation(A) % 0.55/0.67 & empty(A) % 0.55/0.67 & function(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc2_ordinal1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( relation(A) % 0.55/0.67 & function(A) % 0.55/0.67 & one_to_one(A) % 0.55/0.67 & empty(A) % 0.55/0.67 & epsilon_transitive(A) % 0.55/0.67 & epsilon_connected(A) % 0.55/0.67 & ordinal(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc2_ordinal2,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( relation(A) % 0.55/0.67 & function(A) % 0.55/0.67 & transfinite_sequence(A) % 0.55/0.67 & ordinal_yielding(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc2_relat_1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( ~ empty(A) % 0.55/0.67 & relation(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc2_subset_1,axiom, % 0.55/0.67 ! [A] : % 0.55/0.67 ? [B] : % 0.55/0.67 ( element(B,powerset(A)) % 0.55/0.67 & empty(B) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc2_xboole_0,axiom, % 0.55/0.67 ? [A] : ~ empty(A) ). % 0.55/0.67 % 0.55/0.67 fof(rc3_arytm_3,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( element(A,positive_rationals) % 0.55/0.67 & empty(A) % 0.55/0.67 & epsilon_transitive(A) % 0.55/0.67 & epsilon_connected(A) % 0.55/0.67 & ordinal(A) % 0.55/0.67 & natural(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc3_finset_1,axiom, % 0.55/0.67 ! [A] : % 0.55/0.67 ( ~ empty(A) % 0.55/0.67 => ? [B] : % 0.55/0.67 ( element(B,powerset(A)) % 0.55/0.67 & ~ empty(B) % 0.55/0.67 & finite(B) ) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc3_funct_1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( relation(A) % 0.55/0.67 & function(A) % 0.55/0.67 & one_to_one(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc3_ordinal1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( ~ empty(A) % 0.55/0.67 & epsilon_transitive(A) % 0.55/0.67 & epsilon_connected(A) % 0.55/0.67 & ordinal(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc3_relat_1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( relation(A) % 0.55/0.67 & relation_empty_yielding(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc4_funct_1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( relation(A) % 0.55/0.67 & relation_empty_yielding(A) % 0.55/0.67 & function(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc4_ordinal1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( relation(A) % 0.55/0.67 & function(A) % 0.55/0.67 & transfinite_sequence(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(rc5_funct_1,axiom, % 0.55/0.67 ? [A] : % 0.55/0.67 ( relation(A) % 0.55/0.67 & relation_non_empty(A) % 0.55/0.67 & function(A) ) ). % 0.55/0.67 % 0.55/0.67 fof(reflexivity_r1_tarski,axiom, % 0.55/0.67 ! [A,B] : subset(A,A) ). % 0.55/0.67 % 0.55/0.67 fof(t19_finset_1,axiom, % 0.55/0.67 ! [A,B] : % 0.55/0.67 ( ( finite(A) % 