%------------------------------------------------------------------------------ % File : CSE---1.7 % Problem : SEU163+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 : n001.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 15:01:28 EDT 2024 % Result : Theorem 0.11s 0.51s % Output : CNFRefutation 0.11s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.03/0.07 % Problem : SEU163+2 : TPTP v8.2.0. Released v3.3.0. % 0.03/0.07 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s % 0.07/0.26 % Computer : n001.cluster.edu % 0.07/0.26 % Model : x86_64 x86_64 % 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.07/0.26 % Memory : 8042.1875MB % 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64 % 0.07/0.26 % CPULimit : 300 % 0.07/0.26 % WCLimit : 300 % 0.07/0.26 % DateTime : Fri Jun 21 18:00:38 EDT 2024 % 0.07/0.26 % CPUTime : % 0.11/0.41 start to proof:theBenchmark % 0.11/0.48 %------------------------------------------- % 0.11/0.48 % File :CSE---1.7 % 0.11/0.48 % Problem :theBenchmark % 0.11/0.48 % Transform :cnf % 0.11/0.48 % Format :tptp:raw % 0.11/0.48 % Command :java -jar mcs_scs.jar %d %s % 0.11/0.48 % 0.11/0.48 % Result :Theorem 0.010000s % 0.11/0.48 % Output :CNFRefutation 0.010000s % 0.11/0.48 %------------------------------------------- % 0.11/0.49 %------------------------------------------------------------------------------ % 0.11/0.49 % File : SEU163+2 : TPTP v8.2.0. Released v3.3.0. % 0.11/0.49 % Domain : Set theory % 0.11/0.49 % Problem : MPTP chainy problem t92_zfmisc_1 % 0.11/0.49 % Version : [Urb07] axioms : Especial. % 0.11/0.49 % English : % 0.11/0.49 % 0.11/0.49 % Refs : [Ban01] Bancerek et al. (2001), On the Characterizations of Co % 0.11/0.49 % : [Urb07] Urban (2006), Email to G. Sutcliffe % 0.11/0.49 % Source : [Urb07] % 0.11/0.49 % Names : chainy-t92_zfmisc_1 [Urb07] % 0.11/0.49 % 0.11/0.49 % Status : Theorem % 0.11/0.49 % Rating : 0.06 v8.1.0, 0.03 v7.1.0, 0.04 v7.0.0, 0.03 v6.4.0, 0.08 v6.2.0, 0.12 v6.1.0, 0.17 v6.0.0, 0.13 v5.5.0, 0.11 v5.4.0, 0.14 v5.3.0, 0.19 v5.2.0, 0.05 v5.0.0, 0.08 v4.1.0, 0.09 v4.0.1, 0.13 v4.0.0, 0.17 v3.7.0, 0.15 v3.5.0, 0.16 v3.3.0 % 0.11/0.49 % Syntax : Number of formulae : 93 ( 36 unt; 0 def) % 0.11/0.49 % Number of atoms : 187 ( 60 equ) % 0.11/0.49 % Maximal formula atoms : 6 ( 2 avg) % 0.11/0.49 % Number of connectives : 125 ( 31 ~; 5 |; 29 &) % 0.11/0.49 % ( 32 <=>; 28 =>; 0 <=; 0 <~>) % 0.11/0.49 % Maximal formula depth : 11 ( 4 avg) % 0.11/0.49 % Maximal term depth : 3 ( 1 avg) % 0.11/0.49 % Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty) % 0.11/0.49 % Number of functors : 10 ( 10 usr; 1 con; 0-2 aty) % 0.11/0.49 % Number of variables : 189 ( 182 !; 7 ?) % 0.11/0.49 % SPC : FOF_THM_RFO_SEQ % 0.11/0.49 % 0.11/0.49 % Comments : Translated by MPTP 0.2 from the original problem in the Mizar % 0.11/0.49 % library, www.mizar.org % 0.11/0.49 %------------------------------------------------------------------------------ % 0.11/0.49 fof(antisymmetry_r2_hidden,axiom, % 0.11/0.49 ! [A,B] : % 0.11/0.49 ( in(A,B) % 0.11/0.49 => ~ in(B,A) ) ). % 0.11/0.49 % 0.11/0.49 fof(antisymmetry_r2_xboole_0,axiom, % 0.11/0.49 ! [A,B] : % 0.11/0.49 ( proper_subset(A,B) % 0.11/0.49 => ~ proper_subset(B,A) ) ). % 0.11/0.49 % 0.11/0.49 fof(commutativity_k2_tarski,axiom, % 0.11/0.49 ! [A,B] : unordered_pair(A,B) = unordered_pair(B,A) ). % 0.11/0.49 % 0.11/0.49 fof(commutativity_k2_xboole_0,axiom, % 0.11/0.49 ! [A,B] : set_union2(A,B) = set_union2(B,A) ). % 0.11/0.49 % 0.11/0.49 fof(commutativity_k3_xboole_0,axiom, % 0.11/0.49 ! [A,B] : set_intersection2(A,B) = set_intersection2(B,A) ). % 0.11/0.49 % 0.11/0.49 fof(d10_xboole_0,axiom, % 0.11/0.49 ! [A,B] : % 0.11/0.49 ( A = B % 0.11/0.49 <=> ( subset(A,B) % 0.11/0.49 & subset(B,A) ) ) ). % 0.11/0.49 % 0.11/0.49 fof(d1_tarski,axiom, % 0.11/0.49 ! [A,B] : % 0.11/0.49 ( B = singleton(A) % 0.11/0.49 <=> ! [C] : % 0.11/0.49 ( in(C,B) % 0.11/0.49 <=> C = A ) ) ). % 