TSTP Solution File: ITP006+2 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : ITP006+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% Computer : n004.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 : Thu Aug 31 03:06:26 EDT 2023
% Result : Theorem 0.56s 0.93s
% Output : CNFRefutation 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : ITP006+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.07/0.14 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %s %d
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun Aug 27 11:44:37 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.21/0.60 start to proof:theBenchmark
% 0.56/0.90 %-------------------------------------------
% 0.56/0.90 % File :CSE---1.6
% 0.56/0.90 % Problem :theBenchmark
% 0.56/0.90 % Transform :cnf
% 0.56/0.90 % Format :tptp:raw
% 0.56/0.90 % Command :java -jar mcs_scs.jar %d %s
% 0.56/0.90
% 0.56/0.90 % Result :Theorem 0.200000s
% 0.56/0.90 % Output :CNFRefutation 0.200000s
% 0.56/0.90 %-------------------------------------------
% 0.56/0.90 %------------------------------------------------------------------------------
% 0.56/0.90 % File : ITP006+2 : TPTP v8.1.2. Bugfixed v7.5.0.
% 0.56/0.90 % Domain : Interactive Theorem Proving
% 0.56/0.90 % Problem : HOL4 set theory export of thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT.p, bushy mode
% 0.56/0.90 % Version : [BG+19] axioms.
% 0.56/0.90 % English :
% 0.56/0.90
% 0.56/0.90 % Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% 0.56/0.90 % : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% 0.56/0.90 % Source : [BG+19]
% 0.56/0.90 % Names : thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT.p [Gau19]
% 0.56/0.90 % : HL402501+2.p [TPAP]
% 0.56/0.90
% 0.56/0.90 % Status : Theorem
% 0.56/0.90 % Rating : 0.58 v8.1.0, 0.61 v7.5.0
% 0.56/0.90 % Syntax : Number of formulae : 52 ( 11 unt; 0 def)
% 0.56/0.90 % Number of atoms : 291 ( 10 equ)
% 0.56/0.90 % Maximal formula atoms : 38 ( 5 avg)
% 0.56/0.90 % Number of connectives : 279 ( 40 ~; 22 |; 30 &)
% 0.56/0.90 % ( 47 <=>; 140 =>; 0 <=; 0 <~>)
% 0.56/0.90 % Maximal formula depth : 24 ( 6 avg)
% 0.56/0.91 % Maximal term depth : 4 ( 1 avg)
% 0.56/0.91 % Number of predicates : 6 ( 3 usr; 2 prp; 0-2 aty)
% 0.56/0.91 % Number of functors : 21 ( 21 usr; 8 con; 0-2 aty)
% 0.56/0.91 % Number of variables : 112 ( 107 !; 5 ?)
% 0.56/0.91 % SPC : FOF_THM_RFO_SEQ
% 0.56/0.91
% 0.56/0.91 % Comments :
% 0.56/0.91 % Bugfixes : v7.5.0 - Bugfixes in axioms and export.
% 0.56/0.91 %------------------------------------------------------------------------------
% 0.56/0.91 include('Axioms/ITP001/ITP001+2.ax').
% 0.56/0.91 %------------------------------------------------------------------------------
% 0.56/0.91 fof(mem_c_2Ebool_2ET,axiom,
% 0.56/0.91 mem(c_2Ebool_2ET,bool) ).
% 0.56/0.91
% 0.56/0.91 fof(ax_true_p,axiom,
% 0.56/0.91 p(c_2Ebool_2ET) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2EquantHeuristics_2EGUESS__FORALL__GAP,axiom,
% 0.56/0.91 ! [A_27a] :
% 0.56/0.91 ( ne(A_27a)
% 0.56/0.91 => ! [A_27b] :
% 0.56/0.91 ( ne(A_27b)
% 0.56/0.91 => mem(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2EquantHeuristics_2EGUESS__EXISTS__GAP,axiom,
% 0.56/0.91 ! [A_27a] :
% 0.56/0.91 ( ne(A_27a)
% 0.56/0.91 => ! [A_27b] :
% 0.56/0.91 ( ne(A_27b)
% 0.56/0.91 => mem(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2EquantHeuristics_2EGUESS__FORALL__POINT,axiom,
% 0.56/0.91 ! [A_27a] :
% 0.56/0.91 ( ne(A_27a)
% 0.56/0.91 => ! [A_27b] :
% 0.56/0.91 ( ne(A_27b)
% 0.56/0.91 => mem(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2EquantHeuristics_2EGUESS__EXISTS__POINT,axiom,
% 0.56/0.91 ! [A_27a] :
% 0.56/0.91 ( ne(A_27a)
% 0.56/0.91 => ! [A_27b] :
% 0.56/0.91 ( ne(A_27b)
% 0.56/0.91 => mem(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2EquantHeuristics_2EGUESS__FORALL,axiom,
% 0.56/0.91 ! [A_27a] :
% 0.56/0.91 ( ne(A_27a)
% 0.56/0.91 => ! [A_27b] :
% 0.56/0.91 ( ne(A_27b)
% 0.56/0.91 => mem(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2Ebool_2E_3F,axiom,
% 0.56/0.91 ! [A_27a] :
% 0.56/0.91 ( ne(A_27a)
% 0.56/0.91 => mem(c_2Ebool_2E_3F(A_27a),arr(arr(A_27a,bool),bool)) ) ).
% 0.56/0.91
% 0.56/0.91 fof(ax_ex_p,axiom,
% 0.56/0.91 ! [A] :
% 0.56/0.91 ( ne(A)
% 0.56/0.91 => ! [Q] :
% 0.56/0.91 ( mem(Q,arr(A,bool))
% 0.56/0.91 => ( p(ap(c_2Ebool_2E_3F(A),Q))
% 0.56/0.91 <=> ? [X] :
% 0.56/0.91 ( mem(X,A)
% 0.56/0.91 & p(ap(Q,X)) ) ) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2EquantHeuristics_2EGUESS__EXISTS,axiom,
% 0.56/0.91 ! [A_27a] :
% 0.56/0.91 ( ne(A_27a)
% 0.56/0.91 => ! [A_27b] :
% 0.56/0.91 ( ne(A_27b)
% 0.56/0.91 => mem(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),arr(arr(A_27a,A_27b),arr(arr(A_27b,bool),bool))) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2Ebool_2EF,axiom,
% 0.56/0.91 mem(c_2Ebool_2EF,bool) ).
% 0.56/0.91
% 0.56/0.91 fof(ax_false_p,axiom,
% 0.56/0.91 ~ p(c_2Ebool_2EF) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2Ebool_2E_5C_2F,axiom,
% 0.56/0.91 mem(c_2Ebool_2E_5C_2F,arr(bool,arr(bool,bool))) ).
% 0.56/0.91
% 0.56/0.91 fof(ax_or_p,axiom,
% 0.56/0.91 ! [Q] :
% 0.56/0.91 ( mem(Q,bool)
% 0.56/0.91 => ! [R] :
% 0.56/0.91 ( mem(R,bool)
% 0.56/0.91 => ( p(ap(ap(c_2Ebool_2E_5C_2F,Q),R))
% 0.56/0.91 <=> ( p(Q)
% 0.56/0.91 | p(R) ) ) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2Ebool_2E_2F_5C,axiom,
% 0.56/0.91 mem(c_2Ebool_2E_2F_5C,arr(bool,arr(bool,bool))) ).
