%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU161+2 : TPTP v8.2.0. Released v3.3.0. % 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 15:01:26 EDT 2024 % Result : Theorem 0.60s 0.71s % Output : CNFRefutation 0.60s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.04/0.12 % Problem : SEU161+2 : TPTP v8.2.0. Released v3.3.0. % 0.04/0.12 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.13/0.33 % Computer : n029.cluster.edu % 0.13/0.33 % Model : x86_64 x86_64 % 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.13/0.33 % Memory : 8042.1875MB % 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64 % 0.13/0.33 % CPULimit : 300 % 0.13/0.33 % WCLimit : 300 % 0.13/0.33 % DateTime : Fri Jun 21 16:06:24 EDT 2024 % 0.13/0.34 % CPUTime : % 0.52/0.61 start to proof:theBenchmark % 0.60/0.69 %------------------------------------------- % 0.60/0.69 % File :CSE---1.7 % 0.60/0.69 % Problem :theBenchmark % 0.60/0.69 % Transform :cnf % 0.60/0.69 % Format :tptp:raw % 0.60/0.69 % Command :java -jar mcs_scs.jar %d %s % 0.60/0.69 % 0.60/0.69 % Result :Theorem 0.010000s % 0.60/0.69 % Output :CNFRefutation 0.010000s % 0.60/0.69 %------------------------------------------- % 0.60/0.70 %------------------------------------------------------------------------------ % 0.60/0.70 % File : SEU161+2 : TPTP v8.2.0. Released v3.3.0. % 0.60/0.70 % Domain : Set theory % 0.60/0.70 % Problem : MPTP chainy problem t46_zfmisc_1 % 0.60/0.70 % Version : [Urb07] axioms : Especial. % 0.60/0.70 % English : % 0.60/0.70 % 0.60/0.70 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co % 0.60/0.70 % : [Urb07] Urban (2006), Email to G. Sutcliffe % 0.60/0.70 % Source : [Urb07] % 0.60/0.70 % Names : chainy-t46_zfmisc_1 [Urb07] % 0.60/0.70 % 0.60/0.70 % Status : Theorem % 0.60/0.70 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.3.0, 0.12 v6.2.0, 0.16 v6.1.0, 0.17 v5.5.0, 0.15 v5.4.0, 0.21 v5.3.0, 0.22 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.13 v4.0.1, 0.17 v4.0.0, 0.21 v3.7.0, 0.20 v3.5.0, 0.21 v3.4.0, 0.26 v3.3.0 % 0.60/0.70 % Syntax : Number of formulae : 91 ( 36 unt; 0 def) % 0.60/0.70 % Number of atoms : 183 ( 59 equ) % 0.60/0.70 % Maximal formula atoms : 6 ( 2 avg) % 0.60/0.70 % Number of connectives : 122 ( 30 ~; 5 |; 29 &) % 0.60/0.70 % ( 31 <=>; 27 =>; 0 <=; 0 <~>) % 0.60/0.70 % Maximal formula depth : 11 ( 4 avg) % 0.60/0.70 % Maximal term depth : 3 ( 1 avg) % 0.60/0.70 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty) % 0.60/0.70 % Number of functors : 10 ( 10 usr; 1 con; 0-2 aty) % 0.60/0.70 % Number of variables : 185 ( 178 !; 7 ?) % 0.60/0.70 % SPC : FOF_THM_RFO_SEQ % 0.60/0.70 % 0.60/0.70 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.60/0.70 % library, www.mizar.org % 0.60/0.70 %------------------------------------------------------------------------------ % 0.60/0.70 fof(antisymmetry_r2_hidden,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( in(A,B) % 0.60/0.70 => ~ in(B,A) ) ). % 0.60/0.70 % 0.60/0.70 fof(antisymmetry_r2_xboole_0,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( proper_subset(A,B) % 0.60/0.70 => ~ proper_subset(B,A) ) ). % 0.60/0.70 % 0.60/0.70 fof(commutativity_k2_tarski,axiom, % 0.60/0.70 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.60/0.70 % 0.60/0.70 fof(commutativity_k2_xboole_0,axiom, % 0.60/0.70 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.60/0.70 % 0.60/0.70 fof(commutativity_k3_xboole_0,axiom, % 0.60/0.70 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 0.60/0.70 % 0.60/0.70 fof(d10_xboole_0,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( A = B % 0.60/0.70 <=> ( subset(A,B) % 0.60/0.70 & subset(B,A) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(d1_tarski,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( B = singleton(A) % 0.60/0.70 <=> ! [C] : % 0.60/0.70 ( in(C,B) % 0.60/0.70 <=> C = A ) ) ). % 0.60/0.70 % 0.60/0.70 fof(d1_xboole_0,axiom, % 