0.11/0.49 % 0.11/0.49 fof(d1_xboole_0,axiom, % 0.11/0.49 ! [A] : % 0.11/0.49 ( A = empty_set % 0.11/0.49 <=> ! [B] : ~ in(B,A) ) ). % 0.11/0.49 % 0.11/0.49 fof(d1_zfmisc_1,axiom, % 0.11/0.49 ! [A,B] : % 0.11/0.49 ( B = powerset(A) % 0.11/0.49 <=> ! [C] : % 0.11/0.49 ( in(C,B) % 0.11/0.49 <=> subset(C,A) ) ) ). % 0.11/0.49 % 0.11/0.49 fof(d2_tarski,axiom, % 0.11/0.49 ! [A,B,C] : % 0.11/0.49 ( C = unordered_pair(A,B) % 0.11/0.49 <=> ! [D] : % 0.11/0.49 ( in(D,C) % 0.11/0.49 <=> ( D = A % 0.11/0.49 | D = B ) ) ) ). % 0.11/0.49 % 0.11/0.49 fof(d2_xboole_0,axiom, % 0.11/0.49 ! [A,B,C] : % 0.11/0.49 ( C = set_union2(A,B) % 0.11/0.49 <=> ! [D] : % 0.11/0.49 ( in(D,C) % 0.11/0.49 <=> ( in(D,A) % 0.11/0.49 | in(D,B) ) ) ) ). % 0.11/0.49 % 0.11/0.49 fof(d2_zfmisc_1,axiom, % 0.11/0.49 ! [A,B,C] : % 0.11/0.49 ( C = cartesian_product2(A,B) % 0.11/0.49 <=> ! [D] : % 0.11/0.49 ( in(D,C) % 0.11/0.49 <=> ? [E,F] : % 0.11/0.49 ( in(E,A) % 0.11/0.49 & in(F,B) % 0.11/0.49 & D = ordered_pair(E,F) ) ) ) ). % 0.11/0.49 % 0.11/0.49 fof(d3_tarski,axiom, % 0.11/0.49 ! [A,B] : % 0.11/0.49 ( subset(A,B) % 0.11/0.49 <=> ! [C] : % 0.11/0.49 ( in(C,A) % 0.11/0.49 => in(C,B) ) ) ). % 0.11/0.49 % 0.11/0.49 fof(d3_xboole_0,axiom, % 0.11/0.49 ! [A,B,C] : % 0.11/0.49 ( C = set_intersection2(A,B) % 0.11/0.49 <=> ! [D] : % 0.11/0.49 ( in(D,C) % 0.11/0.49 <=> ( in(D,A) % 0.11/0.49 & in(D,B) ) ) ) ). % 0.11/0.49 % 0.11/0.49 fof(d4_tarski,axiom, % 0.11/0.49 ! [A,B] : % 0.11/0.49 ( B = union(A) % 0.11/0.49 <=> ! [C] : % 0.11/0.49 ( in(C,B) % 0.11/0.49 <=> ? [D] : % 0.11/0.49 ( in(C,D) % 0.11/0.49 & in(D,A) ) ) ) ). % 0.11/0.49 % 0.11/0.49 fof(d4_xboole_0,axiom, % 0.11/0.49 ! [A,B,C] : % 0.11/0.49 ( C = set_difference(A,B) % 0.11/0.49 <=> ! [D] : % 0.11/0.49 ( in(D,C) % 0.11/0.49 <=> ( in(D,A) % 0.11/0.49 & ~ in(D,B) ) ) ) ). % 0.11/0.49 % 0.11/0.49 fof(d5_tarski,axiom, % 0.11/0.49 ! [A,B] : ordered_pair(A,B) = unordered_pair(unordered_pair(A,B),singleton(A)) ). % 0.11/0.49 % 0.11/0.49 fof(d7_xboole_0,axiom, % 0.11/0.49 ! [A,B] : % 0.11/0.49 ( disjoint(A,B) % 0.11/0.49 <=> set_intersection2(A,B) = empty_set ) ). % 0.11/0.49 % 0.11/0.49 fof(d8_xboole_0,axiom, % 0.11/0.49 ! [A,B] : % 0.11/0.49 ( proper_subset(A,B) % 0.11/0.49 <=> ( subset(A,B) % 0.11/0.49 & A != B ) ) ). % 0.11/0.49 % 0.11/0.50 fof(dt_k1_tarski,axiom, % 0.11/0.50 $true ). % 0.11/0.50 % 0.11/0.50 fof(dt_k1_xboole_0,axiom, % 0.11/0.50 $true ). % 0.11/0.50 % 0.11/0.50 fof(dt_k1_zfmisc_1,axiom, % 0.11/0.50 $true ). % 0.11/0.50 % 0.11/0.50 fof(dt_k2_tarski,axiom, % 0.11/0.50 $true ). % 0.11/0.50 % 0.11/0.50 fof(dt_k2_xboole_0,axiom, % 0.11/0.50 $true ). % 0.11/0.50 % 0.11/0.50 fof(dt_k2_zfmisc_1,axiom, % 0.11/0.50 $true ). % 0.11/0.50 % 0.11/0.50 fof(dt_k3_tarski,axiom, % 0.11/0.50 $true ). % 0.11/0.50 % 0.11/0.50 fof(dt_k3_xboole_0,axiom, % 0.11/0.50 $true ). % 0.11/0.50 % 0.11/0.50 fof(dt_k4_tarski,axiom, % 0.11/0.50 $true ). % 0.11/0.50 % 0.11/0.50 fof(dt_k4_xboole_0,axiom, % 0.11/0.50 $true ). % 0.11/0.50 % 0.11/0.50 fof(fc1_xboole_0,axiom, % 0.11/0.50 empty(empty_set) ). % 0.11/0.50 % 0.11/0.50 fof(fc1_zfmisc_1,axiom, % 0.11/0.50 ! [A,B] : ~ empty(ordered_pair(A,B)) ). % 0.11/0.50 % 0.11/0.50 fof(fc2_xboole_0,axiom, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( ~ empty(A) % 0.11/0.50 => ~ empty(set_union2(A,B)) ) ). % 0.11/0.50 % 0.11/0.50 fof(fc3_xboole_0,axiom, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( ~ empty(A) % 0.11/0.50 => ~ empty(set_union2(B,A)) ) ). % 0.11/0.50 % 0.11/0.50 fof(idempotence_k2_xboole_0,axiom, % 0.11/0.50 ! [A,B] : set_union2(A,A) = A ). % 0.11/0.50 % 0.11/0.50 fof(idempotence_k3_xboole_0,axiom, % 0.11/0.50 ! [A,B] : set_intersection2(A,A) = A ). % 0.11/0.50 % 0.11/0.50 fof(irreflexivity_r2_xboole_0,axiom, % 0.11/0.50 ! [A,B] : ~ proper_subset(A,A) ). % 0.11/0.50 % 0.11/0.50 fof(l1_zfmisc_1,lemma, % 0.11/0.50 ! [A] : singleton(A) != empty_set ). % 0.11/0.50 % 0.11/0.50 