% 0.56/0.91
% 0.56/0.91 fof(ax_and_p,axiom,
% 0.56/0.91 ! [Q] :
% 0.56/0.91 ( mem(Q,bool)
% 0.56/0.91 => ! [R] :
% 0.56/0.91 ( mem(R,bool)
% 0.56/0.91 => ( p(ap(ap(c_2Ebool_2E_2F_5C,Q),R))
% 0.56/0.91 <=> ( p(Q)
% 0.56/0.91 & p(R) ) ) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2Emin_2E_3D,axiom,
% 0.56/0.91 ! [A_27a] :
% 0.56/0.91 ( ne(A_27a)
% 0.56/0.91 => mem(c_2Emin_2E_3D(A_27a),arr(A_27a,arr(A_27a,bool))) ) ).
% 0.56/0.91
% 0.56/0.91 fof(ax_eq_p,axiom,
% 0.56/0.91 ! [A] :
% 0.56/0.91 ( ne(A)
% 0.56/0.91 => ! [X] :
% 0.56/0.91 ( mem(X,A)
% 0.56/0.91 => ! [Y] :
% 0.56/0.91 ( mem(Y,A)
% 0.56/0.91 => ( p(ap(ap(c_2Emin_2E_3D(A),X),Y))
% 0.56/0.91 <=> X = Y ) ) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2Ebool_2E_7E,axiom,
% 0.56/0.91 mem(c_2Ebool_2E_7E,arr(bool,bool)) ).
% 0.56/0.91
% 0.56/0.91 fof(ax_neg_p,axiom,
% 0.56/0.91 ! [Q] :
% 0.56/0.91 ( mem(Q,bool)
% 0.56/0.91 => ( p(ap(c_2Ebool_2E_7E,Q))
% 0.56/0.91 <=> ~ p(Q) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2Emin_2E_3D_3D_3E,axiom,
% 0.56/0.91 mem(c_2Emin_2E_3D_3D_3E,arr(bool,arr(bool,bool))) ).
% 0.56/0.91
% 0.56/0.91 fof(ax_imp_p,axiom,
% 0.56/0.91 ! [Q] :
% 0.56/0.91 ( mem(Q,bool)
% 0.56/0.91 => ! [R] :
% 0.56/0.91 ( mem(R,bool)
% 0.56/0.91 => ( p(ap(ap(c_2Emin_2E_3D_3D_3E,Q),R))
% 0.56/0.91 <=> ( p(Q)
% 0.56/0.91 => p(R) ) ) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(mem_c_2Ebool_2E_21,axiom,
% 0.56/0.91 ! [A_27a] :
% 0.56/0.91 ( ne(A_27a)
% 0.56/0.91 => mem(c_2Ebool_2E_21(A_27a),arr(arr(A_27a,bool),bool)) ) ).
% 0.56/0.91
% 0.56/0.91 fof(ax_all_p,axiom,
% 0.56/0.91 ! [A] :
% 0.56/0.91 ( ne(A)
% 0.56/0.91 => ! [Q] :
% 0.56/0.91 ( mem(Q,arr(A,bool))
% 0.56/0.91 => ( p(ap(c_2Ebool_2E_21(A),Q))
% 0.56/0.91 <=> ! [X] :
% 0.56/0.91 ( mem(X,A)
% 0.56/0.91 => p(ap(Q,X)) ) ) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(conj_thm_2Ebool_2ETRUTH,axiom,
% 0.56/0.91 $true ).
% 0.56/0.91
% 0.56/0.91 fof(conj_thm_2Ebool_2EIMP__CLAUSES,axiom,
% 0.56/0.91 ! [V0t] :
% 0.56/0.91 ( mem(V0t,bool)
% 0.56/0.91 => ( ( ( $true
% 0.56/0.91 => p(V0t) )
% 0.56/0.91 <=> p(V0t) )
% 0.56/0.91 & ( ( p(V0t)
% 0.56/0.91 => $true )
% 0.56/0.91 <=> $true )
% 0.56/0.91 & ( ( $false
% 0.56/0.91 => p(V0t) )
% 0.56/0.91 <=> $true )
% 0.56/0.91 & ( ( p(V0t)
% 0.56/0.91 => p(V0t) )
% 0.56/0.91 <=> $true )
% 0.56/0.91 & ( ( p(V0t)
% 0.56/0.91 => $false )
% 0.56/0.91 <=> ~ p(V0t) ) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(conj_thm_2Ebool_2ENOT__CLAUSES,axiom,
% 0.56/0.91 ( ! [V0t] :
% 0.56/0.91 ( mem(V0t,bool)
% 0.56/0.91 => ( ~ ~ p(V0t)
% 0.56/0.91 <=> p(V0t) ) )
% 0.56/0.91 & ( ~ $true
% 0.56/0.91 <=> $false )
% 0.56/0.91 & ( ~ $false
% 0.56/0.91 <=> $true ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(conj_thm_2Ebool_2EEQ__SYM__EQ,axiom,
% 0.56/0.91 ! [A_27a] :
% 0.56/0.91 ( ne(A_27a)
% 0.56/0.91 => ! [V0x] :
% 0.56/0.91 ( mem(V0x,A_27a)
% 0.56/0.91 => ! [V1y] :
% 0.56/0.91 ( mem(V1y,A_27a)
% 0.56/0.91 => ( V0x = V1y
% 0.56/0.91 <=> V1y = V0x ) ) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(conj_thm_2Ebool_2EEQ__CLAUSES,axiom,
% 0.56/0.91 ! [V0t] :
% 0.56/0.91 ( mem(V0t,bool)
% 0.56/0.91 => ( ( ( $true
% 0.56/0.91 <=> p(V0t) )
% 0.56/0.91 <=> p(V0t) )
% 0.56/0.91 & ( ( p(V0t)
% 0.56/0.91 <=> $true )
% 0.56/0.91 <=> p(V0t) )
% 0.56/0.91 & ( ( $false
% 0.56/0.91 <=> p(V0t) )
% 0.56/0.91 <=> ~ p(V0t) )
% 0.56/0.91 & ( ( p(V0t)
% 0.56/0.91 <=> $false )
% 0.56/0.91 <=> ~ p(V0t) ) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(conj_thm_2Ebool_2EAND__IMP__INTRO,axiom,
% 0.56/0.91 ! [V0t1] :
% 0.56/0.91 ( mem(V0t1,bool)
% 0.56/0.91 => ! [V1t2] :
% 0.56/0.91 ( mem(V1t2,bool)
% 0.56/0.91 => ! [V2t3] :
% 0.56/0.91 ( mem(V2t3,bool)
% 0.56/0.91 => ( ( p(V0t1)
% 0.56/0.91 => ( p(V1t2)
% 0.56/0.91 => p(V2t3) ) )
% 0.56/0.91 <=> ( ( p(V0t1)
% 0.56/0.91 & p(V1t2) )
% 0.56/0.91 => p(V2t3) ) ) ) ) ) ).
% 0.56/0.91
% 0.56/0.91 fof(conj_thm_2Ebool_2EIMP__CONG,axiom,
% 0.56/0.91 ! [V0x] :
% 0.56/0.91 ( mem(V0x,bool)
% 0.56/0.91 => ! [V1x_27] :
% 0.56/0.91 ( mem(V1x_27,bool)
% 0.56/0.91 => ! [V2y] :
% 0.56/0.91 ( mem(V2y,bool)
% 0.56/0.92 => ! [V3y_27] :
% 0.56/0.92 ( mem(V3y_27,bool)
% 0.56/0.92 => ( ( ( p(V0x)
% 0.56/0.92 <=> p(V1x_27) )
% 0.56/0.92 & ( p(V1x_27)
% 0.56/0.92 => ( p(V2y)
% 0.56/0.92 <=> p(V3y_27) ) ) )
% 0.56/0.92 => ( ( p(V0x)
% 0.56/0.92 => p(V2y) )
% 0.56/0.92 <=> ( p(V1x_27)
% 0.56/0.92 => p(V3y_27) ) ) ) ) ) ) ) ).