0.55/0.67 & finite(B) ) % 0.55/0.67 => finite(cartesian_product2(A,B)) ) ). % 0.55/0.67 % 0.55/0.67 fof(t1_subset,axiom, % 0.55/0.67 ! [A,B] : % 0.55/0.67 ( in(A,B) % 0.55/0.67 => element(A,B) ) ). % 0.55/0.67 % 0.55/0.67 fof(t20_finset_1,conjecture, % 0.55/0.67 ! [A,B,C] : % 0.55/0.67 ( ( finite(A) % 0.55/0.67 & finite(B) % 0.55/0.67 & finite(C) ) % 0.55/0.67 => finite(cartesian_product3(A,B,C)) ) ). % 0.55/0.67 % 0.55/0.67 fof(t2_subset,axiom, % 0.55/0.67 ! [A,B] : % 0.55/0.67 ( element(A,B) % 0.55/0.67 => ( empty(B) % 0.55/0.67 | in(A,B) ) ) ). % 0.55/0.67 % 0.55/0.67 fof(t3_subset,axiom, % 0.55/0.67 ! [A,B] : % 0.55/0.67 ( element(A,powerset(B)) % 0.55/0.67 <=> subset(A,B) ) ). % 0.55/0.67 % 0.55/0.67 fof(t4_subset,axiom, % 0.55/0.67 ! [A,B,C] : % 0.55/0.67 ( ( in(A,B) % 0.55/0.67 & element(B,powerset(C)) ) % 0.55/0.67 => element(A,C) ) ). % 0.55/0.67 % 0.55/0.67 fof(t5_subset,axiom, % 0.55/0.67 ! [A,B,C] : % 0.55/0.67 ~ ( in(A,B) % 0.55/0.67 & element(B,powerset(C)) % 0.55/0.67 & empty(C) ) ). % 0.55/0.67 % 0.55/0.67 fof(t6_boole,axiom, % 0.55/0.67 ! [A] : % 0.55/0.67 ( empty(A) % 0.55/0.67 => A = empty_set ) ). % 0.55/0.67 % 0.55/0.67 fof(t7_boole,axiom, % 0.55/0.67 ! [A,B] : % 0.55/0.67 ~ ( in(A,B) % 0.55/0.67 & empty(B) ) ). % 0.55/0.67 % 0.55/0.67 fof(t8_boole,axiom, % 0.55/0.67 ! [A,B] : % 0.55/0.67 ~ ( empty(A) % 0.55/0.67 & A != B % 0.55/0.67 & empty(B) ) ). % 0.55/0.67 % 0.55/0.67 %------------------------------------------------------------------------------ % 0.55/0.67 %------------------------------------------- % 0.55/0.67 % Proof found % 0.55/0.67 % SZS status Theorem for theBenchmark % 0.55/0.67 % SZS output start Proof % 0.55/0.67 %ClaNum:174(EqnAxiom:32) % 0.55/0.67 %VarNum:135(SingletonVarNum:71) % 0.55/0.67 %MaxLitNum:4 % 0.55/0.67 %MaxfuncDepth:2 % 0.55/0.67 %SharedTerms:109 % 0.55/0.67 %goalClause: 67 68 69 134 % 0.55/0.67 %singleGoalClaCount:4 % 0.55/0.67 [33]P1(a1) % 0.55/0.67 [34]P1(a3) % 0.55/0.67 [35]P1(a25) % 0.55/0.67 [36]P1(a29) % 0.55/0.67 [37]P1(a4) % 0.55/0.67 [38]P1(a6) % 0.55/0.67 [39]P1(a9) % 0.55/0.67 [40]P1(a14) % 0.55/0.67 [41]P2(a1) % 0.55/0.67 [42]P2(a3) % 0.55/0.67 [43]P2(a25) % 0.55/0.67 [44]P2(a29) % 0.55/0.67 [45]P2(a4) % 0.55/0.67 [46]P2(a6) % 0.55/0.67 [47]P2(a9) % 0.55/0.67 [48]P2(a14) % 0.55/0.67 [49]P3(a1) % 0.55/0.67 [50]P3(a3) % 0.55/0.67 [51]P3(a25) % 0.55/0.67 [52]P3(a29) % 0.55/0.67 [53]P3(a4) % 0.55/0.67 [54]P3(a6) % 0.55/0.67 [55]P3(a9) % 0.55/0.67 [56]P3(a14) % 0.55/0.67 [60]P4(a1) % 0.55/0.67 [61]P4(a30) % 0.55/0.67 [62]P4(a5) % 0.55/0.67 [63]P4(a7) % 0.55/0.67 [64]P4(a6) % 0.55/0.67 [65]P4(a9) % 0.55/0.67 [66]P7(a26) % 0.55/0.67 [67]P7(a18) % 0.55/0.67 [68]P7(a23) % 0.55/0.67 [69]P7(a24) % 0.55/0.67 [70]P8(a1) % 0.55/0.67 [71]P8(a27) % 0.55/0.67 [72]P8(a28) % 0.55/0.67 [73]P8(a7) % 0.55/0.67 [74]P8(a6) % 0.55/0.67 [75]P8(a10) % 0.55/0.67 [76]P8(a15) % 0.55/0.67 [77]P8(a19) % 0.55/0.67 [78]P8(a21) % 0.55/0.67 [79]P8(a22) % 0.55/0.67 [82]P13(a1) % 0.55/0.67 [83]P13(a27) % 0.55/0.67 [84]P13(a28) % 0.55/0.67 [85]P13(a30) % 0.55/0.67 [86]P13(a7) % 0.55/0.67 [87]P13(a6) % 0.55/0.67 [88]P13(a10) % 0.55/0.67 [89]P13(a11) % 0.55/0.67 [90]P13(a15) % 0.55/0.67 [91]P13(a20) % 0.55/0.67 [92]P13(a19) % 0.55/0.67 [93]P13(a21) % 0.55/0.67 [94]P13(a22) % 0.55/0.67 [95]P9(a3) % 0.55/0.67 [96]P9(a9) % 0.55/0.67 [97]P12(a1) % 0.55/0.67 [98]P12(a6) % 0.55/0.67 [99]P12(a15) % 0.55/0.67 [101]P15(a1) % 0.55/0.67 [102]P15(a20) % 0.55/0.67 [103]P15(a19) % 0.55/0.67 [104]P10(a27) % 0.55/0.67 [105]P5(a29) % 0.55/0.67 [106]P16(a10) % 0.55/0.67 [107]P16(a21) % 0.55/0.67 [108]P14(a10) % 0.55/0.67 [109]P17(a22) % 0.55/0.67 [120]P6(a4,a31) % 0.55/0.67 [121]P6(a9,a31) % 0.55/0.67 [126]~P4(a31) % 0.55/0.67 [127]~P4(a3) % 0.55/0.67 [128]~P4(a26) % 0.55/0.67 [129]~P4(a4) % 0.55/0.67 [130]~P4(a11) % 0.55/0.67 [131]~P4(a13) % 0.55/0.67 [132]~P4(a14) % 0.55/0.67 [134]~P7(f2(f2(a18,a23),a24)) % 0.55/0.67 [122]P18(x1221,x1221) % 0.55/0.67 [110]P1(f8(x1101)) % 0.55/0.67 [111]P2(f8(x1111)) % 0.55/0.67 [112]P3(f8(x1121)) % 0.55/0.67 [113]P4(f8(x1131)) % 0.55/0.67 [114]P4(f12(x1141)) % 0.55/0.67 [115]P7(f8(x1151)) % 0.55/0.67 [116]P8(f8(x1161)) % 0.55/0.67 [117]P13(f8(x1171)) % 0.55/0.67 [118]P9(f8(x1181)) % 0.55/0.67 [119]P12(f8(x1191)) % 0.55/0.67 [123]P6(f16(x1231),x1231) % 0.55/0.67 [124]P6(f8(x1241),f33(x1241)) % 0.55/0.67 [125]P6(f12(x1251),f33(x1251)) % 0.55/0.67 [133]~P4(f33(x1331)) % 0.55/0.67 [135]~P4(x1351)+E(x1351,a1) % 0.55/0.67 [136]~P4(x1361)+P1(x1361) % 0.55/0.67 [137]~P1(x1371)+P2(x1371) % 0.55/0.67 [138]~P4(x1381)+P2(x1381) % 0.55/0.67 [139]~P1(x1391)+P3(x1391) % 0.55/0.67 [140]~P4(x1401)+P3(x1401) % 0.55/0.67 [141]~P4(x1411)+P7(x1411) % 0.55/0.67 [142]~P4(x1421)+P8(x1421) % 0.55/0.67 [143]~P4(x1431)+P13(x1431) % 0.55/0.67 [144]P4(x1441)+P7(f17(x1441)) % 0.55/0.67 [150]P4(x1501)+~P4(f32(x1501)) % 0.55/0.67 [151]P4(x1511)+~P4(f17(x1511)) % 0.55/0.67 [154]P4(x1541)+P6(f32(x1541),f33(x1541)) % 0.55/0.67 [155]P4(x1551)+P6(f17(x1551),f33(x1551)) % 0.55/0.67 [153]~P4(x1531)+~P11(x1532,x1531) % 0.55/0.67 [162]~P11(x1621,x1622)+P6(x1621,x1622) % 0.55/0.67 [168]~P11(x1682,x1681)+~P11(x1681,x1682) % 0.55/0.67 [164]~P18(x1641,x1642)+P6(x1641,f33(x1642)) % 0.55/0.67 [169]P18(x1691,x1692)+~P6(x1691,f33(x1692)) % 0.55/0.67 [173]P13(x1731)+~P6(x1731,f33(f2(x1732,x1733))) % 0.55/0.67 [146]~P2(x1461)+~P3(x1461)+P1(x1461) % 0.55/0.67 [149]~P1(x1491)+~P4(x1491)+P9(x1491) % 0.55/0.67 [158]~P1(x1581)+P9(x1581)+~P6(x1581,a31) % 0.55/0.67 [145]~P4(x1452)+~P4(x1451)+E(x1451,x1452) % 0.55/0.67 [159]~P6(x1591,x1592)+P1(x1591)+~P1(x1592) % 0.55/0.67 [160]~P6(x1601,x1602)+P2(x1601)+~P1(x1602) % 0.55/0.67 [161]~P6(x1611,x1612)+P3(x1611)+~P1(x1612) % 