fof(l23_zfmisc_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( in(A,B) % 0.11/0.50 => set_union2(singleton(A),B) = B ) ). % 0.11/0.50 % 0.11/0.50 fof(l25_zfmisc_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ~ ( disjoint(singleton(A),B) % 0.11/0.50 & in(A,B) ) ). % 0.11/0.50 % 0.11/0.50 fof(l28_zfmisc_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( ~ in(A,B) % 0.11/0.50 => disjoint(singleton(A),B) ) ). % 0.11/0.50 % 0.11/0.50 fof(l2_zfmisc_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( subset(singleton(A),B) % 0.11/0.50 <=> in(A,B) ) ). % 0.11/0.50 % 0.11/0.50 fof(l32_xboole_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( set_difference(A,B) = empty_set % 0.11/0.50 <=> subset(A,B) ) ). % 0.11/0.50 % 0.11/0.50 fof(l3_zfmisc_1,lemma, % 0.11/0.50 ! [A,B,C] : % 0.11/0.50 ( subset(A,B) % 0.11/0.50 => ( in(C,A) % 0.11/0.50 | subset(A,set_difference(B,singleton(C))) ) ) ). % 0.11/0.50 % 0.11/0.50 fof(l4_zfmisc_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( subset(A,singleton(B)) % 0.11/0.50 <=> ( A = empty_set % 0.11/0.50 | A = singleton(B) ) ) ). % 0.11/0.50 % 0.11/0.50 fof(l50_zfmisc_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( in(A,B) % 0.11/0.50 => subset(A,union(B)) ) ). % 0.11/0.50 % 0.11/0.50 fof(l55_zfmisc_1,lemma, % 0.11/0.50 ! [A,B,C,D] : % 0.11/0.50 ( in(ordered_pair(A,B),cartesian_product2(C,D)) % 0.11/0.50 <=> ( in(A,C) % 0.11/0.50 & in(B,D) ) ) ). % 0.11/0.50 % 0.11/0.50 fof(rc1_xboole_0,axiom, % 0.11/0.50 ? [A] : empty(A) ). % 0.11/0.50 % 0.11/0.50 fof(rc2_xboole_0,axiom, % 0.11/0.50 ? [A] : ~ empty(A) ). % 0.11/0.50 % 0.11/0.50 fof(reflexivity_r1_tarski,axiom, % 0.11/0.50 ! [A,B] : subset(A,A) ). % 0.11/0.50 % 0.11/0.50 fof(symmetry_r1_xboole_0,axiom, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( disjoint(A,B) % 0.11/0.50 => disjoint(B,A) ) ). % 0.11/0.50 % 0.11/0.50 fof(t10_zfmisc_1,lemma, % 0.11/0.50 ! [A,B,C,D] : % 0.11/0.50 ~ ( unordered_pair(A,B) = unordered_pair(C,D) % 0.11/0.50 & A != C % 0.11/0.50 & A != D ) ). % 0.11/0.50 % 0.11/0.50 fof(t12_xboole_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( subset(A,B) % 0.11/0.50 => set_union2(A,B) = B ) ). % 0.11/0.50 % 0.11/0.50 fof(t17_xboole_1,lemma, % 0.11/0.50 ! [A,B] : subset(set_intersection2(A,B),A) ). % 0.11/0.50 % 0.11/0.50 fof(t19_xboole_1,lemma, % 0.11/0.50 ! [A,B,C] : % 0.11/0.50 ( ( subset(A,B) % 0.11/0.50 & subset(A,C) ) % 0.11/0.50 => subset(A,set_intersection2(B,C)) ) ). % 0.11/0.50 % 0.11/0.50 fof(t1_boole,axiom, % 0.11/0.50 ! [A] : set_union2(A,empty_set) = A ). % 0.11/0.50 % 0.11/0.50 fof(t1_xboole_1,lemma, % 0.11/0.50 ! [A,B,C] : % 0.11/0.50 ( ( subset(A,B) % 0.11/0.50 & subset(B,C) ) % 0.11/0.50 => subset(A,C) ) ). % 0.11/0.50 % 0.11/0.50 fof(t1_zfmisc_1,lemma, % 0.11/0.50 powerset(empty_set) = singleton(empty_set) ). % 0.11/0.50 % 0.11/0.50 fof(t26_xboole_1,lemma, % 0.11/0.50 ! [A,B,C] : % 0.11/0.50 ( subset(A,B) % 0.11/0.50 => subset(set_intersection2(A,C),set_intersection2(B,C)) ) ). % 0.11/0.50 % 0.11/0.50 fof(t28_xboole_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( subset(A,B) % 0.11/0.50 => set_intersection2(A,B) = A ) ). % 0.11/0.50 % 0.11/0.50 fof(t2_boole,axiom, % 0.11/0.50 ! [A] : set_intersection2(A,empty_set) = empty_set ). % 0.11/0.50 % 0.11/0.50 fof(t2_tarski,axiom, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( ! [C] : % 0.11/0.50 ( in(C,A) % 0.11/0.50 <=> in(C,B) ) % 0.11/0.50 => A = B ) ). % 0.11/0.50 % 0.11/0.50 fof(t2_xboole_1,lemma, % 0.11/0.50 ! [A] : subset(empty_set,A) ). % 0.11/0.50 % 0.11/0.50 fof(t33_xboole_1,lemma, % 0.11/0.50 ! [A,B,C] : % 0.11/0.50 ( subset(A,B) % 0.11/0.50 => subset(set_difference(A,C),set_difference(B,C)) ) ). % 0.11/0.50 % 0.11/0.50 fof(t33_zfmisc_1,lemma, % 0.11/0.50 ! [A,B,C,D] : % 0.11/0.50 ( ordered_pair(A,B) = ordered_pair(C,D) % 0.11/0.50 => ( A = C % 0.11/0.50 & B = D ) ) ). % 0.11/0.50 % 0.11/0.50 fof(t36_xboole_1,lemma, % 0.11/0.50 ! [A,B] : subset(set_difference(A,B),A) ). % 