% 0.56/0.92
% 0.56/0.92 fof(conj_thm_2EquantHeuristics_2EGUESS__REWRITES,axiom,
% 0.56/0.92 ! [A_27a] :
% 0.56/0.92 ( ne(A_27a)
% 0.56/0.92 => ! [A_27b] :
% 0.56/0.92 ( ne(A_27b)
% 0.56/0.92 => ! [V0i] :
% 0.56/0.92 ( mem(V0i,arr(A_27a,A_27b))
% 0.56/0.92 => ! [V1P] :
% 0.56/0.92 ( mem(V1P,arr(A_27b,bool))
% 0.56/0.92 => ( ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS(A_27a,A_27b),V0i),V1P))
% 0.56/0.92 <=> ! [V2v] :
% 0.56/0.92 ( mem(V2v,A_27b)
% 0.56/0.92 => ( p(ap(V1P,V2v))
% 0.56/0.92 => ? [V3fv] :
% 0.56/0.92 ( mem(V3fv,A_27a)
% 0.56/0.92 & p(ap(V1P,ap(V0i,V3fv))) ) ) ) )
% 0.56/0.92 & ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL(A_27a,A_27b),V0i),V1P))
% 0.56/0.92 <=> ! [V4v] :
% 0.56/0.92 ( mem(V4v,A_27b)
% 0.56/0.92 => ( ~ p(ap(V1P,V4v))
% 0.56/0.92 => ? [V5fv] :
% 0.56/0.92 ( mem(V5fv,A_27a)
% 0.56/0.92 & ~ p(ap(V1P,ap(V0i,V5fv))) ) ) ) )
% 0.56/0.92 & ! [V6i] :
% 0.56/0.92 ( mem(V6i,arr(A_27a,A_27b))
% 0.56/0.92 => ! [V7P] :
% 0.56/0.92 ( mem(V7P,arr(A_27b,bool))
% 0.56/0.92 => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__POINT(A_27a,A_27b),V6i),V7P))
% 0.56/0.92 <=> ! [V8fv] :
% 0.56/0.92 ( mem(V8fv,A_27a)
% 0.56/0.92 => p(ap(V7P,ap(V6i,V8fv))) ) ) ) )
% 0.56/0.92 & ! [V9i] :
% 0.56/0.92 ( mem(V9i,arr(A_27a,A_27b))
% 0.56/0.92 => ! [V10P] :
% 0.56/0.92 ( mem(V10P,arr(A_27b,bool))
% 0.56/0.92 => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27a,A_27b),V9i),V10P))
% 0.56/0.92 <=> ! [V11fv] :
% 0.56/0.92 ( mem(V11fv,A_27a)
% 0.56/0.92 => ~ p(ap(V10P,ap(V9i,V11fv))) ) ) ) )
% 0.56/0.92 & ! [V12i] :
% 0.56/0.92 ( mem(V12i,arr(A_27a,A_27b))
% 0.56/0.92 => ! [V13P] :
% 0.56/0.92 ( mem(V13P,arr(A_27b,bool))
% 0.56/0.92 => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__EXISTS__GAP(A_27a,A_27b),V12i),V13P))
% 0.56/0.92 <=> ! [V14v] :
% 0.56/0.92 ( mem(V14v,A_27b)
% 0.56/0.92 => ( p(ap(V13P,V14v))
% 0.56/0.92 => ? [V15fv] :
% 0.56/0.92 ( mem(V15fv,A_27a)
% 0.56/0.92 & V14v = ap(V12i,V15fv) ) ) ) ) ) )
% 0.56/0.92 & ! [V16i] :
% 0.56/0.92 ( mem(V16i,arr(A_27a,A_27b))
% 0.56/0.92 => ! [V17P] :
% 0.56/0.92 ( mem(V17P,arr(A_27b,bool))
% 0.56/0.92 => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__GAP(A_27a,A_27b),V16i),V17P))
% 0.56/0.92 <=> ! [V18v] :
% 0.56/0.92 ( mem(V18v,A_27b)
% 0.56/0.92 => ( ~ p(ap(V17P,V18v))
% 0.56/0.92 => ? [V19fv] :
% 0.56/0.92 ( mem(V19fv,A_27a)
% 0.56/0.92 & V18v = ap(V16i,V19fv) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.56/0.92
% 0.56/0.92 fof(conj_thm_2Esat_2ENOT__NOT,axiom,
% 0.56/0.92 ! [V0t] :
% 0.56/0.92 ( mem(V0t,bool)
% 0.56/0.92 => ( ~ ~ p(V0t)
% 0.56/0.92 <=> p(V0t) ) ) ).
% 0.56/0.92
% 0.56/0.92 fof(conj_thm_2Esat_2EAND__INV__IMP,axiom,
% 0.56/0.92 ! [V0A] :
% 0.56/0.92 ( mem(V0A,bool)
% 0.56/0.92 => ( p(V0A)
% 0.56/0.92 => ( ~ p(V0A)
% 0.56/0.92 => $false ) ) ) ).
% 0.56/0.92
% 0.56/0.92 fof(conj_thm_2Esat_2EOR__DUAL2,axiom,
% 0.56/0.92 ! [V0A] :
% 0.56/0.92 ( mem(V0A,bool)
% 0.56/0.92 => ! [V1B] :
% 0.56/0.92 ( mem(V1B,bool)
% 0.56/0.92 => ( ( ~ ( p(V0A)
% 0.56/0.92 | p(V1B) )
% 0.56/0.92 => $false )
% 0.56/0.92 <=> ( ( p(V0A)
% 0.56/0.92 => $false )
% 0.56/0.92 => ( ~ p(V1B)
% 0.56/0.92 => $false ) ) ) ) ) ).
% 0.56/0.92
% 0.56/0.92 fof(conj_thm_2Esat_2EOR__DUAL3,axiom,
% 0.56/0.92 ! [V0A] :
% 0.56/0.92 ( mem(V0A,bool)
% 0.56/0.92 => ! [V1B] :
% 0.56/0.92 ( mem(V1B,bool)
% 0.56/0.92 => ( ( ~ ( ~ p(V0A)
% 0.56/0.92 | p(V1B) )
% 0.56/0.92 => $false )
% 0.56/0.92 <=> ( p(V0A)
% 0.56/0.92 => ( ~ p(V1B)
% 0.56/0.92 => $false ) ) ) ) ) ).
% 0.56/0.92
% 0.56/0.92 fof(conj_thm_2Esat_2EAND__INV2,axiom,
% 0.56/0.92 ! [V0A] :
% 0.56/0.92 ( mem(V0A,bool)
% 0.56/0.92 => ( ( ~ p(V0A)
% 0.56/0.92 => $false )
% 0.56/0.92 => ( ( p(V0A)
% 0.56/0.92 => $false )
% 0.56/0.92 => $false ) ) ) ).
% 0.56/0.92
% 0.56/0.92 fof(conj_thm_2Esat_2Edc__eq,axiom,
% 0.56/0.92 ! [V0p] :
% 0.56/0.92 ( mem(V0p,bool)
% 0.56/0.92 => ! [V1q] :
% 0.56/0.92 ( mem(V1q,bool)
% 0.56/0.92 => ! [V2r] :
% 0.56/0.92 ( mem(V2r,bool)
% 0.56/0.92 => ( ( p(V0p)
% 0.56/0.92 <=> ( p(V1q)
% 0.56/0.92 <=> p(V2r) ) )
% 0.56/0.92 <=> ( ( p(V0p)
% 0.56/0.92 | p(V1q)
% 0.56/0.92 | p(V2r) )
% 0.56/0.92 & ( p(V0p)
% 0.56/0.92 | ~ p(V2r)
% 0.56/0.92 | ~ p(V1q) )
% 0.56/0.92 & ( p(V1q)
% 0.56/0.92 | ~ p(V2r)
% 0.56/0.92 | ~ p(V0p) )
% 0.56/0.92 & ( p(V2r)
% 0.56/0.92 | ~ p(V1q)
% 0.56/0.92 | ~ p(V0p) ) ) ) ) ) ) ).