0.55/0.67 [163]~P6(x1632,x1631)+P4(x1631)+P11(x1632,x1631) % 0.55/0.67 [165]P7(x1651)+~P7(x1652)+~P6(x1651,f33(x1652)) % 0.55/0.67 [167]~P7(x1672)+~P7(x1671)+P7(f2(x1671,x1672)) % 0.55/0.67 [170]P4(x1701)+P4(x1702)+~P4(f2(x1702,x1701)) % 0.55/0.68 [171]~P4(x1711)+~P11(x1712,x1713)+~P6(x1713,f33(x1711)) % 0.55/0.68 [172]P6(x1721,x1722)+~P11(x1721,x1723)+~P6(x1723,f33(x1722)) % 0.55/0.68 [152]~P4(x1521)+~P8(x1521)+~P13(x1521)+P12(x1521) % 0.55/0.68 [174]P4(x1741)+P4(x1742)+P4(x1743)+~P4(f2(f2(x1743,x1742),x1741)) % 0.55/0.68 %EqnAxiom % 0.55/0.68 [1]E(x11,x11) % 0.55/0.68 [2]E(x22,x21)+~E(x21,x22) % 0.55/0.68 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.55/0.68 [4]~E(x41,x42)+E(f8(x41),f8(x42)) % 0.55/0.68 [5]~E(x51,x52)+E(f2(x51,x53),f2(x52,x53)) % 0.55/0.68 [6]~E(x61,x62)+E(f2(x63,x61),f2(x63,x62)) % 0.55/0.68 [7]~E(x71,x72)+E(f33(x71),f33(x72)) % 0.55/0.68 [8]~E(x81,x82)+E(f17(x81),f17(x82)) % 0.55/0.68 [9]~E(x91,x92)+E(f12(x91),f12(x92)) % 0.55/0.68 [10]~E(x101,x102)+E(f32(x101),f32(x102)) % 0.55/0.68 [11]~E(x111,x112)+E(f16(x111),f16(x112)) % 0.55/0.68 [12]~P1(x121)+P1(x122)+~E(x121,x122) % 0.55/0.68 [13]~P4(x131)+P4(x132)+~E(x131,x132) % 0.55/0.68 [14]~P7(x141)+P7(x142)+~E(x141,x142) % 0.55/0.68 [15]~P9(x151)+P9(x152)+~E(x151,x152) % 0.55/0.68 [16]~P12(x161)+P12(x162)+~E(x161,x162) % 0.55/0.68 [17]P6(x172,x173)+~E(x171,x172)+~P6(x171,x173) % 0.55/0.68 [18]P6(x183,x182)+~E(x181,x182)+~P6(x183,x181) % 0.55/0.68 [19]~P13(x191)+P13(x192)+~E(x191,x192) % 0.55/0.68 [20]~P2(x201)+P2(x202)+~E(x201,x202) % 0.55/0.68 [21]~P15(x211)+P15(x212)+~E(x211,x212) % 0.55/0.68 [22]~P17(x221)+P17(x222)+~E(x221,x222) % 0.55/0.68 [23]P11(x232,x233)+~E(x231,x232)+~P11(x231,x233) % 0.55/0.68 [24]P11(x243,x242)+~E(x241,x242)+~P11(x243,x241) % 0.55/0.68 [25]~P3(x251)+P3(x252)+~E(x251,x252) % 0.55/0.68 [26]~P8(x261)+P8(x262)+~E(x261,x262) % 0.55/0.68 [27]P18(x272,x273)+~E(x271,x272)+~P18(x271,x273) % 0.55/0.68 [28]P18(x283,x282)+~E(x281,x282)+~P18(x283,x281) % 0.55/0.68 [29]~P5(x291)+P5(x292)+~E(x291,x292) % 0.55/0.68 [30]~P14(x301)+P14(x302)+~E(x301,x302) % 0.55/0.68 [31]~P16(x311)+P16(x312)+~E(x311,x312) % 0.55/0.68 [32]~P10(x321)+P10(x322)+~E(x321,x322) % 0.55/0.68 % 0.55/0.68 %------------------------------------------- % 0.55/0.68 cnf(180,plain, % 0.55/0.68 (P6(f16(x1801),x1801)), % 0.55/0.68 inference(rename_variables,[],[123])). % 0.55/0.68 cnf(188,plain, % 0.55/0.68 (~P7(f2(a18,a23))), % 0.55/0.68 inference(scs_inference,[],[67,69,134,123,180,125,60,141,153,169,173,165,167])). % 0.55/0.68 cnf(229,plain, % 0.55/0.68 ($false), % 0.55/0.68 inference(scs_inference,[],[67,68,188,124,61,64,123,127,38,141,169,153,163,149,167]), % 0.55/0.68 ['proof']). % 0.55/0.68 % SZS output end Proof % 0.55/0.68 % Total time :0.010000s %------------------------------------------------------------------------------