0.60/0.70 ! [A] : % 0.60/0.70 ( A = empty_set % 0.60/0.70 <=> ! [B] : ~ in(B,A) ) ). % 0.60/0.70 % 0.60/0.70 fof(d1_zfmisc_1,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( B = powerset(A) % 0.60/0.70 <=> ! [C] : % 0.60/0.70 ( in(C,B) % 0.60/0.70 <=> subset(C,A) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(d2_tarski,axiom, % 0.60/0.70 ! [A,B,C] : % 0.60/0.70 ( C = unordered_pair(A,B) % 0.60/0.70 <=> ! [D] : % 0.60/0.70 ( in(D,C) % 0.60/0.70 <=> ( D = A % 0.60/0.70 | D = B ) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(d2_xboole_0,axiom, % 0.60/0.70 ! [A,B,C] : % 0.60/0.70 ( C = set_union2(A,B) % 0.60/0.70 <=> ! [D] : % 0.60/0.70 ( in(D,C) % 0.60/0.70 <=> ( in(D,A) % 0.60/0.70 | in(D,B) ) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(d2_zfmisc_1,axiom, % 0.60/0.70 ! [A,B,C] : % 0.60/0.70 ( C = cartesian_product2(A,B) % 0.60/0.70 <=> ! [D] : % 0.60/0.70 ( in(D,C) % 0.60/0.70 <=> ? [E,F] : % 0.60/0.70 ( in(E,A) % 0.60/0.70 & in(F,B) % 0.60/0.70 & D = ordered_pair(E,F) ) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(d3_tarski,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( subset(A,B) % 0.60/0.70 <=> ! [C] : % 0.60/0.70 ( in(C,A) % 0.60/0.70 => in(C,B) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(d3_xboole_0,axiom, % 0.60/0.70 ! [A,B,C] : % 0.60/0.70 ( C = set_intersection2(A,B) % 0.60/0.70 <=> ! [D] : % 0.60/0.70 ( in(D,C) % 0.60/0.70 <=> ( in(D,A) % 0.60/0.70 & in(D,B) ) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(d4_tarski,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( B = union(A) % 0.60/0.70 <=> ! [C] : % 0.60/0.70 ( in(C,B) % 0.60/0.70 <=> ? [D] : % 0.60/0.70 ( in(C,D) % 0.60/0.70 & in(D,A) ) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(d4_xboole_0,axiom, % 0.60/0.70 ! [A,B,C] : % 0.60/0.70 ( C = set_difference(A,B) % 0.60/0.70 <=> ! [D] : % 0.60/0.70 ( in(D,C) % 0.60/0.70 <=> ( in(D,A) % 0.60/0.70 & ~ in(D,B) ) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(d5_tarski,axiom, % 0.60/0.70 ! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ). % 0.60/0.70 % 0.60/0.70 fof(d7_xboole_0,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( disjoint(A,B) % 0.60/0.70 <=> set_intersection2(A,B) = empty_set ) ). % 0.60/0.70 % 0.60/0.70 fof(d8_xboole_0,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( proper_subset(A,B) % 0.60/0.70 <=> ( subset(A,B) % 0.60/0.70 & A != B ) ) ). % 0.60/0.70 % 0.60/0.70 fof(dt_k1_tarski,axiom, % 0.60/0.70 $true ). % 0.60/0.70 % 0.60/0.70 fof(dt_k1_xboole_0,axiom, % 0.60/0.70 $true ). % 0.60/0.70 % 0.60/0.70 fof(dt_k1_zfmisc_1,axiom, % 0.60/0.70 $true ). % 0.60/0.70 % 0.60/0.70 fof(dt_k2_tarski,axiom, % 0.60/0.70 $true ). % 0.60/0.70 % 0.60/0.70 fof(dt_k2_xboole_0,axiom, % 0.60/0.70 $true ). % 0.60/0.70 % 0.60/0.70 fof(dt_k2_zfmisc_1,axiom, % 0.60/0.70 $true ). % 0.60/0.70 % 0.60/0.70 fof(dt_k3_tarski,axiom, % 0.60/0.70 $true ). % 0.60/0.70 % 0.60/0.70 fof(dt_k3_xboole_0,axiom, % 0.60/0.70 $true ). % 0.60/0.70 % 0.60/0.70 fof(dt_k4_tarski,axiom, % 0.60/0.70 $true ). % 0.60/0.70 % 0.60/0.70 fof(dt_k4_xboole_0,axiom, % 0.60/0.70 $true ). % 0.60/0.70 % 0.60/0.70 fof(fc1_xboole_0,axiom, % 0.60/0.70 empty(empty_set) ). % 0.60/0.70 % 0.60/0.70 fof(fc1_zfmisc_1,axiom, % 0.60/0.70 ! [A,B] : ~ empty(ordered_pair(A,B)) ). % 0.60/0.70 % 0.60/0.70 fof(fc2_xboole_0,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( ~ empty(A) % 0.60/0.70 => ~ empty(set_union2(A,B)) ) ). % 0.60/0.70 % 0.60/0.70 fof(fc3_xboole_0,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( ~ empty(A) % 0.60/0.70 => ~ empty(set_union2(B,A)) ) ). % 0.60/0.70 % 0.60/0.70 fof(idempotence_k2_xboole_0,axiom, % 0.60/0.70 ! [A,B] : set_union2(A,A) = A ). % 0.60/0.70 % 0.60/0.70 fof(idempotence_k3_xboole_0,axiom, % 0.60/0.70 ! [A,B] : set_intersection2(A,A) = A ). % 0.60/0.70 % 0.60/0.70 fof(irreflexivity_r2_xboole_0,axiom, % 0.60/0.70 ! [A,B] : ~ proper_subset(A,A) ). % 0.60/0.70 % 