% 0.56/0.92
% 0.56/0.92 fof(conj_thm_2Esat_2Edc__disj,axiom,
% 0.56/0.92 ! [V0p] :
% 0.56/0.92 ( mem(V0p,bool)
% 0.56/0.92 => ! [V1q] :
% 0.56/0.92 ( mem(V1q,bool)
% 0.56/0.92 => ! [V2r] :
% 0.56/0.92 ( mem(V2r,bool)
% 0.56/0.92 => ( ( p(V0p)
% 0.56/0.92 <=> ( p(V1q)
% 0.56/0.92 | p(V2r) ) )
% 0.56/0.92 <=> ( ( p(V0p)
% 0.56/0.92 | ~ p(V1q) )
% 0.56/0.92 & ( p(V0p)
% 0.56/0.92 | ~ p(V2r) )
% 0.56/0.92 & ( p(V1q)
% 0.56/0.92 | p(V2r)
% 0.56/0.92 | ~ p(V0p) ) ) ) ) ) ) ).
% 0.56/0.92
% 0.56/0.93 fof(conj_thm_2Esat_2Edc__imp,axiom,
% 0.56/0.93 ! [V0p] :
% 0.56/0.93 ( mem(V0p,bool)
% 0.56/0.93 => ! [V1q] :
% 0.56/0.93 ( mem(V1q,bool)
% 0.56/0.93 => ! [V2r] :
% 0.56/0.93 ( mem(V2r,bool)
% 0.56/0.93 => ( ( p(V0p)
% 0.56/0.93 <=> ( p(V1q)
% 0.56/0.93 => p(V2r) ) )
% 0.56/0.93 <=> ( ( p(V0p)
% 0.56/0.93 | p(V1q) )
% 0.56/0.93 & ( p(V0p)
% 0.56/0.93 | ~ p(V2r) )
% 0.56/0.93 & ( ~ p(V1q)
% 0.56/0.93 | p(V2r)
% 0.56/0.93 | ~ p(V0p) ) ) ) ) ) ) ).
% 0.56/0.93
% 0.56/0.93 fof(conj_thm_2Esat_2Edc__neg,axiom,
% 0.56/0.93 ! [V0p] :
% 0.56/0.93 ( mem(V0p,bool)
% 0.56/0.93 => ! [V1q] :
% 0.56/0.93 ( mem(V1q,bool)
% 0.56/0.93 => ( ( p(V0p)
% 0.56/0.93 <=> ~ p(V1q) )
% 0.56/0.93 <=> ( ( p(V0p)
% 0.56/0.93 | p(V1q) )
% 0.56/0.93 & ( ~ p(V1q)
% 0.56/0.93 | ~ p(V0p) ) ) ) ) ) ).
% 0.56/0.93
% 0.56/0.93 fof(conj_thm_2Esat_2Epth__ni1,axiom,
% 0.56/0.93 ! [V0p] :
% 0.56/0.93 ( mem(V0p,bool)
% 0.56/0.93 => ! [V1q] :
% 0.56/0.93 ( mem(V1q,bool)
% 0.56/0.93 => ( ~ ( p(V0p)
% 0.56/0.93 => p(V1q) )
% 0.56/0.93 => p(V0p) ) ) ) ).
% 0.56/0.93
% 0.56/0.93 fof(conj_thm_2Esat_2Epth__ni2,axiom,
% 0.56/0.93 ! [V0p] :
% 0.56/0.93 ( mem(V0p,bool)
% 0.56/0.93 => ! [V1q] :
% 0.56/0.93 ( mem(V1q,bool)
% 0.56/0.93 => ( ~ ( p(V0p)
% 0.56/0.93 => p(V1q) )
% 0.56/0.93 => ~ p(V1q) ) ) ) ).
% 0.56/0.93
% 0.56/0.93 fof(conj_thm_2EquantHeuristics_2EGUESS__RULES__WEAKEN__FORALL__POINT,conjecture,
% 0.56/0.93 ! [A_27a] :
% 0.56/0.93 ( ne(A_27a)
% 0.56/0.93 => ! [A_27b] :
% 0.56/0.93 ( ne(A_27b)
% 0.56/0.93 => ! [V0i] :
% 0.56/0.93 ( mem(V0i,arr(A_27b,A_27a))
% 0.56/0.93 => ! [V1P] :
% 0.56/0.93 ( mem(V1P,arr(A_27a,bool))
% 0.56/0.93 => ! [V2Q] :
% 0.56/0.93 ( mem(V2Q,arr(A_27a,bool))
% 0.56/0.93 => ( ! [V3x] :
% 0.56/0.93 ( mem(V3x,A_27a)
% 0.56/0.93 => ( p(ap(V2Q,V3x))
% 0.56/0.93 => p(ap(V1P,V3x)) ) )
% 0.56/0.93 => ( p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27a),V0i),V1P))
% 0.56/0.93 => p(ap(ap(c_2EquantHeuristics_2EGUESS__FORALL__POINT(A_27b,A_27a),V0i),V2Q)) ) ) ) ) ) ) ) ).
