%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU090+1 : TPTP v8.2.0. Released v3.2.0. % Transfm : none % Format : tptp:raw % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % Computer : n026.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 0.69s 0.76s % Output : CNFRefutation 0.69s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.07/0.12 % Problem : SEU090+1 : TPTP v8.2.0. Released v3.2.0. % 0.07/0.12 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s % 0.13/0.34 % Computer : n026.cluster.edu % 0.13/0.34 % Model : x86_64 x86_64 % 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.34 % Memory : 8042.1875MB % 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.34 % CPULimit : 300 % 0.13/0.34 % WCLimit : 300 % 0.13/0.34 % DateTime : Fri Jun 21 13:07:54 EDT 2024 % 0.13/0.34 % CPUTime : % 0.64/0.68 start to proof:theBenchmark % 0.68/0.73 %------------------------------------------- % 0.68/0.73 % File :CSE---1.7 % 0.68/0.73 % Problem :theBenchmark % 0.68/0.73 % Transform :cnf % 0.68/0.73 % Format :tptp:raw % 0.68/0.73 % Command :java -jar mcs_scs.jar %d %s % 0.68/0.73 % 0.68/0.73 % Result :Theorem 0.010000s % 0.68/0.74 % Output :CNFRefutation 0.010000s % 0.68/0.74 %------------------------------------------- % 0.68/0.74 %------------------------------------------------------------------------------ % 0.68/0.74 % File : SEU090+1 : TPTP v8.2.0. Released v3.2.0. % 0.68/0.74 % Domain : Set theory % 0.68/0.74 % Problem : Finite sets, theorem 21 % 0.68/0.74 % Version : [Urb06] axioms : Especial. % 0.68/0.74 % English : % 0.68/0.74 % 0.68/0.74 % Refs : [Dar90] Darmochwal (1990), Finite Sets % 0.68/0.74 % : [Urb06] Urban (2006), Email to G. Sutcliffe % 0.68/0.74 % Source : [Urb06] % 0.68/0.74 % Names : finset_1__t21_finset_1 [Urb06] % 0.68/0.74 % 0.68/0.74 % Status : Theorem % 0.68/0.74 % Rating : 0.14 v7.5.0, 0.12 v7.4.0, 0.10 v7.1.0, 0.17 v7.0.0, 0.23 v6.4.0, 0.27 v6.3.0, 0.21 v6.2.0, 0.16 v6.1.0, 0.27 v6.0.0, 0.26 v5.5.0, 0.30 v5.4.0, 0.36 v5.3.0, 0.37 v5.2.0, 0.25 v5.1.0, 0.24 v5.0.0, 0.29 v4.1.0, 0.35 v4.0.0, 0.33 v3.7.0, 0.35 v3.5.0, 0.26 v3.4.0, 0.37 v3.3.0, 0.21 v3.2.0 % 0.68/0.74 % Syntax : Number of formulae : 63 ( 8 unt; 0 def) % 0.68/0.74 % Number of atoms : 203 ( 3 equ) % 0.68/0.74 % Maximal formula atoms : 10 ( 3 avg) % 0.69/0.74 % Number of connectives : 169 ( 29 ~; 1 |; 108 &) % 0.69/0.74 % ( 1 <=>; 30 =>; 0 <=; 0 <~>) % 0.69/0.74 % Maximal formula depth : 12 ( 5 avg) % 0.69/0.74 % Maximal term depth : 3 ( 1 avg) % 0.69/0.74 % Number of predicates : 19 ( 18 usr; 0 prp; 1-2 aty) % 0.69/0.74 % Number of functors : 6 ( 6 usr; 2 con; 0-4 aty) % 0.69/0.74 % Number of variables : 96 ( 70 !; 26 ?) % 0.69/0.74 % SPC : FOF_THM_RFO_SEQ % 0.69/0.74 % 0.69/0.74 