0.11/0.50 % 0.11/0.50 fof(t37_xboole_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( set_difference(A,B) = empty_set % 0.11/0.50 <=> subset(A,B) ) ). % 0.11/0.50 % 0.11/0.50 fof(t37_zfmisc_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( subset(singleton(A),B) % 0.11/0.50 <=> in(A,B) ) ). % 0.11/0.50 % 0.11/0.50 fof(t38_zfmisc_1,lemma, % 0.11/0.50 ! [A,B,C] : % 0.11/0.50 ( subset(unordered_pair(A,B),C) % 0.11/0.50 <=> ( in(A,C) % 0.11/0.50 & in(B,C) ) ) ). % 0.11/0.50 % 0.11/0.50 fof(t39_xboole_1,lemma, % 0.11/0.50 ! [A,B] : set_union2(A,set_difference(B,A)) = set_union2(A,B) ). % 0.11/0.50 % 0.11/0.50 fof(t39_zfmisc_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( subset(A,singleton(B)) % 0.11/0.50 <=> ( A = empty_set % 0.11/0.50 | A = singleton(B) ) ) ). % 0.11/0.50 % 0.11/0.50 fof(t3_boole,axiom, % 0.11/0.50 ! [A] : set_difference(A,empty_set) = A ). % 0.11/0.50 % 0.11/0.50 fof(t3_xboole_0,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( ~ ( ~ disjoint(A,B) % 0.11/0.50 & ! [C] : % 0.11/0.50 ~ ( in(C,A) % 0.11/0.50 & in(C,B) ) ) % 0.11/0.50 & ~ ( ? [C] : % 0.11/0.50 ( in(C,A) % 0.11/0.50 & in(C,B) ) % 0.11/0.50 & disjoint(A,B) ) ) ). % 0.11/0.50 % 0.11/0.50 fof(t3_xboole_1,lemma, % 0.11/0.50 ! [A] : % 0.11/0.50 ( subset(A,empty_set) % 0.11/0.50 => A = empty_set ) ). % 0.11/0.50 % 0.11/0.50 fof(t40_xboole_1,lemma, % 0.11/0.50 ! [A,B] : set_difference(set_union2(A,B),B) = set_difference(A,B) ). % 0.11/0.50 % 0.11/0.50 fof(t45_xboole_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( subset(A,B) % 0.11/0.50 => B = set_union2(A,set_difference(B,A)) ) ). % 0.11/0.50 % 0.11/0.50 fof(t46_zfmisc_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( in(A,B) % 0.11/0.50 => set_union2(singleton(A),B) = B ) ). % 0.11/0.50 % 0.11/0.50 fof(t48_xboole_1,lemma, % 0.11/0.50 ! [A,B] : set_difference(A,set_difference(A,B)) = set_intersection2(A,B) ). % 0.11/0.50 % 0.11/0.50 fof(t4_boole,axiom, % 0.11/0.50 ! [A] : set_difference(empty_set,A) = empty_set ). % 0.11/0.50 % 0.11/0.50 fof(t4_xboole_0,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( ~ ( ~ disjoint(A,B) % 0.11/0.50 & ! [C] : ~ in(C,set_intersection2(A,B)) ) % 0.11/0.50 & ~ ( ? [C] : in(C,set_intersection2(A,B)) % 0.11/0.50 & disjoint(A,B) ) ) ). % 0.11/0.50 % 0.11/0.50 fof(t60_xboole_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ~ ( subset(A,B) % 0.11/0.50 & proper_subset(B,A) ) ). % 0.11/0.50 % 0.11/0.50 fof(t63_xboole_1,lemma, % 0.11/0.50 ! [A,B,C] : % 0.11/0.50 ( ( subset(A,B) % 0.11/0.50 & disjoint(B,C) ) % 0.11/0.50 => disjoint(A,C) ) ). % 0.11/0.50 % 0.11/0.50 fof(t65_zfmisc_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( set_difference(A,singleton(B)) = A % 0.11/0.50 <=> ~ in(B,A) ) ). % 0.11/0.50 % 0.11/0.50 fof(t69_enumset1,lemma, % 0.11/0.50 ! [A] : unordered_pair(A,A) = singleton(A) ). % 0.11/0.50 % 0.11/0.50 fof(t6_boole,axiom, % 0.11/0.50 ! [A] : % 0.11/0.50 ( empty(A) % 0.11/0.50 => A = empty_set ) ). % 0.11/0.50 % 0.11/0.50 fof(t6_zfmisc_1,lemma, % 0.11/0.50 ! [A,B] : % 0.11/0.50 ( subset(singleton(A),singleton(B)) % 0.11/0.50 => A = B ) ). % 0.11/0.50 % 0.11/0.50 fof(t7_boole,axiom, % 0.11/0.51 ! [A,B] : % 0.11/0.51 ~ ( in(A,B) % 0.11/0.51 & empty(B) ) ). % 0.11/0.51 % 0.11/0.51 fof(t7_xboole_1,lemma, % 0.11/0.51 ! [A,B] : subset(A,set_union2(A,B)) ). % 0.11/0.51 % 0.11/0.51 fof(t83_xboole_1,lemma, % 0.11/0.51 ! [A,B] : % 0.11/0.51 ( disjoint(A,B) % 0.11/0.51 <=> set_difference(A,B) = A ) ). % 0.11/0.51 % 0.11/0.51 fof(t8_boole,axiom, % 0.11/0.51 ! [A,B] : % 0.11/0.51 ~ ( empty(A) % 0.11/0.51 & A != B % 0.11/0.51 & empty(B) ) ). % 0.11/0.51 % 0.11/0.51 fof(t8_xboole_1,lemma, % 0.11/0.51 ! [A,B,C] : % 0.11/0.51 ( ( subset(A,B) % 0.11/0.51 & subset(C,B) ) % 0.11/0.51 => subset(set_union2(A,C),B) ) ). % 0.11/0.51 % 0.11/0.51 fof(t8_zfmisc_1,lemma, % 0.11/0.51 ! [A,B,C] : % 0.11/0.51 ( singleton(A) = unordered_pair(B,C) % 0.11/0.51 => A = B ) ). % 0.11/0.51 % 0.11/0.51 