% 0.56/0.93
% 0.56/0.93 %------------------------------------------------------------------------------
% 0.56/0.93 %-------------------------------------------
% 0.56/0.93 % Proof found
% 0.56/0.93 % SZS status Theorem for theBenchmark
% 0.56/0.93 % SZS output start Proof
% 0.56/0.93 %ClaNum:218(EqnAxiom:108)
% 0.56/0.93 %VarNum:809(SingletonVarNum:262)
% 0.56/0.93 %MaxLitNum:7
% 0.56/0.93 %MaxfuncDepth:3
% 0.56/0.93 %SharedTerms:38
% 0.56/0.93 %goalClause: 111 112 117 118 119 123 125 147
% 0.56/0.93 %singleGoalClaCount:7
% 0.56/0.93 [109]P1(a1)
% 0.56/0.93 [110]P1(a4)
% 0.56/0.93 [111]P1(a5)
% 0.56/0.93 [112]P1(a33)
% 0.56/0.93 [113]P9(a6)
% 0.56/0.93 [114]P2(a6,a1)
% 0.56/0.93 [115]P2(a7,a1)
% 0.56/0.93 [124]~P9(a7)
% 0.56/0.93 [116]P2(a8,f2(a1,a1))
% 0.56/0.93 [117]P2(a34,f2(a33,a5))
% 0.56/0.93 [118]P2(a35,f2(a5,a1))
% 0.56/0.93 [119]P2(a36,f2(a5,a1))
% 0.56/0.93 [120]P2(a9,f2(a1,f2(a1,a1)))
% 0.56/0.93 [121]P2(a10,f2(a1,f2(a1,a1)))
% 0.56/0.93 [122]P2(a13,f2(a1,f2(a1,a1)))
% 0.56/0.93 [123]P9(f3(f3(f15(a33,a5),a34),a35))
% 0.56/0.93 [125]~P9(f3(f3(f15(a33,a5),a34),a36))
% 0.56/0.93 [126]P3(x1261)+~P2(x1261,a1)
% 0.56/0.93 [127]P4(x1271)+~P2(x1271,a1)
% 0.56/0.93 [148]~P1(x1481)+P2(f12(x1481),f2(f2(x1481,a1),a1))
% 0.56/0.93 [149]~P1(x1491)+P2(f11(x1491),f2(f2(x1491,a1),a1))
% 0.56/0.93 [150]~P1(x1501)+P2(f14(x1501),f2(x1501,f2(x1501,a1)))
% 0.56/0.93 [128]~P2(x1282,x1281)+E(f3(f37(x1281),x1282),x1282)
% 0.56/0.93 [133]~P2(x1333,x1331)+E(f3(f39(x1331,x1332),x1333),x1332)
% 0.56/0.93 [131]P9(x1311)+~P2(x1311,a1)+P9(f3(a8,x1311))
% 0.56/0.93 [140]~P9(x1401)+~P2(x1401,a1)+~P9(f3(a8,x1401))
% 0.56/0.93 [147]~P2(x1471,a5)+~P9(f3(a36,x1471))+P9(f3(a35,x1471))
% 0.56/0.93 [129]~P1(x1292)+~P1(x1291)+P1(f2(x1291,x1292))
% 0.56/0.93 [184]~P1(x1842)+~P1(x1841)+P2(f16(x1841,x1842),f2(f2(x1841,x1842),f2(f2(x1842,a1),a1)))
% 0.56/0.93 [185]~P1(x1852)+~P1(x1851)+P2(f17(x1851,x1852),f2(f2(x1851,x1852),f2(f2(x1852,a1),a1)))
% 0.56/0.93 [186]~P1(x1862)+~P1(x1861)+P2(f15(x1861,x1862),f2(f2(x1861,x1862),f2(f2(x1862,a1),a1)))
% 0.56/0.93 [187]~P1(x1872)+~P1(x1871)+P2(f19(x1871,x1872),f2(f2(x1871,x1872),f2(f2(x1872,a1),a1)))
% 0.56/0.93 [188]~P1(x1882)+~P1(x1881)+P2(f20(x1881,x1882),f2(f2(x1881,x1882),f2(f2(x1882,a1),a1)))
% 0.56/0.93 [189]~P1(x1892)+~P1(x1891)+P2(f18(x1891,x1892),f2(f2(x1891,x1892),f2(f2(x1892,a1),a1)))
% 0.56/0.93 [135]~P9(x1353)+P9(x1351)+P5(x1352,x1353,x1351)
% 0.56/0.93 [137]~P9(x1372)+P9(x1371)+P5(x1372,x1373,x1371)
% 0.56/0.93 [139]~P9(x1391)+~P9(x1392)+P5(x1391,x1392,x1393)
% 0.56/0.93 [160]~P2(x1602,x1604)+~P2(x1601,f2(x1604,x1603))+P2(f3(x1601,x1602),x1603)
% 0.56/0.93 [196]~P6(x1964,x1963,x1962,x1961)+P2(f24(x1961,x1962,x1963,x1964),x1963)+P9(f3(f3(f18(x1964,x1963),x1962),x1961))
% 0.56/0.93 [197]~P6(x1974,x1973,x1972,x1971)+P2(f25(x1971,x1972,x1973,x1974),x1973)+P9(f3(f3(f20(x1974,x1973),x1972),x1971))
% 0.56/0.93 [198]~P6(x1984,x1983,x1982,x1981)+P9(f3(x1981,f24(x1981,x1982,x1983,x1984)))+P9(f3(f3(f18(x1984,x1983),x1982),x1981))
% 0.56/0.93 [200]~P6(x2001,x2002,x2003,x2004)+~P9(f3(x2004,f25(x2004,x2003,x2002,x2001)))+P9(f3(f3(f20(x2001,x2002),x2003),x2004))
% 0.56/0.93 [156]P9(x1561)+~P2(x1562,a1)+~P2(x1561,a1)+P9(f3(f3(a13,x1561),x1562))
% 0.56/0.93 [157]~P9(x1572)+~P2(x1571,a1)+~P2(x1572,a1)+P9(f3(f3(a9,x1571),x1572))
% 0.56/0.93 [158]~P9(x1581)+~P2(x1582,a1)+~P2(x1581,a1)+P9(f3(f3(a9,x1581),x1582))
% 0.56/0.93 [159]~P9(x1592)+~P2(x1591,a1)+~P2(x1592,a1)+P9(f3(f3(a13,x1591),x1592))
% 0.56/0.93 [166]~P1(x1661)+P2(f21(x1661,x1662),x1661)+~P2(x1662,f2(x1661,a1))+P9(f3(f11(x1661),x1662))
% 0.56/0.93 [170]P9(x1701)+~P2(x1701,a1)+~P2(x1702,a1)+~P9(f3(f3(a10,x1702),x1701))
% 0.56/0.93 [171]P9(x1711)+~P2(x1711,a1)+~P2(x1712,a1)+~P9(f3(f3(a10,x1711),x1712))
% 0.56/0.93 [178]~P1(x1781)+P2(f22(x1781,x1782),x1781)+~P2(x1782,f2(x1781,a1))+~P9(f3(f12(x1781),x1782))
% 0.56/0.93 [181]~P1(x1812)+~P2(x1811,f2(x1812,a1))+~P9(f3(f12(x1812),x1811))+P9(f3(x1811,f22(x1812,x1811)))
% 0.56/0.93 [183]~P1(x1831)+~P2(x1832,f2(x1831,a1))+~P9(f3(x1832,f21(x1831,x1832)))+P9(f3(f11(x1831),x1832))
% 0.56/0.93 [143]~P9(x1433)+P9(x1431)+P5(x1432,x1431,x1433)+P9(x1432)
% 0.56/0.93 [151]~P5(x1513,x1512,x1511)+P9(x1511)+P9(x1512)+P9(x1513)
% 0.56/0.93 [152]~P5(x1522,x1521,x1523)+P9(x1521)+~P9(x1522)+~P9(x1523)
% 0.56/0.93 [153]~P5(x1531,x1532,x1533)+P9(x1531)+~P9(x1532)+~P9(x1533)
% 0.56/0.93 [154]P7(x1541,x1542,x1543)+~P2(x1543,a1)+~P2(x1542,a1)+~P2(x1541,a1)
% 0.56/0.93 [155]P8(x1551,x1552,x1553)+~P2(x1553,a1)+~P2(x1552,a1)+~P2(x1551,a1)
% 0.56/0.93 [191]E(x1911,x1912)+~P2(x1912,f2(x1913,x1914))+~P2(x1911,f2(x1913,x1914))+P2(f23(x1913,x1914,x1911,x1912),x1913)