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.69/0.74 % library, www.mizar.org % 0.69/0.74 %------------------------------------------------------------------------------ % 0.69/0.74 fof(antisymmetry_r2_hidden,axiom, % 0.69/0.74 ! [A,B] : % 0.69/0.74 ( in(A,B) % 0.69/0.74 => ~ in(B,A) ) ). % 0.69/0.74 % 0.69/0.74 fof(cc1_arytm_3,axiom, % 0.69/0.74 ! [A] : % 0.69/0.74 ( ordinal(A) % 0.69/0.74 => ! [B] : % 0.69/0.74 ( element(B,A) % 0.69/0.74 => ( epsilon_transitive(B) % 0.69/0.74 & epsilon_connected(B) % 0.69/0.74 & ordinal(B) ) ) ) ). % 0.69/0.74 % 0.69/0.74 fof(cc1_finset_1,axiom, % 0.69/0.74 ! [A] : % 0.69/0.74 ( empty(A) % 0.69/0.74 => finite(A) ) ). % 0.69/0.74 % 0.69/0.74 fof(cc1_funct_1,axiom, % 0.69/0.74 ! [A] : % 0.69/0.74 ( empty(A) % 0.69/0.74 => function(A) ) ). % 0.69/0.74 % 0.69/0.74 fof(cc1_ordinal1,axiom, % 0.69/0.74 ! [A] : % 0.69/0.74 ( ordinal(A) % 0.69/0.74 => ( epsilon_transitive(A) % 0.69/0.74 & epsilon_connected(A) ) ) ). % 0.69/0.74 % 0.69/0.74 fof(cc1_relat_1,axiom, % 0.69/0.74 ! [A] : % 0.69/0.74 ( empty(A) % 0.69/0.74 => relation(A) ) ). % 0.69/0.74 % 0.69/0.74 fof(cc1_relset_1,axiom, % 0.69/0.74 ! [A,B,C] : % 0.69/0.74 ( element(C,powerset(cartesian_product2(A,B))) % 0.69/0.74 => relation(C) ) ). % 0.69/0.74 % 0.69/0.74 fof(cc2_arytm_3,axiom, % 0.69/0.74 ! [A] : % 0.69/0.74 ( ( empty(A) % 0.69/0.74 & ordinal(A) ) % 0.69/0.74 => ( epsilon_transitive(A) % 0.69/0.74 & epsilon_connected(A) % 0.69/0.74 & ordinal(A) % 0.69/0.74 & natural(A) ) ) ). % 0.69/0.74 % 0.69/0.74 fof(cc2_finset_1,axiom, % 0.69/0.74 ! [A] : % 0.69/0.74 ( finite(A) % 0.69/0.74 => ! [B] : % 0.69/0.74 ( element(B,powerset(A)) % 0.69/0.74 => finite(B) ) ) ). % 0.69/0.74 % 0.69/0.75 fof(cc2_funct_1,axiom, % 0.69/0.75 ! [A] : % 0.69/0.75 ( ( relation(A) % 0.69/0.75 & empty(A) % 0.69/0.75 & function(A) ) % 0.69/0.75 => ( relation(A) % 0.69/0.75 & function(A) % 0.69/0.75 & one_to_one(A) ) ) ). % 0.69/0.75 % 0.69/0.75 fof(cc2_ordinal1,axiom, % 0.69/0.75 ! [A] : % 0.69/0.75 ( ( epsilon_transitive(A) % 0.69/0.75 & epsilon_connected(A) ) % 0.69/0.75 => ordinal(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(cc3_ordinal1,axiom, % 0.69/0.75 ! [A] : % 0.69/0.75 ( empty(A) % 0.69/0.75 => ( epsilon_transitive(A) % 0.69/0.75 & epsilon_connected(A) % 0.69/0.75 & ordinal(A) ) ) ). % 0.69/0.75 % 0.69/0.75 fof(cc4_arytm_3,axiom, % 0.69/0.75 ! [A] : % 0.69/0.75 ( element(A,positive_rationals) % 0.69/0.75 => ( ordinal(A) % 0.69/0.75 => ( epsilon_transitive(A) % 0.69/0.75 & epsilon_connected(A) % 0.69/0.75 & ordinal(A) % 0.69/0.75 & natural(A) ) ) ) ). % 0.69/0.75 % 0.69/0.75 fof(d4_zfmisc_1,axiom, % 0.69/0.75 ! [A,B,C,D] : cartesian_product4(A,B,C,D) = cartesian_product2(cartesian_product3(A,B,C),D) ). % 0.69/0.75 % 0.69/0.75 