fof(t92_zfmisc_1,conjecture, % 0.11/0.51 ! [A,B] : % 0.11/0.51 ( in(A,B) % 0.11/0.51 => subset(A,union(B)) ) ). % 0.11/0.51 % 0.11/0.51 fof(t9_zfmisc_1,lemma, % 0.11/0.51 ! [A,B,C] : % 0.11/0.51 ( singleton(A) = unordered_pair(B,C) % 0.11/0.51 => B = C ) ). % 0.11/0.51 % 0.11/0.51 %------------------------------------------------------------------------------ % 0.11/0.51 %------------------------------------------- % 0.11/0.51 % Proof found % 0.11/0.51 % SZS status Theorem for theBenchmark % 0.11/0.51 % SZS output start Proof % 0.11/0.51 %ClaNum:217(EqnAxiom:71) % 0.11/0.51 %VarNum:870(SingletonVarNum:324) % 0.11/0.51 %MaxLitNum:5 % 0.11/0.51 %MaxfuncDepth:3 % 0.11/0.51 %SharedTerms:14 % 0.11/0.51 %goalClause: 74 95 % 0.11/0.51 %singleGoalClaCount:2 % 0.11/0.51 [72]P1(a1) % 0.11/0.51 [73]P1(a3) % 0.11/0.51 [74]P3(a11,a17) % 0.11/0.51 [92]~P1(a12) % 0.11/0.51 [79]E(f29(a1,a1),f19(a1)) % 0.11/0.51 [95]~P4(a11,f30(a17)) % 0.11/0.51 [76]P4(a1,x761) % 0.11/0.51 [80]P4(x801,x801) % 0.11/0.51 [94]~P5(x941,x941) % 0.11/0.51 [75]E(f18(a1,x751),a1) % 0.11/0.51 [77]E(f28(x771,a1),x771) % 0.11/0.51 [78]E(f18(x781,a1),x781) % 0.11/0.51 [81]E(f28(x811,x811),x811) % 0.11/0.51 [93]~E(f29(x931,x931),a1) % 0.11/0.51 [84]E(f18(x841,f18(x841,a1)),a1) % 0.11/0.51 [87]E(f18(x871,f18(x871,x871)),x871) % 0.11/0.51 [82]E(f29(x821,x822),f29(x822,x821)) % 0.11/0.51 [83]E(f28(x831,x832),f28(x832,x831)) % 0.11/0.51 [85]P4(x851,f28(x851,x852)) % 0.11/0.51 [86]P4(f18(x861,x862),x861) % 0.11/0.51 [88]E(f28(x881,f18(x882,x881)),f28(x881,x882)) % 0.11/0.51 [89]E(f18(f28(x891,x892),x892),f18(x891,x892)) % 0.11/0.51 [90]E(f18(x901,f18(x901,x902)),f18(x902,f18(x902,x901))) % 0.11/0.51 [96]~P1(f29(f29(x961,x962),f29(x961,x961))) % 0.11/0.51 [97]~P1(x971)+E(x971,a1) % 0.11/0.51 [101]~P4(x1011,a1)+E(x1011,a1) % 0.11/0.51 [102]P3(f20(x1021),x1021)+E(x1021,a1) % 0.11/0.51 [100]~E(x1001,x1002)+P4(x1001,x1002) % 0.11/0.51 [103]~P3(x1032,x1031)+~E(x1031,a1) % 0.11/0.51 [104]~P5(x1041,x1042)+~E(x1041,x1042) % 0.11/0.51 [105]~P1(x1051)+~P3(x1052,x1051) % 0.11/0.51 [110]~P5(x1101,x1102)+P4(x1101,x1102) % 0.11/0.51 [111]~P2(x1112,x1111)+P2(x1111,x1112) % 0.11/0.51 [122]~P3(x1222,x1221)+~P3(x1221,x1222) % 0.11/0.51 [123]~P5(x1232,x1231)+~P5(x1231,x1232) % 0.11/0.51 [124]~P4(x1242,x1241)+~P5(x1241,x1242) % 0.11/0.51 [107]~P4(x1071,x1072)+E(f18(x1071,x1072),a1) % 0.11/0.51 [109]P4(x1091,x1092)+~E(f18(x1091,x1092),a1) % 0.11/0.51 [112]~P4(x1121,x1122)+E(f28(x1121,x1122),x1122) % 0.11/0.51 [113]~P2(x1131,x1132)+E(f18(x1131,x1132),x1131) % 0.11/0.51 [114]P2(x1141,x1142)+~E(f18(x1141,x1142),x1141) % 0.11/0.51 [120]~E(x1201,a1)+P4(x1201,f29(x1202,x1202)) % 0.11/0.51 [121]~P3(x1211,x1212)+P4(x1211,f30(x1212)) % 0.11/0.51 [133]P1(x1331)+~P1(f28(x1332,x1331)) % 0.11/0.51 [134]P1(x1341)+~P1(f28(x1341,x1342)) % 0.11/0.51 [135]P3(x1351,x1352)+P2(f29(x1351,x1351),x1352) % 0.11/0.51 [136]P4(x1361,x1362)+P3(f4(x1361,x1362),x1361) % 0.11/0.51 [137]P2(x1371,x1372)+P3(f13(x1371,x1372),x1372) % 0.11/0.51 [138]P2(x1381,x1382)+P3(f13(x1381,x1382),x1381) % 0.11/0.51 [148]~P3(x1481,x1482)+P4(f29(x1481,x1481),x1482) % 0.11/0.51 [166]P4(x1661,x1662)+~P3(f4(x1661,x1662),x1662) % 0.11/0.51 [174]~P3(x1741,x1742)+~P2(f29(x1741,x1741),x1742) % 0.11/0.51 [180]E(x1801,x1802)+~P4(f29(x1801,x1801),f29(x1802,x1802)) % 0.11/0.51 [139]P3(x1392,x1391)+E(f18(x1391,f29(x1392,x1392)),x1391) % 0.11/0.51 [146]~P2(x1461,x1462)+E(f18(x1461,f18(x1461,x1462)),a1) % 0.11/0.51 [149]~P4(x1491,x1492)+E(f28(x1491,f18(x1492,x1491)),x1492) % 0.11/0.51 [150]~P4(x1501,x1502)+E(f18(x1501,f18(x1501,x1502)),x1501) % 0.11/0.51 [152]~P3(x1521,x1522)+E(f28(f29(x1521,x1521),x1522),x1522) % 0.11/0.51 [161]P2(x1611,x1612)+~E(f18(x1611,f18(x1611,x1612)),a1) % 0.11/0.51 [175]~P3(x1752,x1751)+~E(f18(x1751,f29(x1752,x1752)),x1751) % 0.11/0.51 [186]P2(x1861,x1862)+P3(f16(x1861,x1862),f18(x1861,f18(x1861,x1862))) % 0.11/0.51 [127]E(x1271,x1272)+~E(f29(x1273,x1273),f29(x1271,x1272)) % 