% 0.56/0.93 [199]E(x1991,x1992)+~P2(x1992,f2(x1993,x1994))+~P2(x1991,f2(x1993,x1994))+~E(f3(x1991,f23(x1993,x1994,x1991,x1992)),f3(x1992,f23(x1993,x1994,x1991,x1992)))
% 0.56/0.93 [192]~P2(x1923,x1924)+~P6(x1924,x1925,x1922,x1921)+P9(f3(x1921,f3(x1922,x1923)))+P9(f3(f3(f20(x1924,x1925),x1922),x1921))
% 0.56/0.93 [193]~P6(x1931,x1932,x1933,x1934)+~P2(x1935,x1931)+~P9(f3(x1934,f3(x1933,x1935)))+P9(f3(f3(f18(x1931,x1932),x1933),x1934))
% 0.56/0.93 [130]P9(x1302)+P9(x1301)+E(x1301,x1302)+~P2(x1302,a1)+~P2(x1301,a1)
% 0.56/0.93 [132]~P9(x1322)+~P9(x1321)+E(x1321,x1322)+~P2(x1322,a1)+~P2(x1321,a1)
% 0.56/0.93 [161]~P9(x1612)+~P9(x1611)+~P2(x1612,a1)+~P2(x1611,a1)+P9(f3(f3(a10,x1611),x1612))
% 0.56/0.93 [176]P9(x1761)+P9(x1762)+~P2(x1761,a1)+~P2(x1762,a1)+~P9(f3(f3(a9,x1762),x1761))
% 0.56/0.93 [177]P9(x1771)+~P9(x1772)+~P2(x1771,a1)+~P2(x1772,a1)+~P9(f3(f3(a13,x1772),x1771))
% 0.56/0.93 [179]~P1(x1791)+~P2(x1793,x1791)+~P2(x1792,f2(x1791,a1))+~P9(f3(x1792,x1793))+P9(f3(f12(x1791),x1792))
% 0.56/0.93 [180]~P2(x1802,x1803)+~P1(x1803)+~P2(x1801,f2(x1803,a1))+P9(f3(x1801,x1802))+~P9(f3(f11(x1803),x1801))
% 0.56/0.93 [169]~E(x1692,x1693)+~P1(x1691)+~P2(x1693,x1691)+~P2(x1692,x1691)+P9(f3(f3(f14(x1691),x1692),x1693))
% 0.56/0.93 [182]~P2(x1822,x1823)+~P2(x1821,x1823)+E(x1821,x1822)+~P1(x1823)+~P9(f3(f3(f14(x1823),x1821),x1822))
% 0.56/0.93 [190]~P1(x1902)+~P1(x1901)+P6(x1901,x1902,x1903,x1904)+~P2(x1903,f2(x1901,x1902))+~P2(x1904,f2(x1902,a1))
% 0.56/0.93 [201]~P2(x2012,x2014)+~P6(x2015,x2014,x2013,x2011)+P2(f26(x2011,x2013,x2014,x2015,x2012),x2015)+P9(f3(x2011,x2012))+~P9(f3(f3(f20(x2015,x2014),x2013),x2011))
% 0.56/0.93 [202]~P2(x2025,x2023)+~P6(x2024,x2023,x2022,x2021)+P2(f38(x2021,x2022,x2023,x2024,x2025),x2024)+~P9(f3(x2021,x2025))+~P9(f3(f3(f18(x2024,x2023),x2022),x2021))
% 0.56/0.93 [205]~P2(x2055,x2053)+~P6(x2054,x2053,x2052,x2051)+~P9(f3(x2051,x2055))+~P9(f3(f3(f18(x2054,x2053),x2052),x2051))+P9(f3(x2051,f3(x2052,f38(x2051,x2052,x2053,x2054,x2055))))
% 0.56/0.93 [210]~P6(x2104,x2103,x2105,x2101)+~P2(x2102,x2103)+P9(f3(x2101,x2102))+~P9(f3(f3(f20(x2104,x2103),x2105),x2101))+~P9(f3(x2101,f3(x2105,f26(x2101,x2105,x2103,x2104,x2102))))
% 0.56/0.93 [206]~P6(x2064,x2063,x2062,x2061)+~P2(x2065,f2(x2064,x2063))+P2(f29(x2061,x2062,x2063,x2064,x2065,x2066),x2064)+~P2(x2066,f2(x2063,a1))+P9(f3(f3(f19(x2064,x2063),x2065),x2066))
% 0.56/0.93 [207]~P6(x2074,x2073,x2072,x2071)+~P2(x2075,f2(x2074,x2073))+P2(f30(x2071,x2072,x2073,x2074,x2075,x2076),x2074)+~P2(x2076,f2(x2073,a1))+P9(f3(f3(f15(x2074,x2073),x2075),x2076))
% 0.56/0.93 [208]~P6(x2084,x2083,x2082,x2081)+~P2(x2085,f2(x2084,x2083))+P2(f28(x2081,x2082,x2083,x2084,x2085,x2086),x2083)+~P2(x2086,f2(x2083,a1))+P9(f3(f3(f17(x2084,x2083),x2085),x2086))
% 0.56/0.93 [209]~P6(x2094,x2093,x2092,x2091)+~P2(x2095,f2(x2094,x2093))+P2(f27(x2091,x2092,x2093,x2094,x2095,x2096),x2093)+~P2(x2096,f2(x2093,a1))+P9(f3(f3(f16(x2094,x2093),x2095),x2096))
% 0.56/0.93 [211]~P6(x2111,x2112,x2116,x2115)+~P2(x2113,f2(x2111,x2112))+~P2(x2114,f2(x2112,a1))+P9(f3(x2114,f28(x2115,x2116,x2112,x2111,x2113,x2114)))+P9(f3(f3(f17(x2111,x2112),x2113),x2114))
% 0.56/0.93 [212]~P6(x2121,x2122,x2125,x2126)+~P2(x2123,f2(x2121,x2122))+~P2(x2124,f2(x2122,a1))+~P9(f3(x2124,f27(x2126,x2125,x2122,x2121,x2123,x2124)))+P9(f3(f3(f16(x2121,x2122),x2123),x2124))
% 0.56/0.93 [213]~P6(x2131,x2132,x2136,x2135)+~P2(x2133,f2(x2131,x2132))+~P2(x2134,f2(x2132,a1))+P9(f3(x2134,f3(x2133,f30(x2135,x2136,x2132,x2131,x2133,x2134))))+P9(f3(f3(f15(x2131,x2132),x2133),x2134))
% 0.56/0.93 [218]~P6(x2181,x2182,x2185,x2186)+~P2(x2183,f2(x2181,x2182))+~P2(x2184,f2(x2182,a1))+~P9(f3(x2184,f3(x2183,f29(x2186,x2185,x2182,x2181,x2183,x2184))))+P9(f3(f3(f19(x2181,x2182),x2183),x2184))
% 0.56/0.93 [194]~P6(x1944,x1945,x1946,x1947)+~P2(x1943,x1944)+~P2(x1942,f2(x1944,x1945))+~P2(x1941,f2(x1945,a1))+P9(f3(x1941,f3(x1942,x1943)))+~P9(f3(f3(f19(x1944,x1945),x1942),x1941))
% 0.56/0.93 [195]~P2(x1951,x1952)+~P6(x1952,x1953,x1954,x1955)+~P2(x1956,f2(x1952,x1953))+~P2(x1957,f2(x1953,a1))+~P9(f3(x1957,f3(x1956,x1951)))+~P9(f3(f3(f15(x1952,x1953),x1956),x1957))
% 0.56/0.93 [203]~P2(x2037,x2031)+~P6(x2031,x2032,x2036,x2035)+~P2(x2033,f2(x2031,x2032))+~E(f27(x2035,x2036,x2032,x2031,x2033,x2034),f3(x2033,x2037))+~P2(x2034,f2(x2032,a1))+P9(f3(f3(f16(x2031,x2032),x2033),x2034))
% 0.56/0.93 [204]~P2(x2047,x2041)+~P6(x2041,x2042,x2046,x2045)+~P2(x2043,f2(x2041,x2042))+~E(f28(x2045,x2046,x2042,x2041,x2043,x2044),f3(x2043,x2047))+~P2(x2044,f2(x2042,a1))+P9(f3(f3(f17(x2041,x2042),x2043),x2044))
% 0.56/0.93 [214]~P2(x2142,x2145)+~P6(x2146,x2145,x2144,x2143)+~P2(x2147,f2(x2146,x2145))+P2(f32(x2143,x2144,x2145,x2146,x2147,x2141,x2142),x2146)+~P2(x2141,f2(x2145,a1))+P9(f3(x2141,x2142))+~P9(f3(f3(f16(x2146,x2145),x2147),x2141))