fof(existence_m1_subset_1,axiom, % 0.69/0.75 ! [A] : % 0.69/0.75 ? [B] : element(B,A) ). % 0.69/0.75 % 0.69/0.75 fof(fc12_relat_1,axiom, % 0.69/0.75 ( empty(empty_set) % 0.69/0.75 & relation(empty_set) % 0.69/0.75 & relation_empty_yielding(empty_set) ) ). % 0.69/0.75 % 0.69/0.75 fof(fc14_finset_1,axiom, % 0.69/0.75 ! [A,B] : % 0.69/0.75 ( ( finite(A) % 0.69/0.75 & finite(B) ) % 0.69/0.75 => finite(cartesian_product2(A,B)) ) ). % 0.69/0.75 % 0.69/0.75 fof(fc15_finset_1,axiom, % 0.69/0.75 ! [A,B,C] : % 0.69/0.75 ( ( finite(A) % 0.69/0.75 & finite(B) % 0.69/0.75 & finite(C) ) % 0.69/0.75 => finite(cartesian_product3(A,B,C)) ) ). % 0.69/0.75 % 0.69/0.75 fof(fc1_subset_1,axiom, % 0.69/0.75 ! [A] : ~ empty(powerset(A)) ). % 0.69/0.75 % 0.69/0.75 fof(fc1_xboole_0,axiom, % 0.69/0.75 empty(empty_set) ). % 0.69/0.75 % 0.69/0.75 fof(fc2_ordinal1,axiom, % 0.69/0.75 ( relation(empty_set) % 0.69/0.75 & relation_empty_yielding(empty_set) % 0.69/0.75 & function(empty_set) % 0.69/0.75 & one_to_one(empty_set) % 0.69/0.75 & empty(empty_set) % 0.69/0.75 & epsilon_transitive(empty_set) % 0.69/0.75 & epsilon_connected(empty_set) % 0.69/0.75 & ordinal(empty_set) ) ). % 0.69/0.75 % 0.69/0.75 fof(fc4_relat_1,axiom, % 0.69/0.75 ( empty(empty_set) % 0.69/0.75 & relation(empty_set) ) ). % 0.69/0.75 % 0.69/0.75 fof(fc4_subset_1,axiom, % 0.69/0.75 ! [A,B] : % 0.69/0.75 ( ( ~ empty(A) % 0.69/0.75 & ~ empty(B) ) % 0.69/0.75 => ~ empty(cartesian_product2(A,B)) ) ). % 0.69/0.75 % 0.69/0.75 fof(fc5_subset_1,axiom, % 0.69/0.75 ! [A,B,C] : % 0.69/0.75 ( ( ~ empty(A) % 0.69/0.75 & ~ empty(B) % 0.69/0.75 & ~ empty(C) ) % 0.69/0.75 => ~ empty(cartesian_product3(A,B,C)) ) ). % 0.69/0.75 % 0.69/0.75 fof(fc6_subset_1,axiom, % 0.69/0.75 ! [A,B,C,D] : % 0.69/0.75 ( ( ~ empty(A) % 0.69/0.75 & ~ empty(B) % 0.69/0.75 & ~ empty(C) % 0.69/0.75 & ~ empty(D) ) % 0.69/0.75 => ~ empty(cartesian_product4(A,B,C,D)) ) ). % 0.69/0.75 % 0.69/0.75 fof(fc8_arytm_3,axiom, % 0.69/0.75 ~ empty(positive_rationals) ). % 0.69/0.75 % 0.69/0.75 fof(rc1_arytm_3,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( ~ empty(A) % 0.69/0.75 & epsilon_transitive(A) % 0.69/0.75 & epsilon_connected(A) % 0.69/0.75 & ordinal(A) % 0.69/0.75 & natural(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc1_finset_1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( ~ empty(A) % 0.69/0.75 & finite(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc1_funcop_1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( relation(A) % 0.69/0.75 & function(A) % 0.69/0.75 & function_yielding(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc1_funct_1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( relation(A) % 0.69/0.75 & function(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc1_ordinal1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( epsilon_transitive(A) % 0.69/0.75 & epsilon_connected(A) % 0.69/0.75 & ordinal(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc1_ordinal2,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( epsilon_transitive(A) % 0.69/0.75 & epsilon_connected(A) % 0.69/0.75 & ordinal(A) % 0.69/0.75 & being_limit_ordinal(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc1_relat_1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( empty(A) % 0.69/0.75 & relation(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc1_subset_1,axiom, % 0.69/0.75 ! [A] : % 0.69/0.75 ( ~ empty(A) % 0.69/0.75 => ? [B] : % 0.69/0.75 ( element(B,powerset(A)) % 0.69/0.75 & ~ empty(B) ) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc1_xboole_0,axiom, % 0.69/0.75 ? [A] : empty(A) ). % 0.69/0.75 % 0.69/0.75 fof(rc2_arytm_3,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( element(A,positive_rationals) % 0.69/0.75 & ~ empty(A) % 0.69/0.75 & epsilon_transitive(A) % 0.69/0.75 & epsilon_connected(A) % 0.69/0.75 & ordinal(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc2_finset_1,axiom, % 0.69/0.75 ! [A] : % 0.69/0.75 ? [B] : % 0.69/0.75 ( element(B,powerset(A)) % 0.69/0.75 & empty(B) % 0.69/0.75 & relation(B) % 0.69/0.75 & function(B) % 0.69/0.75 & one_to_one(B) % 0.69/0.75 & epsilon_transitive(B) % 0.69/0.75 & epsilon_connected(B) % 0.69/0.75 & ordinal(B) % 0.69/0.75 & natural(B) % 0.69/0.75 & finite(B) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc2_funct_1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( relation(A) % 0.69/0.75 & empty(A) % 0.69/0.75 & function(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc2_ordinal1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( relation(A) % 0.69/0.75 & function(A) % 0.69/0.75 & one_to_one(A) % 0.69/0.75 & empty(A) % 0.69/0.75 & epsilon_transitive(A) % 0.69/0.75 & epsilon_connected(A) % 0.69/0.75 & ordinal(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc2_ordinal2,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( relation(A) % 0.69/0.75 & function(A) % 0.69/0.75 & transfinite_sequence(A) % 0.69/0.75 & ordinal_yielding(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc2_relat_1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( ~ empty(A) % 0.69/0.75 & relation(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc2_subset_1,axiom, % 0.69/0.75 ! [A] : % 0.69/0.75 ? [B] : % 0.69/0.75 ( element(B,powerset(A)) % 0.69/0.75 & empty(B) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc2_xboole_0,axiom, % 0.69/0.75 ? [A] : ~ empty(A) ). % 0.69/0.75 % 0.69/0.75 fof(rc3_arytm_3,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( element(A,positive_rationals) % 