0.11/0.51 [128]E(x1281,x1282)+~E(f29(x1281,x1281),f29(x1282,x1283)) % 0.11/0.51 [162]P3(x1621,x1622)+~P4(f29(x1623,x1621),x1622) % 0.11/0.51 [163]P3(x1631,x1632)+~P4(f29(x1631,x1633),x1632) % 0.11/0.51 [176]~P4(x1761,x1763)+P4(f18(x1761,x1762),f18(x1763,x1762)) % 0.11/0.51 [191]~P2(x1911,x1912)+~P3(x1913,f18(x1911,f18(x1911,x1912))) % 0.11/0.51 [193]~P4(x1931,x1933)+P4(f18(x1931,f18(x1931,x1932)),f18(x1933,f18(x1933,x1932))) % 0.11/0.51 [194]E(x1941,x1942)+~E(f29(f29(x1943,x1941),f29(x1943,x1943)),f29(f29(x1944,x1942),f29(x1944,x1944))) % 0.11/0.51 [195]E(x1951,x1952)+~E(f29(f29(x1951,x1953),f29(x1951,x1951)),f29(f29(x1952,x1954),f29(x1952,x1952))) % 0.11/0.51 [201]P3(x2011,x2012)+~P3(f29(f29(x2013,x2011),f29(x2013,x2013)),f2(x2014,x2012)) % 0.11/0.51 [202]P3(x2021,x2022)+~P3(f29(f29(x2021,x2023),f29(x2021,x2021)),f2(x2022,x2024)) % 0.11/0.51 [98]~P1(x982)+~P1(x981)+E(x981,x982) % 0.11/0.51 [115]P5(x1151,x1152)+~P4(x1151,x1152)+E(x1151,x1152) % 0.11/0.51 [129]~P4(x1292,x1291)+~P4(x1291,x1292)+E(x1291,x1292) % 0.11/0.51 [158]E(f14(x1582,x1581),x1582)+P3(f14(x1582,x1581),x1581)+E(x1581,f29(x1582,x1582)) % 0.11/0.51 [168]E(x1681,f29(x1682,x1682))+~P4(x1681,f29(x1682,x1682))+E(x1681,a1) % 0.11/0.51 [169]E(x1691,x1692)+P3(f15(x1691,x1692),x1692)+P3(f15(x1691,x1692),x1691) % 0.11/0.51 [172]P3(f21(x1722,x1721),x1721)+P4(f21(x1722,x1721),x1722)+E(x1721,f19(x1722)) % 0.11/0.51 [173]P3(f6(x1732,x1731),x1731)+P3(f9(x1732,x1731),x1732)+E(x1731,f30(x1732)) % 0.11/0.51 [179]~E(f14(x1792,x1791),x1792)+~P3(f14(x1792,x1791),x1791)+E(x1791,f29(x1792,x1792)) % 0.11/0.51 [181]P3(f6(x1812,x1811),x1811)+P3(f6(x1812,x1811),f9(x1812,x1811))+E(x1811,f30(x1812)) % 0.11/0.51 [183]E(x1831,x1832)+~P3(f15(x1831,x1832),x1832)+~P3(f15(x1831,x1832),x1831) % 0.11/0.51 [185]~P3(f21(x1852,x1851),x1851)+~P4(f21(x1852,x1851),x1852)+E(x1851,f19(x1852)) % 0.11/0.51 [140]~P4(x1403,x1402)+P3(x1401,x1402)+~P3(x1401,x1403) % 0.11/0.51 [141]~P4(x1411,x1413)+P4(x1411,x1412)+~P4(x1413,x1412) % 0.11/0.51 [142]~P2(x1423,x1422)+P2(x1421,x1422)+~P4(x1421,x1423) % 0.11/0.51 [155]~P2(x1553,x1552)+~P3(x1551,x1552)+~P3(x1551,x1553) % 0.11/0.51 [125]~P4(x1251,x1253)+P3(x1251,x1252)+~E(x1252,f19(x1253)) % 0.11/0.51 [126]~P3(x1261,x1263)+P4(x1261,x1262)+~E(x1263,f19(x1262)) % 0.11/0.51 [131]~P3(x1311,x1313)+E(x1311,x1312)+~E(x1313,f29(x1312,x1312)) % 0.11/0.51 [170]~P3(x1702,x1703)+~P3(x1701,x1703)+P4(f29(x1701,x1702),x1703) % 0.11/0.51 [171]~P4(x1712,x1713)+~P4(x1711,x1713)+P4(f28(x1711,x1712),x1713) % 0.11/0.51 [188]~P3(x1881,x1883)+~E(x1883,f30(x1882))+P3(x1881,f7(x1882,x1883,x1881)) % 0.11/0.51 [189]~P3(x1893,x1892)+~E(x1892,f30(x1891))+P3(f7(x1891,x1892,x1893),x1891) % 0.11/0.51 [198]P3(f23(x1982,x1983,x1981),x1981)+P3(f27(x1982,x1983,x1981),x1982)+E(x1981,f2(x1982,x1983)) % 0.11/0.51 [199]P3(f23(x1992,x1993,x1991),x1991)+P3(f5(x1992,x1993,x1991),x1993)+E(x1991,f2(x1992,x1993)) % 0.11/0.51 [200]P3(f10(x2002,x2003,x2001),x2001)+P3(f10(x2002,x2003,x2001),x2002)+E(x2001,f18(x2002,x2003)) % 0.11/0.51 [205]~E(f22(x2052,x2053,x2051),x2053)+~P3(f22(x2052,x2053,x2051),x2051)+E(x2051,f29(x2052,x2053)) % 0.11/0.51 [206]~E(f22(x2062,x2063,x2061),x2062)+~P3(f22(x2062,x2063,x2061),x2061)+E(x2061,f29(x2062,x2063)) % 0.11/0.51 [207]P3(f10(x2072,x2073,x2071),x2071)+~P3(f10(x2072,x2073,x2071),x2073)+E(x2071,f18(x2072,x2073)) % 0.11/0.51 [209]~P3(f24(x2092,x2093,x2091),x2091)+~P3(f24(x2092,x2093,x2091),x2093)+E(x2091,f28(x2092,x2093)) % 0.11/0.51 [210]~P3(f24(x2102,x2103,x2101),x2101)+~P3(f24(x2102,x2103,x2101),x2102)+E(x2101,f28(x2102,x2103)) % 0.11/0.51 [184]~P4(x1842,x1843)+P3(x1841,x1842)+P4(x1842,f18(x1843,f29(x1841,x1841))) % 0.11/0.51 [187]~P4(x1871,x1873)+~P4(x1871,x1872)+P4(x1871,f18(x1872,f18(x1872,x1873))) % 0.11/0.51 [203]P3(f8(x2032,x2033,x2031),x2031)+P3(f8(x2032,x2033,x2031),x2033)+E(x2031,f18(x2032,f18(x2032,x2033))) % 0.11/0.51 [204]P3(f8(x2042,x2043,x2041),x2041)+P3(f8(x2042,x2043,x2041),x2042)+E(x2041,f18(x2042,f18(x2042,x2043))) % 