% 0.56/0.93 [215]~P2(x2157,x2154)+~P6(x2155,x2154,x2153,x2152)+~P2(x2151,f2(x2155,x2154))+~P2(x2156,f2(x2154,a1))+P9(f3(x2156,x2157))+E(f3(x2151,f32(x2152,x2153,x2154,x2155,x2151,x2156,x2157)),x2157)+~P9(f3(f3(f16(x2155,x2154),x2151),x2156))
% 0.56/0.93 [216]~P2(x2167,x2163)+~P6(x2164,x2163,x2162,x2161)+~P2(x2165,f2(x2164,x2163))+P2(f31(x2161,x2162,x2163,x2164,x2165,x2166,x2167),x2164)+~P2(x2166,f2(x2163,a1))+~P9(f3(x2166,x2167))+~P9(f3(f3(f17(x2164,x2163),x2165),x2166))
% 0.56/0.93 [217]~P2(x2177,x2174)+~P6(x2175,x2174,x2173,x2172)+~P2(x2171,f2(x2175,x2174))+~P2(x2176,f2(x2174,a1))+~P9(f3(x2176,x2177))+E(f3(x2171,f31(x2172,x2173,x2174,x2175,x2171,x2176,x2177)),x2177)+~P9(f3(f3(f17(x2175,x2174),x2171),x2176))
% 0.56/0.93 %EqnAxiom
% 0.56/0.93 [1]E(x11,x11)
% 0.56/0.93 [2]E(x22,x21)+~E(x21,x22)
% 0.56/0.93 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.56/0.93 [4]~E(x41,x42)+E(f2(x41,x43),f2(x42,x43))
% 0.56/0.93 [5]~E(x51,x52)+E(f2(x53,x51),f2(x53,x52))
% 0.56/0.93 [6]~E(x61,x62)+E(f3(x61,x63),f3(x62,x63))
% 0.56/0.93 [7]~E(x71,x72)+E(f3(x73,x71),f3(x73,x72))
% 0.56/0.93 [8]~E(x81,x82)+E(f30(x81,x83,x84,x85,x86,x87),f30(x82,x83,x84,x85,x86,x87))
% 0.56/0.93 [9]~E(x91,x92)+E(f30(x93,x91,x94,x95,x96,x97),f30(x93,x92,x94,x95,x96,x97))
% 0.56/0.93 [10]~E(x101,x102)+E(f30(x103,x104,x101,x105,x106,x107),f30(x103,x104,x102,x105,x106,x107))
% 0.56/0.93 [11]~E(x111,x112)+E(f30(x113,x114,x115,x111,x116,x117),f30(x113,x114,x115,x112,x116,x117))
% 0.56/0.93 [12]~E(x121,x122)+E(f30(x123,x124,x125,x126,x121,x127),f30(x123,x124,x125,x126,x122,x127))
% 0.56/0.93 [13]~E(x131,x132)+E(f30(x133,x134,x135,x136,x137,x131),f30(x133,x134,x135,x136,x137,x132))
% 0.56/0.93 [14]~E(x141,x142)+E(f29(x141,x143,x144,x145,x146,x147),f29(x142,x143,x144,x145,x146,x147))
% 0.56/0.93 [15]~E(x151,x152)+E(f29(x153,x151,x154,x155,x156,x157),f29(x153,x152,x154,x155,x156,x157))
% 0.56/0.93 [16]~E(x161,x162)+E(f29(x163,x164,x161,x165,x166,x167),f29(x163,x164,x162,x165,x166,x167))
% 0.56/0.93 [17]~E(x171,x172)+E(f29(x173,x174,x175,x171,x176,x177),f29(x173,x174,x175,x172,x176,x177))
% 0.56/0.93 [18]~E(x181,x182)+E(f29(x183,x184,x185,x186,x181,x187),f29(x183,x184,x185,x186,x182,x187))
% 0.56/0.93 [19]~E(x191,x192)+E(f29(x193,x194,x195,x196,x197,x191),f29(x193,x194,x195,x196,x197,x192))
% 0.56/0.93 [20]~E(x201,x202)+E(f15(x201,x203),f15(x202,x203))
% 0.56/0.93 [21]~E(x211,x212)+E(f15(x213,x211),f15(x213,x212))
% 0.56/0.93 [22]~E(x221,x222)+E(f19(x221,x223),f19(x222,x223))
% 0.56/0.93 [23]~E(x231,x232)+E(f19(x233,x231),f19(x233,x232))
% 0.56/0.93 [24]~E(x241,x242)+E(f11(x241),f11(x242))
% 0.56/0.93 [25]~E(x251,x252)+E(f32(x251,x253,x254,x255,x256,x257,x258),f32(x252,x253,x254,x255,x256,x257,x258))
% 0.56/0.93 [26]~E(x261,x262)+E(f32(x263,x261,x264,x265,x266,x267,x268),f32(x263,x262,x264,x265,x266,x267,x268))
% 0.56/0.93 [27]~E(x271,x272)+E(f32(x273,x274,x271,x275,x276,x277,x278),f32(x273,x274,x272,x275,x276,x277,x278))
% 0.56/0.93 [28]~E(x281,x282)+E(f32(x283,x284,x285,x281,x286,x287,x288),f32(x283,x284,x285,x282,x286,x287,x288))
% 0.56/0.93 [29]~E(x291,x292)+E(f32(x293,x294,x295,x296,x291,x297,x298),f32(x293,x294,x295,x296,x292,x297,x298))
% 0.56/0.93 [30]~E(x301,x302)+E(f32(x303,x304,x305,x306,x307,x301,x308),f32(x303,x304,x305,x306,x307,x302,x308))
% 0.56/0.93 [31]~E(x311,x312)+E(f32(x313,x314,x315,x316,x317,x318,x311),f32(x313,x314,x315,x316,x317,x318,x312))
% 0.56/0.93 [32]~E(x321,x322)+E(f18(x321,x323),f18(x322,x323))
% 0.56/0.93 [33]~E(x331,x332)+E(f18(x333,x331),f18(x333,x332))
% 0.56/0.93 [34]~E(x341,x342)+E(f17(x341,x343),f17(x342,x343))
% 0.56/0.93 [35]~E(x351,x352)+E(f17(x353,x351),f17(x353,x352))
% 0.56/0.93 [36]~E(x361,x362)+E(f12(x361),f12(x362))
% 0.56/0.93 [37]~E(x371,x372)+E(f38(x371,x373,x374,x375,x376),f38(x372,x373,x374,x375,x376))
% 0.56/0.93 [38]~E(x381,x382)+E(f38(x383,x381,x384,x385,x386),f38(x383,x382,x384,x385,x386))
% 0.56/0.93 [39]~E(x391,x392)+E(f38(x393,x394,x391,x395,x396),f38(x393,x394,x392,x395,x396))
% 0.56/0.93 [40]~E(x401,x402)+E(f38(x403,x404,x405,x401,x406),f38(x403,x404,x405,x402,x406))
% 0.56/0.93 [41]~E(x411,x412)+E(f38(x413,x414,x415,x416,x411),f38(x413,x414,x415,x416,x412))
% 0.56/0.93 [42]~E(x421,x422)+E(f28(x421,x423,x424,x425,x426,x427),f28(x422,x423,x424,x425,x426,x427))
% 0.56/0.93 [43]~E(x431,x432)+E(f28(x433,x431,x434,x435,x436,x437),f28(x433,x432,x434,x435,x436,x437))
% 0.56/0.93 [44]~E(x441,x442)+E(f28(x443,x444,x441,x445,x446,x447),f28(x443,x444,x442,x445,x446,x447))
% 0.56/0.93 [45]~E(x451,x452)+E(f28(x453,x454,x455,x451,x456,x457),f28(x453,x454,x455,x452,x456,x457))