0.69/0.75 & empty(A) % 0.69/0.75 & epsilon_transitive(A) % 0.69/0.75 & epsilon_connected(A) % 0.69/0.75 & ordinal(A) % 0.69/0.75 & natural(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc3_finset_1,axiom, % 0.69/0.75 ! [A] : % 0.69/0.75 ( ~ empty(A) % 0.69/0.75 => ? [B] : % 0.69/0.75 ( element(B,powerset(A)) % 0.69/0.75 & ~ empty(B) % 0.69/0.75 & finite(B) ) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc3_funct_1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( relation(A) % 0.69/0.75 & function(A) % 0.69/0.75 & one_to_one(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc3_ordinal1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( ~ empty(A) % 0.69/0.75 & epsilon_transitive(A) % 0.69/0.75 & epsilon_connected(A) % 0.69/0.75 & ordinal(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc3_relat_1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( relation(A) % 0.69/0.75 & relation_empty_yielding(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc4_funct_1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( relation(A) % 0.69/0.75 & relation_empty_yielding(A) % 0.69/0.75 & function(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc4_ordinal1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( relation(A) % 0.69/0.75 & function(A) % 0.69/0.75 & transfinite_sequence(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(rc5_funct_1,axiom, % 0.69/0.75 ? [A] : % 0.69/0.75 ( relation(A) % 0.69/0.75 & relation_non_empty(A) % 0.69/0.75 & function(A) ) ). % 0.69/0.75 % 0.69/0.75 fof(reflexivity_r1_tarski,axiom, % 0.69/0.75 ! [A,B] : subset(A,A) ). % 0.69/0.75 % 0.69/0.75 fof(t19_finset_1,axiom, % 0.69/0.75 ! [A,B] : % 0.69/0.75 ( ( finite(A) % 0.69/0.75 & finite(B) ) % 0.69/0.75 => finite(cartesian_product2(A,B)) ) ). % 0.69/0.75 % 0.69/0.75 fof(t1_subset,axiom, % 0.69/0.75 ! [A,B] : % 0.69/0.75 ( in(A,B) % 0.69/0.75 => element(A,B) ) ). % 0.69/0.75 % 0.69/0.75 fof(t20_finset_1,axiom, % 0.69/0.75 ! [A,B,C] : % 0.69/0.75 ( ( finite(A) % 0.69/0.75 & finite(B) % 0.69/0.75 & finite(C) ) % 0.69/0.75 => finite(cartesian_product3(A,B,C)) ) ). % 0.69/0.75 % 0.69/0.75 fof(t21_finset_1,conjecture, % 0.69/0.75 ! [A,B,C,D] : % 0.69/0.75 ( ( finite(A) % 0.69/0.75 & finite(B) % 0.69/0.75 & finite(C) % 0.69/0.75 & finite(D) ) % 0.69/0.75 => finite(cartesian_product4(A,B,C,D)) ) ). % 0.69/0.75 % 0.69/0.75 fof(t2_subset,axiom, % 0.69/0.75 ! [A,B] : % 0.69/0.75 ( element(A,B) % 0.69/0.75 => ( empty(B) % 0.69/0.75 | in(A,B) ) ) ). % 0.69/0.75 % 0.69/0.75 fof(t3_subset,axiom, % 0.69/0.75 ! [A,B] : % 0.69/0.75 ( element(A,powerset(B)) % 0.69/0.75 <=> subset(A,B) ) ). % 0.69/0.75 % 0.69/0.75 fof(t4_subset,axiom, % 0.69/0.75 ! [A,B,C] : % 0.69/0.75 ( ( in(A,B) % 0.69/0.75 & element(B,powerset(C)) ) % 0.69/0.76 => element(A,C) ) ). % 0.69/0.76 % 0.69/0.76 fof(t5_subset,axiom, % 0.69/0.76 ! [A,B,C] : % 0.69/0.76 ~ ( in(A,B) % 0.69/0.76 & element(B,powerset(C)) % 0.69/0.76 & empty(C) ) ). % 0.69/0.76 % 0.69/0.76 fof(t6_boole,axiom, % 0.69/0.76 ! [A] : % 0.69/0.76 ( empty(A) % 0.69/0.76 => A = empty_set ) ). % 0.69/0.76 % 0.69/0.76 fof(t7_boole,axiom, % 0.69/0.76 ! [A,B] : % 0.69/0.76 ~ ( in(A,B) % 0.69/0.76 & empty(B) ) ). % 0.69/0.76 % 0.69/0.76 fof(t8_boole,axiom, % 0.69/0.76 ! [A,B] : % 0.69/0.76 ~ ( empty(A) % 0.69/0.76 & A != B % 0.69/0.76 & empty(B) ) ). % 0.69/0.76 % 0.69/0.76 %------------------------------------------------------------------------------ % 0.69/0.76 %------------------------------------------- % 0.69/0.76 % Proof found % 0.69/0.76 % SZS status Theorem for theBenchmark % 0.69/0.76 % SZS output start Proof % 0.69/0.76 %ClaNum:181(EqnAxiom:35) % 0.69/0.76 %VarNum:149(SingletonVarNum:78) % 0.69/0.76 %MaxLitNum:5 % 0.69/0.76 %MaxfuncDepth:2 % 0.69/0.76 %SharedTerms:111 % 0.69/0.76 %goalClause: 70 71 72 73 138 % 0.69/0.76 %singleGoalClaCount:5 % 0.69/0.76 [36]P1(a1) % 0.69/0.76 [37]P1(a4) % 0.69/0.76 [38]P1(a26) % 0.69/0.76 [39]P1(a31) % 0.69/0.76 [40]P1(a5) % 0.69/0.76 [41]P1(a7) % 0.69/0.76 [42]P1(a10) % 0.69/0.76 [43]P1(a15) % 0.69/0.76 [44]P2(a1) % 0.69/0.76 [45]P2(a4) % 0.69/0.76 [46]P2(a26) % 0.69/0.76 [47]P2(a31) % 0.69/0.76 [48]P2(a5) % 0.69/0.76 [49]P2(a7) % 0.69/0.76 [50]P2(a10) % 0.69/0.76 [51]P2(a15) % 0.69/0.76 [52]P3(a1) % 0.69/0.76 [53]P3(a4) % 0.69/0.76 [54]P3(a26) % 0.69/0.76 [55]P3(a31) % 0.69/0.76 [56]P3(a5) % 0.69/0.76 [57]P3(a7) % 0.69/0.76 [58]P3(a10) % 0.69/0.76 [59]P3(a15) % 0.69/0.76 [63]P4(a1) % 0.69/0.76 [64]P4(a32) % 0.69/0.76 [65]P4(a6) % 0.69/0.76 [66]P4(a8) % 0.69/0.76 [67]P4(a7) % 0.69/0.76 [68]P4(a10) % 0.69/0.76 [69]P7(a27) % 0.69/0.76 [70]P7(a19) % 0.69/0.76 [71]P7(a24) % 0.69/0.76 [72]P7(a25) % 0.69/0.76 [73]P7(a28) % 0.69/0.76 [74]P8(a1) % 0.69/0.76 [75]P8(a29) % 0.69/0.76 [76]P8(a30) % 0.69/0.76 [77]P8(a8) % 0.69/0.76 [78]P8(a7) % 0.69/0.76 [79]P8(a11) % 0.69/0.76 [80]P8(a16) % 0.69/0.76 [81]P8(a20) % 0.69/0.76 [82]P8(a22) % 0.69/0.76 [83]P8(a23) % 0.69/0.76 [86]P13(a1) % 0.69/0.76 [87]P13(a29) % 0.69/0.76 [88]P13(a30) % 0.69/0.76 [89]P13(a32) % 0.69/0.76 [90]P13(a8) % 0.69/0.76 [91]P13(a7) % 0.69/0.76 [92]P13(a11) % 0.69/0.76 [93]P13(a12) % 0.69/0.76 [94]P13(a16) % 0.69/0.76 [95]P13(a21) % 0.69/0.76 [96]P13(a20) % 0.69/0.76 [97]P13(a22) % 0.69/0.76 [98]P13(a23) % 0.69/0.76 [99]P9(a4) % 0.69/0.76 [100]P9(a10) % 0.69/0.76 [101]P12(a1) % 0.69/0.76 [102]P12(a7) % 0.69/0.76 [103]P12(a16) % 0.69/0.76 [105]P15(a1) % 0.69/0.76 [106]P15(a21) % 0.69/0.76 [107]P15(a20) % 0.69/0.76 [108]P10(a29) % 0.69/0.76 [109]P5(a31) % 