0.11/0.51 [216]P3(f23(x2162,x2163,x2161),x2161)+E(x2161,f2(x2162,x2163))+E(f29(f29(f27(x2162,x2163,x2161),f5(x2162,x2163,x2161)),f29(f27(x2162,x2163,x2161),f27(x2162,x2163,x2161))),f23(x2162,x2163,x2161)) % 0.11/0.51 [116]P3(x1161,x1162)+~E(x1161,x1163)+~E(x1162,f29(x1164,x1163)) % 0.11/0.51 [117]P3(x1171,x1172)+~E(x1171,x1173)+~E(x1172,f29(x1173,x1174)) % 0.11/0.51 [130]E(x1301,x1302)+E(x1301,x1303)+~E(f29(x1301,x1304),f29(x1303,x1302)) % 0.11/0.51 [143]~P3(x1431,x1434)+P3(x1431,x1432)+~E(x1432,f28(x1433,x1434)) % 0.11/0.51 [144]~P3(x1441,x1443)+P3(x1441,x1442)+~E(x1442,f28(x1443,x1444)) % 0.11/0.51 [145]~P3(x1451,x1453)+P3(x1451,x1452)+~E(x1453,f18(x1452,x1454)) % 0.11/0.51 [157]~P3(x1574,x1573)+~P3(x1574,x1571)+~E(x1571,f18(x1572,x1573)) % 0.11/0.51 [213]~P3(x2134,x2133)+~E(x2133,f2(x2131,x2132))+P3(f25(x2131,x2132,x2133,x2134),x2131) % 0.11/0.51 [214]~P3(x2144,x2143)+~E(x2143,f2(x2141,x2142))+P3(f26(x2141,x2142,x2143,x2144),x2142) % 0.11/0.51 [177]~P3(x1771,x1773)+P3(x1771,x1772)+~E(x1773,f18(x1774,f18(x1774,x1772))) % 0.11/0.51 [196]~P3(x1962,x1964)+~P3(x1961,x1963)+P3(f29(f29(x1961,x1962),f29(x1961,x1961)),f2(x1963,x1964)) % 0.11/0.51 [217]~P3(x2174,x2173)+~E(x2173,f2(x2171,x2172))+E(f29(f29(f25(x2171,x2172,x2173,x2174),f26(x2171,x2172,x2173,x2174)),f29(f25(x2171,x2172,x2173,x2174),f25(x2171,x2172,x2173,x2174))),x2174) % 0.11/0.51 [190]~P3(x1903,x1902)+~P3(f6(x1902,x1901),x1903)+~P3(f6(x1902,x1901),x1901)+E(x1901,f30(x1902)) % 0.11/0.51 [197]E(f22(x1972,x1973,x1971),x1973)+E(f22(x1972,x1973,x1971),x1972)+P3(f22(x1972,x1973,x1971),x1971)+E(x1971,f29(x1972,x1973)) % 0.11/0.51 [208]P3(f24(x2082,x2083,x2081),x2081)+P3(f24(x2082,x2083,x2081),x2083)+P3(f24(x2082,x2083,x2081),x2082)+E(x2081,f28(x2082,x2083)) % 0.11/0.51 [212]P3(f10(x2122,x2123,x2121),x2123)+~P3(f10(x2122,x2123,x2121),x2121)+~P3(f10(x2122,x2123,x2121),x2122)+E(x2121,f18(x2122,x2123)) % 0.11/0.51 [215]~P3(f8(x2152,x2153,x2151),x2151)+~P3(f8(x2152,x2153,x2151),x2153)+~P3(f8(x2152,x2153,x2151),x2152)+E(x2151,f18(x2152,f18(x2152,x2153))) % 0.11/0.51 [132]~P3(x1321,x1324)+E(x1321,x1322)+E(x1321,x1323)+~E(x1324,f29(x1323,x1322)) % 0.11/0.51 [156]~P3(x1561,x1564)+P3(x1561,x1562)+~P3(x1564,x1563)+~E(x1562,f30(x1563)) % 0.11/0.51 [159]~P3(x1591,x1594)+P3(x1591,x1592)+P3(x1591,x1593)+~E(x1592,f18(x1594,x1593)) % 0.11/0.51 [160]~P3(x1601,x1604)+P3(x1601,x1602)+P3(x1601,x1603)+~E(x1604,f28(x1603,x1602)) % 0.11/0.51 [182]~P3(x1821,x1824)+~P3(x1821,x1823)+P3(x1821,x1822)+~E(x1822,f18(x1823,f18(x1823,x1824))) % 0.11/0.51 [211]~P3(x2115,x2113)+~P3(x2114,x2112)+~P3(f23(x2112,x2113,x2111),x2111)+E(x2111,f2(x2112,x2113))+~E(f23(x2112,x2113,x2111),f29(f29(x2114,x2115),f29(x2114,x2114))) % 0.11/0.51 [192]~P3(x1926,x1924)+~P3(x1925,x1923)+P3(x1921,x1922)+~E(x1922,f2(x1923,x1924))+~E(x1921,f29(f29(x1925,x1926),f29(x1925,x1925))) % 0.11/0.51 %EqnAxiom % 0.11/0.51 [1]E(x11,x11) % 0.11/0.51 [2]E(x22,x21)+~E(x21,x22) % 0.11/0.51 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33) % 0.11/0.51 [4]~E(x41,x42)+E(f18(x41,x43),f18(x42,x43)) % 0.11/0.51 [5]~E(x51,x52)+E(f18(x53,x51),f18(x53,x52)) % 0.11/0.51 [6]~E(x61,x62)+E(f28(x61,x63),f28(x62,x63)) % 0.11/0.51 [7]~E(x71,x72)+E(f28(x73,x71),f28(x73,x72)) % 0.11/0.51 [8]~E(x81,x82)+E(f2(x81,x83),f2(x82,x83)) % 0.11/0.51 [9]~E(x91,x92)+E(f2(x93,x91),f2(x93,x92)) % 0.11/0.51 [10]~E(x101,x102)+E(f29(x101,x103),f29(x102,x103)) % 0.11/0.51 [11]~E(x111,x112)+E(f29(x113,x111),f29(x113,x112)) % 0.11/0.51 [12]~E(x121,x122)+E(f19(x121),f19(x122)) % 0.11/0.51 [13]~E(x131,x132)+E(f8(x131,x133,x134),f8(x132,x133,x134)) % 0.11/0.51 [14]~E(x141,x142)+E(f8(x143,x141,x144),f8(x143,x142,x144)) % 0.11/0.51 [15]~E(x151,x152)+E(f8(x153,x154,x151),f8(x153,x154,x152)) % 0.11/0.51 [16]~E(x161,x162)+E(f22(x161,x163,x164),f22(x162,x163,x164)) % 0.11/0.51 [17]~E(x171,x172)+E(f22(x173,x171,x174),f22(x173,x172,x174)) % 0.11/0.51 [18]~E(x181,x182)+E(f22(x183,x184,x181),f22(x183,x184,x182)) % 