0.60/0.70 fof(l1_zfmisc_1,lemma, % 0.60/0.70 ! [A] : singleton(A) != empty_set ). % 0.60/0.70 % 0.60/0.70 fof(l23_zfmisc_1,lemma, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( in(A,B) % 0.60/0.70 => set_union2(singleton(A),B) = B ) ). % 0.60/0.70 % 0.60/0.70 fof(l25_zfmisc_1,lemma, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ~ ( disjoint(singleton(A),B) % 0.60/0.70 & in(A,B) ) ). % 0.60/0.70 % 0.60/0.70 fof(l28_zfmisc_1,lemma, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( ~ in(A,B) % 0.60/0.70 => disjoint(singleton(A),B) ) ). % 0.60/0.70 % 0.60/0.70 fof(l2_zfmisc_1,lemma, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( subset(singleton(A),B) % 0.60/0.70 <=> in(A,B) ) ). % 0.60/0.70 % 0.60/0.70 fof(l32_xboole_1,lemma, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( set_difference(A,B) = empty_set % 0.60/0.70 <=> subset(A,B) ) ). % 0.60/0.70 % 0.60/0.70 fof(l3_zfmisc_1,lemma, % 0.60/0.70 ! [A,B,C] : % 0.60/0.70 ( subset(A,B) % 0.60/0.70 => ( in(C,A) % 0.60/0.70 | subset(A,set_difference(B,singleton(C))) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(l4_zfmisc_1,lemma, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( subset(A,singleton(B)) % 0.60/0.70 <=> ( A = empty_set % 0.60/0.70 | A = singleton(B) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(l50_zfmisc_1,lemma, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( in(A,B) % 0.60/0.70 => subset(A,union(B)) ) ). % 0.60/0.70 % 0.60/0.70 fof(l55_zfmisc_1,lemma, % 0.60/0.70 ! [A,B,C,D] : % 0.60/0.70 ( in(ordered_pair(A,B),cartesian_product2(C,D)) % 0.60/0.70 <=> ( in(A,C) % 0.60/0.70 & in(B,D) ) ) ). % 0.60/0.70 % 0.60/0.70 fof(rc1_xboole_0,axiom, % 0.60/0.70 ? [A] : empty(A) ). % 0.60/0.70 % 0.60/0.70 fof(rc2_xboole_0,axiom, % 0.60/0.70 ? [A] : ~ empty(A) ). % 0.60/0.70 % 0.60/0.70 fof(reflexivity_r1_tarski,axiom, % 0.60/0.70 ! [A,B] : subset(A,A) ). % 0.60/0.70 % 0.60/0.70 fof(symmetry_r1_xboole_0,axiom, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( disjoint(A,B) % 0.60/0.70 => disjoint(B,A) ) ). % 0.60/0.70 % 0.60/0.70 fof(t10_zfmisc_1,lemma, % 0.60/0.70 ! [A,B,C,D] : % 0.60/0.70 ~ ( unordered_pair(A,B) = unordered_pair(C,D) % 0.60/0.70 & A != C % 0.60/0.70 & A != D ) ). % 0.60/0.70 % 0.60/0.70 fof(t12_xboole_1,lemma, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( subset(A,B) % 0.60/0.70 => set_union2(A,B) = B ) ). % 0.60/0.70 % 0.60/0.70 fof(t17_xboole_1,lemma, % 0.60/0.70 ! [A,B] : subset(set_intersection2(A,B),A) ). % 0.60/0.70 % 0.60/0.70 fof(t19_xboole_1,lemma, % 0.60/0.70 ! [A,B,C] : % 0.60/0.70 ( ( subset(A,B) % 0.60/0.70 & subset(A,C) ) % 0.60/0.70 => subset(A,set_intersection2(B,C)) ) ). % 0.60/0.70 % 0.60/0.70 fof(t1_boole,axiom, % 0.60/0.70 ! [A] : set_union2(A,empty_set) = A ). % 0.60/0.70 % 0.60/0.70 fof(t1_xboole_1,lemma, % 0.60/0.70 ! [A,B,C] : % 0.60/0.70 ( ( subset(A,B) % 0.60/0.70 & subset(B,C) ) % 0.60/0.70 => subset(A,C) ) ). % 0.60/0.70 % 0.60/0.70 fof(t1_zfmisc_1,lemma, % 0.60/0.70 powerset(empty_set) = singleton(empty_set) ). % 0.60/0.70 % 0.60/0.70 fof(t26_xboole_1,lemma, % 0.60/0.70 ! [A,B,C] : % 0.60/0.70 ( subset(A,B) % 0.60/0.70 => subset(set_intersection2(A,C),set_intersection2(B,C)) ) ). % 0.60/0.70 % 0.60/0.70 fof(t28_xboole_1,lemma, % 0.60/0.70 ! [A,B] : % 0.60/0.70 ( subset(A,B) % 0.60/0.70 => set_intersection2(A,B) = A ) ). % 0.60/0.70 % 0.60/0.70 fof(t2_boole,axiom, % 0.60/0.70 ! [A] : set_intersection2(A,empty_set) = empty_set ). % 0.60/0.70 % 0.60/0.70 fof(t2_tarski,axiom, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ( ! [C] : % 0.60/0.71 ( in(C,A) % 0.60/0.71 <=> in(C,B) ) % 0.60/0.71 => A = B ) ). % 0.60/0.71 % 0.60/0.71 fof(t2_xboole_1,lemma, % 0.60/0.71 ! [A] : subset(empty_set,A) ). % 0.60/0.71 % 0.60/0.71 fof(t33_xboole_1,lemma, % 0.60/0.71 ! [A,B,C] : % 0.60/0.71 ( subset(A,B) % 0.60/0.71 => subset(set_difference(A,C),set_difference(B,C)) ) ). % 0.60/0.71 % 0.60/0.71 fof(t33_zfmisc_1,lemma, % 