0.69/0.76 [110]P16(a11) % 0.69/0.76 [111]P16(a22) % 0.69/0.76 [112]P14(a11) % 0.69/0.76 [113]P17(a23) % 0.69/0.76 [124]P6(a5,a33) % 0.69/0.76 [125]P6(a10,a33) % 0.69/0.76 [130]~P4(a33) % 0.69/0.76 [131]~P4(a4) % 0.69/0.76 [132]~P4(a27) % 0.69/0.76 [133]~P4(a5) % 0.69/0.76 [134]~P4(a12) % 0.69/0.76 [135]~P4(a14) % 0.69/0.76 [136]~P4(a15) % 0.69/0.76 [138]~P7(f3(f2(a19,a24,a25),a28)) % 0.69/0.76 [126]P18(x1261,x1261) % 0.69/0.76 [114]P1(f9(x1141)) % 0.69/0.76 [115]P2(f9(x1151)) % 0.69/0.76 [116]P3(f9(x1161)) % 0.69/0.76 [117]P4(f9(x1171)) % 0.69/0.76 [118]P4(f13(x1181)) % 0.69/0.76 [119]P7(f9(x1191)) % 0.69/0.76 [120]P8(f9(x1201)) % 0.69/0.76 [121]P13(f9(x1211)) % 0.69/0.76 [122]P9(f9(x1221)) % 0.69/0.76 [123]P12(f9(x1231)) % 0.69/0.76 [127]P6(f17(x1271),x1271) % 0.69/0.76 [128]P6(f9(x1281),f35(x1281)) % 0.69/0.76 [129]P6(f13(x1291),f35(x1291)) % 0.69/0.76 [137]~P4(f35(x1371)) % 0.69/0.76 [139]~P4(x1391)+E(x1391,a1) % 0.69/0.76 [140]~P4(x1401)+P1(x1401) % 0.69/0.76 [141]~P1(x1411)+P2(x1411) % 0.69/0.76 [142]~P4(x1421)+P2(x1421) % 0.69/0.76 [143]~P1(x1431)+P3(x1431) % 0.69/0.76 [144]~P4(x1441)+P3(x1441) % 0.69/0.76 [145]~P4(x1451)+P7(x1451) % 0.69/0.76 [146]~P4(x1461)+P8(x1461) % 0.69/0.76 [147]~P4(x1471)+P13(x1471) % 0.69/0.76 [148]P4(x1481)+P7(f18(x1481)) % 0.69/0.76 [154]P4(x1541)+~P4(f34(x1541)) % 0.69/0.76 [155]P4(x1551)+~P4(f18(x1551)) % 0.69/0.76 [158]P4(x1581)+P6(f34(x1581),f35(x1581)) % 0.69/0.76 [159]P4(x1591)+P6(f18(x1591),f35(x1591)) % 0.69/0.76 [157]~P4(x1571)+~P11(x1572,x1571) % 0.69/0.76 [166]~P11(x1661,x1662)+P6(x1661,x1662) % 0.69/0.76 [172]~P11(x1722,x1721)+~P11(x1721,x1722) % 0.69/0.76 [168]~P18(x1681,x1682)+P6(x1681,f35(x1682)) % 0.69/0.76 [173]P18(x1731,x1732)+~P6(x1731,f35(x1732)) % 0.69/0.76 [177]P13(x1771)+~P6(x1771,f35(f3(x1772,x1773))) % 0.69/0.76 [150]~P2(x1501)+~P3(x1501)+P1(x1501) % 0.69/0.76 [153]~P1(x1531)+~P4(x1531)+P9(x1531) % 0.69/0.76 [162]~P1(x1621)+P9(x1621)+~P6(x1621,a33) % 0.69/0.76 [149]~P4(x1492)+~P4(x1491)+E(x1491,x1492) % 0.69/0.76 [163]~P6(x1631,x1632)+P1(x1631)+~P1(x1632) % 0.69/0.76 [164]~P6(x1641,x1642)+P2(x1641)+~P1(x1642) % 0.69/0.76 [165]~P6(x1651,x1652)+P3(x1651)+~P1(x1652) % 0.69/0.76 [167]~P6(x1672,x1671)+P4(x1671)+P11(x1672,x1671) % 0.69/0.76 [169]P7(x1691)+~P7(x1692)+~P6(x1691,f35(x1692)) % 0.69/0.76 [171]~P7(x1712)+~P7(x1711)+P7(f3(x1711,x1712)) % 0.69/0.76 [174]P4(x1741)+P4(x1742)+~P4(f3(x1742,x1741)) % 0.69/0.76 [175]~P4(x1751)+~P11(x1752,x1753)+~P6(x1753,f35(x1751)) % 0.69/0.76 [176]P6(x1761,x1762)+~P11(x1761,x1763)+~P6(x1763,f35(x1762)) % 0.69/0.76 [156]~P4(x1561)+~P8(x1561)+~P13(x1561)+P12(x1561) % 0.69/0.76 [179]~P7(x1793)+~P7(x1792)+~P7(x1791)+P7(f2(x1791,x1792,x1793)) % 0.69/0.76 [180]P4(x1801)+P4(x1802)+P4(x1803)+~P4(f2(x1803,x1802,x1801)) % 