0.11/0.51 [19]~E(x191,x192)+E(f5(x191,x193,x194),f5(x192,x193,x194)) % 0.11/0.51 [20]~E(x201,x202)+E(f5(x203,x201,x204),f5(x203,x202,x204)) % 0.11/0.51 [21]~E(x211,x212)+E(f5(x213,x214,x211),f5(x213,x214,x212)) % 0.11/0.51 [22]~E(x221,x222)+E(f23(x221,x223,x224),f23(x222,x223,x224)) % 0.11/0.51 [23]~E(x231,x232)+E(f23(x233,x231,x234),f23(x233,x232,x234)) % 0.11/0.51 [24]~E(x241,x242)+E(f23(x243,x244,x241),f23(x243,x244,x242)) % 0.11/0.51 [25]~E(x251,x252)+E(f30(x251),f30(x252)) % 0.11/0.51 [26]~E(x261,x262)+E(f21(x261,x263),f21(x262,x263)) % 0.11/0.51 [27]~E(x271,x272)+E(f21(x273,x271),f21(x273,x272)) % 0.11/0.51 [28]~E(x281,x282)+E(f4(x281,x283),f4(x282,x283)) % 0.11/0.51 [29]~E(x291,x292)+E(f4(x293,x291),f4(x293,x292)) % 0.11/0.51 [30]~E(x301,x302)+E(f26(x301,x303,x304,x305),f26(x302,x303,x304,x305)) % 0.11/0.51 [31]~E(x311,x312)+E(f26(x313,x311,x314,x315),f26(x313,x312,x314,x315)) % 0.11/0.51 [32]~E(x321,x322)+E(f26(x323,x324,x321,x325),f26(x323,x324,x322,x325)) % 0.11/0.51 [33]~E(x331,x332)+E(f26(x333,x334,x335,x331),f26(x333,x334,x335,x332)) % 0.11/0.51 [34]~E(x341,x342)+E(f25(x341,x343,x344,x345),f25(x342,x343,x344,x345)) % 0.11/0.51 [35]~E(x351,x352)+E(f25(x353,x351,x354,x355),f25(x353,x352,x354,x355)) % 0.11/0.51 [36]~E(x361,x362)+E(f25(x363,x364,x361,x365),f25(x363,x364,x362,x365)) % 0.11/0.51 [37]~E(x371,x372)+E(f25(x373,x374,x375,x371),f25(x373,x374,x375,x372)) % 0.11/0.51 [38]~E(x381,x382)+E(f13(x381,x383),f13(x382,x383)) % 0.11/0.51 [39]~E(x391,x392)+E(f13(x393,x391),f13(x393,x392)) % 0.11/0.51 [40]~E(x401,x402)+E(f6(x401,x403),f6(x402,x403)) % 0.11/0.51 [41]~E(x411,x412)+E(f6(x413,x411),f6(x413,x412)) % 0.11/0.51 [42]~E(x421,x422)+E(f14(x421,x423),f14(x422,x423)) % 0.11/0.51 [43]~E(x431,x432)+E(f14(x433,x431),f14(x433,x432)) % 0.11/0.51 [44]~E(x441,x442)+E(f24(x441,x443,x444),f24(x442,x443,x444)) % 0.11/0.51 [45]~E(x451,x452)+E(f24(x453,x451,x454),f24(x453,x452,x454)) % 0.11/0.51 [46]~E(x461,x462)+E(f24(x463,x464,x461),f24(x463,x464,x462)) % 0.11/0.51 [47]~E(x471,x472)+E(f10(x471,x473,x474),f10(x472,x473,x474)) % 0.11/0.51 [48]~E(x481,x482)+E(f10(x483,x481,x484),f10(x483,x482,x484)) % 0.11/0.51 [49]~E(x491,x492)+E(f10(x493,x494,x491),f10(x493,x494,x492)) % 0.11/0.51 [50]~E(x501,x502)+E(f9(x501,x503),f9(x502,x503)) % 0.11/0.51 [51]~E(x511,x512)+E(f9(x513,x511),f9(x513,x512)) % 0.11/0.51 [52]~E(x521,x522)+E(f15(x521,x523),f15(x522,x523)) % 0.11/0.51 [53]~E(x531,x532)+E(f15(x533,x531),f15(x533,x532)) % 0.11/0.51 [54]~E(x541,x542)+E(f20(x541),f20(x542)) % 0.11/0.51 [55]~E(x551,x552)+E(f16(x551,x553),f16(x552,x553)) % 0.11/0.51 [56]~E(x561,x562)+E(f16(x563,x561),f16(x563,x562)) % 0.11/0.51 [57]~E(x571,x572)+E(f7(x571,x573,x574),f7(x572,x573,x574)) % 0.11/0.51 [58]~E(x581,x582)+E(f7(x583,x581,x584),f7(x583,x582,x584)) % 0.11/0.51 [59]~E(x591,x592)+E(f7(x593,x594,x591),f7(x593,x594,x592)) % 0.11/0.51 [60]~E(x601,x602)+E(f27(x601,x603,x604),f27(x602,x603,x604)) % 0.11/0.51 [61]~E(x611,x612)+E(f27(x613,x611,x614),f27(x613,x612,x614)) % 0.11/0.51 [62]~E(x621,x622)+E(f27(x623,x624,x621),f27(x623,x624,x622)) % 0.11/0.51 [63]~P1(x631)+P1(x632)+~E(x631,x632) % 0.11/0.51 [64]P3(x642,x643)+~E(x641,x642)+~P3(x641,x643) % 0.11/0.51 [65]P3(x653,x652)+~E(x651,x652)+~P3(x653,x651) % 0.11/0.51 [66]P4(x662,x663)+~E(x661,x662)+~P4(x661,x663) % 0.11/0.51 [67]P4(x673,x672)+~E(x671,x672)+~P4(x673,x671) % 0.11/0.51 [68]P2(x682,x683)+~E(x681,x682)+~P2(x681,x683) % 0.11/0.51 [69]P2(x693,x692)+~E(x691,x692)+~P2(x693,x691) % 0.11/0.51 [70]P5(x702,x703)+~E(x701,x702)+~P5(x701,x703) % 0.11/0.51 [71]P5(x713,x712)+~E(x711,x712)+~P5(x713,x711) % 0.11/0.51 % 0.11/0.51 %------------------------------------------- % 0.11/0.51 cnf(245,plain, % 0.11/0.51 ($false), % 0.11/0.51 inference(scs_inference,[],[74,95,121]), % 0.11/0.51 ['proof']). % 0.11/0.51 % SZS output end Proof % 0.11/0.51 % Total time :0.010000s %------------------------------------------------------------------------------