0.60/0.71 ! [A,B,C,D] : % 0.60/0.71 ( ordered_pair(A,B) = ordered_pair(C,D) % 0.60/0.71 => ( A = C % 0.60/0.71 & B = D ) ) ). % 0.60/0.71 % 0.60/0.71 fof(t36_xboole_1,lemma, % 0.60/0.71 ! [A,B] : subset(set_difference(A,B),A) ). % 0.60/0.71 % 0.60/0.71 fof(t37_xboole_1,lemma, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ( set_difference(A,B) = empty_set % 0.60/0.71 <=> subset(A,B) ) ). % 0.60/0.71 % 0.60/0.71 fof(t37_zfmisc_1,lemma, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ( subset(singleton(A),B) % 0.60/0.71 <=> in(A,B) ) ). % 0.60/0.71 % 0.60/0.71 fof(t38_zfmisc_1,lemma, % 0.60/0.71 ! [A,B,C] : % 0.60/0.71 ( subset(unordered_pair(A,B),C) % 0.60/0.71 <=> ( in(A,C) % 0.60/0.71 & in(B,C) ) ) ). % 0.60/0.71 % 0.60/0.71 fof(t39_xboole_1,lemma, % 0.60/0.71 ! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B) ). % 0.60/0.71 % 0.60/0.71 fof(t39_zfmisc_1,lemma, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ( subset(A,singleton(B)) % 0.60/0.71 <=> ( A = empty_set % 0.60/0.71 | A = singleton(B) ) ) ). % 0.60/0.71 % 0.60/0.71 fof(t3_boole,axiom, % 0.60/0.71 ! [A] : set_difference(A,empty_set) = A ). % 0.60/0.71 % 0.60/0.71 fof(t3_xboole_0,lemma, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ( ~ ( ~ disjoint(A,B) % 0.60/0.71 & ! [C] : % 0.60/0.71 ~ ( in(C,A) % 0.60/0.71 & in(C,B) ) ) % 0.60/0.71 & ~ ( ? [C] : % 0.60/0.71 ( in(C,A) % 0.60/0.71 & in(C,B) ) % 0.60/0.71 & disjoint(A,B) ) ) ). % 0.60/0.71 % 0.60/0.71 fof(t3_xboole_1,lemma, % 0.60/0.71 ! [A] : % 0.60/0.71 ( subset(A,empty_set) % 0.60/0.71 => A = empty_set ) ). % 0.60/0.71 % 0.60/0.71 fof(t40_xboole_1,lemma, % 0.60/0.71 ! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) ). % 0.60/0.71 % 0.60/0.71 fof(t45_xboole_1,lemma, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ( subset(A,B) % 0.60/0.71 => B = set_union2(A,set_difference(B,A)) ) ). % 0.60/0.71 % 0.60/0.71 fof(t46_zfmisc_1,conjecture, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ( in(A,B) % 0.60/0.71 => set_union2(singleton(A),B) = B ) ). % 0.60/0.71 % 0.60/0.71 fof(t48_xboole_1,lemma, % 0.60/0.71 ! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ). % 0.60/0.71 % 0.60/0.71 fof(t4_boole,axiom, % 0.60/0.71 ! [A] : set_difference(empty_set,A) = empty_set ). % 0.60/0.71 % 0.60/0.71 fof(t4_xboole_0,lemma, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ( ~ ( ~ disjoint(A,B) % 0.60/0.71 & ! [C] : ~ in(C,set_intersection2(A,B)) ) % 0.60/0.71 & ~ ( ? [C] : in(C,set_intersection2(A,B)) % 0.60/0.71 & disjoint(A,B) ) ) ). % 0.60/0.71 % 0.60/0.71 fof(t60_xboole_1,lemma, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ~ ( subset(A,B) % 0.60/0.71 & proper_subset(B,A) ) ). % 0.60/0.71 % 0.60/0.71 fof(t63_xboole_1,lemma, % 0.60/0.71 ! [A,B,C] : % 0.60/0.71 ( ( subset(A,B) % 0.60/0.71 & disjoint(B,C) ) % 0.60/0.71 => disjoint(A,C) ) ). % 0.60/0.71 % 0.60/0.71 fof(t69_enumset1,lemma, % 0.60/0.71 ! [A] : unordered_pair(A,A) = singleton(A) ). % 0.60/0.71 % 0.60/0.71 fof(t6_boole,axiom, % 0.60/0.71 ! [A] : % 0.60/0.71 ( empty(A) % 0.60/0.71 => A = empty_set ) ). % 0.60/0.71 % 0.60/0.71 fof(t6_zfmisc_1,lemma, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ( subset(singleton(A),singleton(B)) % 0.60/0.71 => A = B ) ). % 0.60/0.71 % 0.60/0.71 fof(t7_boole,axiom, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ~ ( in(A,B) % 0.60/0.71 & empty(B) ) ). % 0.60/0.71 % 0.60/0.71 fof(t7_xboole_1,lemma, % 0.60/0.71 ! [A,B] : subset(A,set_union2(A,B)) ). % 0.60/0.71 % 0.60/0.71 fof(t83_xboole_1,lemma, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ( disjoint(A,B) % 0.60/0.71 <=> set_difference(A,B) = A ) ). % 0.60/0.71 % 0.60/0.71 fof(t8_boole,axiom, % 0.60/0.71 ! [A,B] : % 0.60/0.71 ~ ( empty(A) % 0.60/0.71 & A != B % 0.60/0.71 & empty(B) ) ). % 0.60/0.71 % 0.60/0.71 fof(t8_xboole_1,lemma, % 0.60/0.71 ! [A,B,C] : % 0.60/0.71 ( ( subset(A,B) % 0.60/0.71 & subset(C,B) ) % 0.60/0.71 => subset(set_union2(A,C),B) ) ). % 0.60/0.71 % 0.60/0.71 fof(t8_zfmisc_1,lemma, % 0.60/0.71 ! [A,B,C] : % 0.60/0.71 ( singleton(A) = unordered_pair(B,C) % 0.60/0.71 => A = B ) ). % 0.60/0.71 % 0.60/0.71 fof(t9_zfmisc_1,lemma, % 0.60/0.71 ! [A,B,C] : % 0.60/0.71 ( singleton(A) = unordered_pair(B,C) % 0.60/0.71 => B = C ) ). % 0.60/0.71 % 0.60/0.71 %------------------------------------------------------------------------------ % 0.60/0.71 %------------------------------------------- % 0.60/0.71 % Proof found % 0.60/0.71 % SZS status Theorem for theBenchmark % 0.60/0.71 % SZS output start Proof % 0.60/0.71 %ClaNum:214(EqnAxiom:71) % 0.60/0.71 %VarNum:858(SingletonVarNum:320) % 0.60/0.71 %MaxLitNum:5 % 0.60/0.71 %MaxfuncDepth:3 % 0.60/0.71 %SharedTerms:15 % 0.60/0.71 %goalClause: 74 95 % 0.60/0.71 %singleGoalClaCount:2 % 0.60/0.71 [72]P1(a1) % 0.60/0.71 [73]P1(a3) % 0.60/0.71 [74]P3(a11,a16) % 0.60/0.71 [92]~P1(a12) % 0.60/0.71 [79]E(f29(a1,a1),f18(a1)) % 0.60/0.71 [95]~E(f28(f29(a11,a11),a16),a16) % 0.60/0.71 [76]P4(a1,x761) % 0.60/0.71 [80]P4(x801,x801) % 0.60/0.71 [94]~P5(x941,x941) % 0.60/0.71 [75]E(f17(a1,x751),a1) % 0.60/0.71 [77]E(f28(x771,a1),x771) % 0.60/0.71 [78]E(f17(x781,a1),x781) % 0.60/0.71 [81]E(f28(x811,x811),x811) % 0.60/0.71 [93]~E(f29(x931,x931),a1) % 0.60/0.71 [84]E(f17(x841,f17(x841,a1)),a1) % 0.60/0.71 [87]E(f17(x871,f17(x871,x871)),x871) % 0.60/0.71 [82]E(f29(x821,x822),f29(x822,x821)) % 0.60/0.71 [83]E(f28(x831,x832),f28(x832,x831)) % 0.60/0.71 [85]P4(x851,f28(x851,x852)) % 0.60/0.71 [86]P4(f17(x861,x862),x861) % 0.60/0.71 [88]E(f28(x881,f17(x882,x881)),f28(x881,x882)) % 0.60/0.71 [89]E(f17(f28(x891,x892),x892),f17(x891,x892)) % 0.60/0.71 [90]E(f17(x901,f17(x901,x902)),f17(x902,f17(x902,x901))) % 0.60/0.71 [96]~P1(f29(f29(x961,x962),f29(x961,x961))) % 0.60/0.71 [97]~P1(x971)+E(x971,a1) % 0.60/0.71 [101]~P4(x1011,a1)+E(x1011,a1) % 0.60/0.71 [102]P3(f19(x1021),x1021)+E(x1021,a1) % 0.60/0.71 [100]~E(x1001,x1002)+P4(x1001,x1002) % 0.60/0.71 [103]~P3(x1032,x1031)+~E(x1031,a1) % 0.60/0.71 [104]~P5(x1041,x1042)+~E(x1041,x1042) % 0.60/0.71 [105]~P1(x1051)+~P3(x1052,x1051) % 0.60/0.71 [110]~P5(x1101,x1102)+P4(x1101,x1102) % 0.60/0.71 [111]~P2(x1112,x1111)+P2(x1111,x1112) % 0.60/0.71 [122]~P3(x1222,x1221)+~P3(x1221,x1222) % 0.60/0.71 [123]~P5(x1232,x1231)+~P5(x1231,x1232) % 0.60/0.71 [124]~P4(x1242,x1241)+~P5(x1241,x1242) % 0.60/0.71 [107]~P4(x1071,x1072)+E(f17(x1071,x1072),a1) % 0.60/0.71 [109]P4(x1091,x1092)+~E(f17(x1091,x1092),a1) % 0.60/0.71 [112]~P4(x1121,x1122)+E(f28(x1121,x1122),x1122) % 0.60/0.71 [113]~P2(x1131,x1132)+E(f17(x1131,x1132),x1131) % 0.60/0.71 [114]P2(x1141,x1142)+~E(f17(x1141,x1142),x1141) % 0.60/0.71 [120]~E(x1201,a1)+P4(x1201,f29(x1202,x1202)) % 0.60/0.71 [121]~P3(x1211,x1212)+P4(x1211,f30(x1212)) % 0.60/0.71 [133]P1(x1331)+~P1(f28(x1332,x1331)) % 0.60/0.71 [134]P1(x1341)+~P1(f28(x1341,x1342)) % 0.60/0.71 [135]P3(x1351,x1352)+P2(f29(x1351,x1351),x1352) % 0.60/0.71 [136]P4(x1361,x1362)+P3(f4(x1361,x1362),x1361) % 0.60/0.71 [137]P2(x1371,x1372)+P3(f13(x1371,x1372),x1372) % 0.60/0.71 [138]P2(x1381,x1382)+P3(f13(x1381,x1382),x1381) % 0.60/0.71 [147]~P3(x1471,x1472)+P4(f29(x1471,x1471),x1472) % 0.60/0.71 [164]P4(x1641,x1642)+~P3(f4(x1641,x1642),x1642) % 0.60/0.71 [172]~P3(x1721,x1722)+~P2(f29(x1721,x1721),x1722) % 0.60/0.71 [177]E(x1771,x1772)+~P4(f29(x1771,x1771),f29(x1772,x1772)) % 0.60/0.71 [145]~P2(x1451,x1452)+E(f17(x1451,f17(x1451,x1452)),a1) % 0.60/0.71 [148]~P4(x1481,x1482)+E(f28(x1481,f17(x1482,x1481)),x1482) % 0.60/0.71 [149]~P4(x1491,x1492)+E(f17(x1491,f17(x1491,x1492)),x1491) % 0.60/0.71 [150]~P3(x1501,x1502)+E(f28(f29(x1501,x1501),x1502),x1502) % 0.60/0.71 [159]P2(x1591,x1592)+~E(f17(x1591,f17(x1591,x1592)),a1) % 0.60/0.71 [183]P2(x1831,x1832)+P3(f20(x1831,x1832),f17(x1831,f17(x1831,x1832))) % 0.60/0.71 [127]E(x1271,x1272)+~E(f29(x1273,x1273),f29(x1271,x1272)) % 0.60/0.71 [128]E(x1281,x1282)+~E(f29(x1281,x1281),f29(x1282,x1283)) % 