0.69/0.76 [181]P4(x1811)+P4(x1812)+P4(x1813)+P4(x1814)+~P4(f3(f2(x1814,x1813,x1812),x1811)) % 0.69/0.76 %EqnAxiom % 0.69/0.76 [1]E(x11,x11) % 0.69/0.76 [2]E(x22,x21)+~E(x21,x22) % 0.69/0.76 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.69/0.76 [4]~E(x41,x42)+E(f9(x41),f9(x42)) % 0.69/0.76 [5]~E(x51,x52)+E(f3(x51,x53),f3(x52,x53)) % 0.69/0.76 [6]~E(x61,x62)+E(f3(x63,x61),f3(x63,x62)) % 0.69/0.76 [7]~E(x71,x72)+E(f2(x71,x73,x74),f2(x72,x73,x74)) % 0.69/0.76 [8]~E(x81,x82)+E(f2(x83,x81,x84),f2(x83,x82,x84)) % 0.69/0.76 [9]~E(x91,x92)+E(f2(x93,x94,x91),f2(x93,x94,x92)) % 0.69/0.76 [10]~E(x101,x102)+E(f35(x101),f35(x102)) % 0.69/0.76 [11]~E(x111,x112)+E(f13(x111),f13(x112)) % 0.69/0.76 [12]~E(x121,x122)+E(f34(x121),f34(x122)) % 0.69/0.76 [13]~E(x131,x132)+E(f18(x131),f18(x132)) % 0.69/0.76 [14]~E(x141,x142)+E(f17(x141),f17(x142)) % 0.69/0.76 [15]~P1(x151)+P1(x152)+~E(x151,x152) % 0.69/0.76 [16]~P4(x161)+P4(x162)+~E(x161,x162) % 0.69/0.76 [17]P6(x172,x173)+~E(x171,x172)+~P6(x171,x173) % 0.69/0.76 [18]P6(x183,x182)+~E(x181,x182)+~P6(x183,x181) % 0.69/0.76 [19]P11(x192,x193)+~E(x191,x192)+~P11(x191,x193) % 0.69/0.76 [20]P11(x203,x202)+~E(x201,x202)+~P11(x203,x201) % 0.69/0.76 [21]~P12(x211)+P12(x212)+~E(x211,x212) % 0.69/0.76 [22]P18(x222,x223)+~E(x221,x222)+~P18(x221,x223) % 0.69/0.76 [23]P18(x233,x232)+~E(x231,x232)+~P18(x233,x231) % 0.69/0.76 [24]~P7(x241)+P7(x242)+~E(x241,x242) % 0.69/0.76 [25]~P13(x251)+P13(x252)+~E(x251,x252) % 0.69/0.76 [26]~P2(x261)+P2(x262)+~E(x261,x262) % 0.69/0.76 [27]~P3(x271)+P3(x272)+~E(x271,x272) % 0.69/0.76 [28]~P9(x281)+P9(x282)+~E(x281,x282) % 0.69/0.76 [29]~P8(x291)+P8(x292)+~E(x291,x292) % 0.69/0.76 [30]~P17(x301)+P17(x302)+~E(x301,x302) % 0.69/0.76 [31]~P15(x311)+P15(x312)+~E(x311,x312) % 0.69/0.76 [32]~P10(x321)+P10(x322)+~E(x321,x322) % 0.69/0.76 [33]~P5(x331)+P5(x332)+~E(x331,x332) % 0.69/0.76 [34]~P14(x341)+P14(x342)+~E(x341,x342) % 0.69/0.76 [35]~P16(x351)+P16(x352)+~E(x351,x352) % 0.69/0.76 % 0.69/0.76 %------------------------------------------- % 0.69/0.76 cnf(187,plain, % 0.69/0.76 (P6(f17(x1871),x1871)), % 0.69/0.76 inference(rename_variables,[],[127])). % 0.69/0.76 cnf(193,plain, % 0.69/0.76 (P6(f17(x1931),x1931)), % 0.69/0.76 inference(rename_variables,[],[127])). % 0.69/0.76 cnf(198,plain, % 0.69/0.76 (P6(f17(x1981),x1981)), % 0.69/0.76 inference(rename_variables,[],[127])). % 0.69/0.76 cnf(208,plain, % 0.69/0.76 ($false), % 0.69/0.76 inference(scs_inference,[],[70,71,72,73,138,127,187,193,198,129,63,130,124,36,40,145,157,173,177,169,171,167,153,162,175,20,179]), % 0.69/0.76 ['proof']). % 0.69/0.76 % SZS output end Proof % 0.69/0.76 % Total time :0.010000s %------------------------------------------------------------------------------