0.60/0.71 [160]P3(x1601,x1602)+~P4(f29(x1603,x1601),x1602) % 0.60/0.71 [161]P3(x1611,x1612)+~P4(f29(x1611,x1613),x1612) % 0.60/0.71 [173]~P4(x1731,x1733)+P4(f17(x1731,x1732),f17(x1733,x1732)) % 0.60/0.71 [188]~P2(x1881,x1882)+~P3(x1883,f17(x1881,f17(x1881,x1882))) % 0.60/0.71 [190]~P4(x1901,x1903)+P4(f17(x1901,f17(x1901,x1902)),f17(x1903,f17(x1903,x1902))) % 0.60/0.71 [191]E(x1911,x1912)+~E(f29(f29(x1913,x1911),f29(x1913,x1913)),f29(f29(x1914,x1912),f29(x1914,x1914))) % 0.60/0.71 [192]E(x1921,x1922)+~E(f29(f29(x1921,x1923),f29(x1921,x1921)),f29(f29(x1922,x1924),f29(x1922,x1922))) % 0.60/0.71 [198]P3(x1981,x1982)+~P3(f29(f29(x1983,x1981),f29(x1983,x1983)),f2(x1984,x1982)) % 0.60/0.71 [199]P3(x1991,x1992)+~P3(f29(f29(x1991,x1993),f29(x1991,x1991)),f2(x1992,x1994)) % 0.60/0.71 [98]~P1(x982)+~P1(x981)+E(x981,x982) % 0.60/0.71 [115]P5(x1151,x1152)+~P4(x1151,x1152)+E(x1151,x1152) % 0.60/0.71 [129]~P4(x1292,x1291)+~P4(x1291,x1292)+E(x1291,x1292) % 0.60/0.71 [156]E(f14(x1562,x1561),x1562)+P3(f14(x1562,x1561),x1561)+E(x1561,f29(x1562,x1562)) % 0.60/0.71 [166]E(x1661,f29(x1662,x1662))+~P4(x1661,f29(x1662,x1662))+E(x1661,a1) % 0.60/0.71 [167]E(x1671,x1672)+P3(f15(x1671,x1672),x1672)+P3(f15(x1671,x1672),x1671) % 0.60/0.71 [170]P3(f21(x1702,x1701),x1701)+P4(f21(x1702,x1701),x1702)+E(x1701,f18(x1702)) % 0.60/0.71 [171]P3(f6(x1712,x1711),x1711)+P3(f9(x1712,x1711),x1712)+E(x1711,f30(x1712)) % 0.60/0.71 [176]~E(f14(x1762,x1761),x1762)+~P3(f14(x1762,x1761),x1761)+E(x1761,f29(x1762,x1762)) % 0.60/0.71 [178]P3(f6(x1782,x1781),x1781)+P3(f6(x1782,x1781),f9(x1782,x1781))+E(x1781,f30(x1782)) % 0.60/0.71 [180]E(x1801,x1802)+~P3(f15(x1801,x1802),x1802)+~P3(f15(x1801,x1802),x1801) % 0.60/0.71 [182]~P3(f21(x1822,x1821),x1821)+~P4(f21(x1822,x1821),x1822)+E(x1821,f18(x1822)) % 0.60/0.71 [139]~P4(x1393,x1392)+P3(x1391,x1392)+~P3(x1391,x1393) % 0.60/0.71 [140]~P4(x1401,x1403)+P4(x1401,x1402)+~P4(x1403,x1402) % 0.60/0.71 [141]~P2(x1413,x1412)+P2(x1411,x1412)+~P4(x1411,x1413) % 0.60/0.71 [153]~P2(x1533,x1532)+~P3(x1531,x1532)+~P3(x1531,x1533) % 0.60/0.71 [125]~P4(x1251,x1253)+P3(x1251,x1252)+~E(x1252,f18(x1253)) % 0.60/0.71 [126]~P3(x1261,x1263)+P4(x1261,x1262)+~E(x1263,f18(x1262)) % 0.60/0.71 [131]~P3(x1311,x1313)+E(x1311,x1312)+~E(x1313,f29(x1312,x1312)) % 0.60/0.71 [168]~P3(x1682,x1683)+~P3(x1681,x1683)+P4(f29(x1681,x1682),x1683) % 0.60/0.71 [169]~P4(x1692,x1693)+~P4(x1691,x1693)+P4(f28(x1691,x1692),x1693) % 0.60/0.71 [185]~P3(x1851,x1853)+~E(x1853,f30(x1852))+P3(x1851,f7(x1852,x1853,x1851)) % 0.60/0.71 [186]~P3(x1863,x1862)+~E(x1862,f30(x1861))+P3(f7(x1861,x1862,x1863),x1861) % 0.60/0.71 [195]P3(f23(x1952,x1953,x1951),x1951)+P3(f27(x1952,x1953,x1951),x1952)+E(x1951,f2(x1952,x1953)) % 0.60/0.71 [196]P3(f23(x1962,x1963,x1961),x1961)+P3(f5(x1962,x1963,x1961),x1963)+E(x1961,f2(x1962,x1963)) % 0.60/0.71 [197]P3(f10(x1972,x1973,x1971),x1971)+P3(f10(x1972,x1973,x1971),x1972)+E(x1971,f17(x1972,x1973)) % 0.60/0.71 [202]~E(f22(x2022,x2023,x2021),x2023)+~P3(f22(x2022,x2023,x2021),x2021)+E(x2021,f29(x2022,x2023)) % 0.60/0.71 [203]~E(f22(x2032,x2033,x2031),x2032)+~P3(f22(x2032,x2033,x2031),x2031)+E(x2031,f29(x2032,x2033)) % 0.60/0.71 [204]P3(f10(x2042,x2043,x2041),x2041)+~P3(f10(x2042,x2043,x2041),x2043)+E(x2041,f17(x2042,x2043)) % 0.60/0.71 [206]~P3(f24(x2062,x2063,x2061),x2061)+~P3(f24(x2062,x2063,x2061),x2063)+E(x2061,f28(x2062,x2063)) % 0.60/0.71 [207]~P3(f24(x2072,x2073,x2071),x2071)+~P3(f24(x2072,x2073,x2071),x2072)+E(x2071,f28(x2072,x2073)) % 0.60/0.71 [181]~P4(x1812,x1813)+P3(x1811,x1812)+P4(x1812,f17(x1813,f29(x1811,x1811))) % 0.60/0.71 [184]~P4(x1841,x1843)+~P4(x1841,x1842)+P4(x1841,f17(x1842,f17(x1842,x1843))) % 0.60/0.71 [200]P3(f8(x2002,x2003,x2001),x2001)+P3(f8(x2002,x2003,x2001),x2003)+E(x2001,f17(x2002,f17(x2002,x2003))) % 0.60/0.71 [201]P3(f8(x2012,x2013,x2011),x2011)+P3(f8(x2012,x2013,x2011),x2012)+E(x2011,f17(x2012,f17(x2012,x2013))) % 0.60/0.71 [213]P3(f23(x2132,x2133,x2131),x2131)+E(x2131,f2(x2132,x2133))+E(f29(f29(f27(x2132,x2133,x2131),f5(x2132,x2133,x2131)),f29(f27(x2132,x2133,x2131),f27(x2132,x2133,x2131))),f23(x2132,x2133,x2131)) % 0.60/0.71 [116]P3(x1161,x1162)+~E(x1161,x1163)+~E(x1162,f29(x1164,x1163)) % 0.60/0.71 [117]P3(x1171,x1172)+~E(x1171,x1173)+~E(x1172,f29(x1173,x1174)) % 0.60/0.71 [130]E(x1301,x1302)+E(x1301,x1303)+~E(f29(x1301,x1304),f29(x1303,x1302)) % 0.60/0.71 [142]~P3(x1421,x1424)+P3(x1421,x1422)+~E(x1422,f28(x1423,x1424)) % 0.60/0.71 [143]~P3(x1431,x1433)+P3(x1431,x1432)+~E(x1432,f28(x1433,x1434)) % 0.60/0.71 [144]~P3(x1441,x1443)+P3(x1441,x1442)+~E(x1443,f17(x1442,x1444)) % 0.60/0.71 [155]~P3(x1554,x1553)+~P3(x1554,x1551)+~E(x1551,f17(x1552,x1553)) % 0.60/0.71 [210]~P3(x2104,x2103)+~E(x2103,f2(x2101,x2102))+P3(f25(x2101,x2102,x2103,x2104),x2101) % 0.60/0.71 [211]~P3(x2114,x2113)+~E(x2113,f2(x2111,x2112))+P3(f26(x2111,x2112,x2113,x2114),x2112) % 0.60/0.71 [174]~P3(x1741,x1743)+P3(x1741,x1742)+~E(x1743,f17(x1744,f17(x1744,x1742))) % 0.60/0.71 [193]~P3(x1932,x1934)+~P3(x1931,x1933)+P3(f29(f29(x1931,x1932),f29(x1931,x1931)),f2(x1933,x1934)) % 0.60/0.71 [214]~P3(x2144,x2143)+~E(x2143,f2(x2141,x2142))+E(f29(f29(f25(x2141,x2142,x2143,x2144),f26(x2141,x2142,x2143,x2144)),f29(f25(x2141,x2142,x2143,x2144),f25(x2141,x2142,x2143,x2144))),x2144) % 0.60/0.71 [187]~P3(x1873,x1872)+~P3(f6(x1872,x1871),x1873)+~P3(f6(x1872,x1871),x1871)+E(x1871,f30(x1872)) % 0.60/0.71 [194]E(f22(x1942,x1943,x1941),x1943)+E(f22(x1942,x1943,x1941),x1942)+P3(f22(x1942,x1943,x1941),x1941)+E(x1941,f29(x1942,x1943)) % 0.60/0.71 [205]P3(f24(x2052,x2053,x2051),x2051)+P3(f24(x2052,x2053,x2051),x2053)+P3(f24(x2052,x2053,x2051),x2052)+E(x2051,f28(x2052,x2053)) % 0.60/0.71 [209]P3(f10(x2092,x2093,x2091),x2093)+~P3(f10(x2092,x2093,x2091),x2091)+~P3(f10(x2092,x2093,x2091),x2092)+E(x2091,f17(x2092,x2093)) % 0.60/0.71 [212]~P3(f8(x2122,x2123,x2121),x2121)+~P3(f8(x2122,x2123,x2121),x2123)+~P3(f8(x2122,x2123,x2121),x2122)+E(x2121,f17(x2122,f17(x2122,x2123))) % 0.60/0.71 [132]~P3(x1321,x1324)+E(x1321,x1322)+E(x1321,x1323)+~E(x1324,f29(x1323,x1322)) % 0.60/0.71 [154]~P3(x1541,x1544)+P3(x1541,x1542)+~P3(x1544,x1543)+~E(x1542,f30(x1543)) % 0.60/0.71 [157]~P3(x1571,x1574)+P3(x1571,x1572)+P3(x1571,x1573)+~E(x1572,f17(x1574,x1573)) % 0.60/0.71 [158]~P3(x1581,x1584)+P3(x1581,x1582)+P3(x1581,x1583)+~E(x1584,f28(x1583,x1582)) % 0.60/0.71 [179]~P3(x1791,x1794)+~P3(x1791,x1793)+P3(x1791,x1792)+~E(x1792,f17(x1793,f17(x1793,x1794))) % 0.60/0.71 [208]~P3(x2085,x2083)+~P3(x2084,x2082)+~P3(f23(x2082,x2083,x2081),x2081)+E(x2081,f2(x2082,x2083))+~E(f23(x2082,x2083,x2081),f29(f29(x2084,x2085),f29(x2084,x2084))) % 0.60/0.71 [189]~P3(x1896,x1894)+~P3(x1895,x1893)+P3(x1891,x1892)+~E(x1892,f2(x1893,x1894))+~E(x1891,f29(f29(x1895,x1896),f29(x1895,x1895))) % 0.60/0.71 %EqnAxiom % 0.60/0.71 [1]E(x11,x11) % 0.60/0.71 [2]E(x22,x21)+~E(x21,x22) % 0.60/0.71 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.60/0.71 [4]~E(x41,x42)+E(f17(x41,x43),f17(x42,x43)) % 0.60/0.71 [5]~E(x51,x52)+E(f17(x53,x51),f17(x53,x52)) % 0.60/0.71 [6]~E(x61,x62)+E(f28(x61,x63),f28(x62,x63)) % 0.60/0.71 [7]~E(x71,x72)+E(f28(x73,x71),f28(x73,x72)) % 0.60/0.71 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.60/0.71 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.60/0.71 [10]~E(x101,x102)+E(f29(x101,x103),f29(x102,x103)) % 0.60/0.71 [11]~E(x111,x112)+E(f29(x113,x111),f29(x113,x112)) % 0.60/0.71 [12]~E(x121,x122)+E(f18(x121),f18(x122)) % 0.60/0.71 [13]~E(x131,x132)+E(f8(x131,x133,x134),f8(x132,x133,x134)) % 0.60/0.71 [14]~E(x141,x142)+E(f8(x143,x141,x144),f8(x143,x142,x144)) % 0.60/0.71 [15]~E(x151,x152)+E(f8(x153,x154,x151),f8(x153,x154,x152)) % 0.60/0.71 [16]~E(x161,x162)+E(f22(x161,x163,x164),f22(x162,x163,x164)) % 0.60/0.71 [17]~E(x171,x172)+E(f22(x173,x171,x174),f22(x173,x172,x174)) % 0.60/0.71 [18]~E(x181,x182)+E(f22(x183,x184,x181),f22(x183,x184,x182)) % 0.60/0.71 [19]~E(x191,x192)+E(f14(x191,x193),f14(x192,x193)) % 0.60/0.71 [20]~E(x201,x202)+E(f14(x203,x201),f14(x203,x202)) % 0.60/0.71 [21]~E(x211,x212)+E(f10(x211,x213,x214),f10(x212,x213,x214)) % 0.60/0.71 [22]~E(x221,x222)+E(f10(x223,x221,x224),f10(x223,x222,x224)) % 0.60/0.71 [23]~E(x231,x232)+E(f10(x233,x234,x231),f10(x233,x234,x232)) % 0.60/0.71 [24]~E(x241,x242)+E(f15(x241,x243),f15(x242,x243)) % 0.60/0.71 [25]~E(x251,x252)+E(f15(x253,x251),f15(x253,x252)) % 0.60/0.71 [26]~E(x261,x262)+E(f21(x261,x263),f21(x262,x263)) % 0.60/0.71 [27]~E(x271,x272)+E(f21(x273,x271),f21(x273,x272)) % 0.60/0.71 [28]~E(x281,x282)+E(f6(x281,x283),f6(x282,x283)) % 0.60/0.71 [29]~E(x291,x292)+E(f6(x293,x291),f6(x293,x292)) % 0.60/0.71 [30]~E(x301,x302)+E(f9(x301,x303),f9(x302,x303)) % 0.60/0.71 [31]~E(x311,x312)+E(f9(x313,x311),f9(x313,x312)) % 0.60/0.71 [32]~E(x321,x322)+E(f25(x321,x323,x324,x325),f25(x322,x323,x324,x325)) % 0.60/0.71 [33]~E(x331,x332)+E(f25(x333,x331,x334,x335),f25(x333,x332,x334,x335)) % 0.60/0.71 [34]~E(x341,x342)+E(f25(x343,x344,x341,x345),f25(x343,x344,x342,x345)) % 0.60/0.71 [35]~E(x351,x352)+E(f25(x353,x354,x355,x351),f25(x353,x354,x355,x352)) % 0.60/0.71 [36]~E(x361,x362)+E(f30(x361),f30(x362)) % 0.60/0.71 [37]~E(x371,x372)+E(f26(x371,x373,x374,x375),f26(x372,x373,x374,x375)) % 0.60/0.71 [38]~E(x381,x382)+E(f26(x383,x381,x384,x385),f26(x383,x382,x384,x385)) % 0.60/0.71 [39]~E(x391,x392)+E(f26(x393,x394,x391,x395),f26(x393,x394,x392,x395)) % 0.60/0.71 [40]~E(x401,x402)+E(f26(x403,x404,x405,x401),f26(x403,x404,x405,x402)) % 0.60/0.71 [41]~E(x411,x412)+E(f23(x411,x413,x414),f23(x412,x413,x414)) % 0.60/0.71 [42]~E(x421,x422)+E(f23(x423,x421,x424),f23(x423,x422,x424)) % 0.60/0.71 [43]~E(x431,x432)+E(f23(x433,x434,x431),f23(x433,x434,x432)) % 0.60/0.71 [44]~E(x441,x442)+E(f24(x441,x443,x444),f24(x442,x443,x444)) % 0.60/0.71 [45]~E(x451,x452)+E(f24(x453,x451,x454),f24(x453,x452,x454)) % 0.60/0.71 [46]~E(x461,x462)+E(f24(x463,x464,x461),f24(x463,x464,x462)) % 0.60/0.71 [47]~E(x471,x472)+E(f5(x471,x473,x474),f5(x472,x473,x474)) % 0.60/0.71 [48]~E(x481,x482)+E(f5(x483,x481,x484),f5(x483,x482,x484)) % 0.60/0.71 [49]~E(x491,x492)+E(f5(x493,x494,x491),f5(x493,x494,x492)) % 0.60/0.71 [50]~E(x501,x502)+E(f4(x501,x503),f4(x502,x503)) % 0.60/0.71 [51]~E(x511,x512)+E(f4(x513,x511),f4(x513,x512)) % 0.60/0.71 [52]~E(x521,x522)+E(f27(x521,x523,x524),f27(x522,x523,x524)) % 0.60/0.71 [53]~E(x531,x532)+E(f27(x533,x531,x534),f27(x533,x532,x534)) % 0.60/0.71 [54]~E(x541,x542)+E(f27(x543,x544,x541),f27(x543,x544,x542)) % 0.60/0.71 [55]~E(x551,x552)+E(f13(x551,x553),f13(x552,x553)) % 0.60/0.71 [56]~E(x561,x562)+E(f13(x563,x561),f13(x563,x562)) % 0.60/0.71 [57]~E(x571,x572)+E(f20(x571,x573),f20(x572,x573)) % 0.60/0.71 [58]~E(x581,x582)+E(f20(x583,x581),f20(x583,x582)) % 0.60/0.71 [59]~E(x591,x592)+E(f19(x591),f19(x592)) % 0.60/0.71 [60]~E(x601,x602)+E(f7(x601,x603,x604),f7(x602,x603,x604)) % 0.60/0.71 [61]~E(x611,x612)+E(f7(x613,x611,x614),f7(x613,x612,x614)) % 0.60/0.71 [62]~E(x621,x622)+E(f7(x623,x624,x621),f7(x623,x624,x622)) % 0.60/0.71 [63]~P1(x631)+P1(x632)+~E(x631,x632) % 0.60/0.71 [64]P3(x642,x643)+~E(x641,x642)+~P3(x641,x643) % 0.60/0.71 [65]P3(x653,x652)+~E(x651,x652)+~P3(x653,x651) % 0.60/0.71 [66]P4(x662,x663)+~E(x661,x662)+~P4(x661,x663) % 0.60/0.71 [67]P4(x673,x672)+~E(x671,x672)+~P4(x673,x671) % 0.60/0.71 [68]P2(x682,x683)+~E(x681,x682)+~P2(x681,x683) % 0.60/0.71 [69]P2(x693,x692)+~E(x691,x692)+~P2(x693,x691) % 0.60/0.71 [70]P5(x702,x703)+~E(x701,x702)+~P5(x701,x703) % 0.60/0.71 [71]P5(x713,x712)+~E(x711,x712)+~P5(x713,x711) % 0.60/0.71 % 0.60/0.71 %------------------------------------------- % 0.60/0.71 cnf(242,plain, % 0.60/0.71 ($false), % 0.60/0.71 inference(scs_inference,[],[74,95,150]), % 0.60/0.71 ['proof']). % 0.60/0.71 % SZS output end Proof % 0.60/0.71 % Total time :0.010000s %------------------------------------------------------------------------------