% 0.56/0.93 [46]~E(x461,x462)+E(f28(x463,x464,x465,x466,x461,x467),f28(x463,x464,x465,x466,x462,x467))
% 0.56/0.93 [47]~E(x471,x472)+E(f28(x473,x474,x475,x476,x477,x471),f28(x473,x474,x475,x476,x477,x472))
% 0.56/0.93 [48]~E(x481,x482)+E(f14(x481),f14(x482))
% 0.56/0.93 [49]~E(x491,x492)+E(f27(x491,x493,x494,x495,x496,x497),f27(x492,x493,x494,x495,x496,x497))
% 0.56/0.93 [50]~E(x501,x502)+E(f27(x503,x501,x504,x505,x506,x507),f27(x503,x502,x504,x505,x506,x507))
% 0.56/0.93 [51]~E(x511,x512)+E(f27(x513,x514,x511,x515,x516,x517),f27(x513,x514,x512,x515,x516,x517))
% 0.56/0.94 [52]~E(x521,x522)+E(f27(x523,x524,x525,x521,x526,x527),f27(x523,x524,x525,x522,x526,x527))
% 0.56/0.94 [53]~E(x531,x532)+E(f27(x533,x534,x535,x536,x531,x537),f27(x533,x534,x535,x536,x532,x537))
% 0.56/0.94 [54]~E(x541,x542)+E(f27(x543,x544,x545,x546,x547,x541),f27(x543,x544,x545,x546,x547,x542))
% 0.56/0.94 [55]~E(x551,x552)+E(f20(x551,x553),f20(x552,x553))
% 0.56/0.94 [56]~E(x561,x562)+E(f20(x563,x561),f20(x563,x562))
% 0.56/0.94 [57]~E(x571,x572)+E(f37(x571),f37(x572))
% 0.56/0.94 [58]~E(x581,x582)+E(f16(x581,x583),f16(x582,x583))
% 0.56/0.94 [59]~E(x591,x592)+E(f16(x593,x591),f16(x593,x592))
% 0.56/0.94 [60]~E(x601,x602)+E(f21(x601,x603),f21(x602,x603))
% 0.56/0.94 [61]~E(x611,x612)+E(f21(x613,x611),f21(x613,x612))
% 0.56/0.94 [62]~E(x621,x622)+E(f22(x621,x623),f22(x622,x623))
% 0.56/0.94 [63]~E(x631,x632)+E(f22(x633,x631),f22(x633,x632))
% 0.56/0.94 [64]~E(x641,x642)+E(f39(x641,x643),f39(x642,x643))
% 0.56/0.94 [65]~E(x651,x652)+E(f39(x653,x651),f39(x653,x652))
% 0.56/0.94 [66]~E(x661,x662)+E(f25(x661,x663,x664,x665),f25(x662,x663,x664,x665))
% 0.56/0.94 [67]~E(x671,x672)+E(f25(x673,x671,x674,x675),f25(x673,x672,x674,x675))
% 0.56/0.94 [68]~E(x681,x682)+E(f25(x683,x684,x681,x685),f25(x683,x684,x682,x685))
% 0.56/0.94 [69]~E(x691,x692)+E(f25(x693,x694,x695,x691),f25(x693,x694,x695,x692))
% 0.56/0.94 [70]~E(x701,x702)+E(f23(x701,x703,x704,x705),f23(x702,x703,x704,x705))
% 0.56/0.94 [71]~E(x711,x712)+E(f23(x713,x711,x714,x715),f23(x713,x712,x714,x715))
% 0.56/0.94 [72]~E(x721,x722)+E(f23(x723,x724,x721,x725),f23(x723,x724,x722,x725))
% 0.56/0.94 [73]~E(x731,x732)+E(f23(x733,x734,x735,x731),f23(x733,x734,x735,x732))
% 0.56/0.94 [74]~E(x741,x742)+E(f31(x741,x743,x744,x745,x746,x747,x748),f31(x742,x743,x744,x745,x746,x747,x748))
% 0.56/0.94 [75]~E(x751,x752)+E(f31(x753,x751,x754,x755,x756,x757,x758),f31(x753,x752,x754,x755,x756,x757,x758))
% 0.56/0.94 [76]~E(x761,x762)+E(f31(x763,x764,x761,x765,x766,x767,x768),f31(x763,x764,x762,x765,x766,x767,x768))
% 0.56/0.94 [77]~E(x771,x772)+E(f31(x773,x774,x775,x771,x776,x777,x778),f31(x773,x774,x775,x772,x776,x777,x778))
% 0.56/0.94 [78]~E(x781,x782)+E(f31(x783,x784,x785,x786,x781,x787,x788),f31(x783,x784,x785,x786,x782,x787,x788))
% 0.56/0.94 [79]~E(x791,x792)+E(f31(x793,x794,x795,x796,x797,x791,x798),f31(x793,x794,x795,x796,x797,x792,x798))
% 0.56/0.94 [80]~E(x801,x802)+E(f31(x803,x804,x805,x806,x807,x808,x801),f31(x803,x804,x805,x806,x807,x808,x802))
% 0.56/0.94 [81]~E(x811,x812)+E(f26(x811,x813,x814,x815,x816),f26(x812,x813,x814,x815,x816))
% 0.56/0.94 [82]~E(x821,x822)+E(f26(x823,x821,x824,x825,x826),f26(x823,x822,x824,x825,x826))
% 0.56/0.94 [83]~E(x831,x832)+E(f26(x833,x834,x831,x835,x836),f26(x833,x834,x832,x835,x836))
% 0.56/0.94 [84]~E(x841,x842)+E(f26(x843,x844,x845,x841,x846),f26(x843,x844,x845,x842,x846))
% 0.56/0.94 [85]~E(x851,x852)+E(f26(x853,x854,x855,x856,x851),f26(x853,x854,x855,x856,x852))
% 0.56/0.94 [86]~E(x861,x862)+E(f24(x861,x863,x864,x865),f24(x862,x863,x864,x865))
% 0.56/0.94 [87]~E(x871,x872)+E(f24(x873,x871,x874,x875),f24(x873,x872,x874,x875))
% 0.56/0.94 [88]~E(x881,x882)+E(f24(x883,x884,x881,x885),f24(x883,x884,x882,x885))
% 0.56/0.94 [89]~E(x891,x892)+E(f24(x893,x894,x895,x891),f24(x893,x894,x895,x892))
% 0.56/0.94 [90]~P1(x901)+P1(x902)+~E(x901,x902)
% 0.56/0.94 [91]~P9(x911)+P9(x912)+~E(x911,x912)
% 0.56/0.94 [92]P2(x922,x923)+~E(x921,x922)+~P2(x921,x923)
% 0.56/0.94 [93]P2(x933,x932)+~E(x931,x932)+~P2(x933,x931)
% 0.56/0.94 [94]P5(x942,x943,x944)+~E(x941,x942)+~P5(x941,x943,x944)
% 0.56/0.94 [95]P5(x953,x952,x954)+~E(x951,x952)+~P5(x953,x951,x954)
% 0.56/0.94 [96]P5(x963,x964,x962)+~E(x961,x962)+~P5(x963,x964,x961)
% 0.56/0.94 [97]P6(x972,x973,x974,x975)+~E(x971,x972)+~P6(x971,x973,x974,x975)
% 0.56/0.94 [98]P6(x983,x982,x984,x985)+~E(x981,x982)+~P6(x983,x981,x984,x985)
% 0.56/0.94 [99]P6(x993,x994,x992,x995)+~E(x991,x992)+~P6(x993,x994,x991,x995)
% 0.56/0.94 [100]P6(x1003,x1004,x1005,x1002)+~E(x1001,x1002)+~P6(x1003,x1004,x1005,x1001)
% 0.56/0.94 [101]P7(x1012,x1013,x1014)+~E(x1011,x1012)+~P7(x1011,x1013,x1014)
% 0.56/0.94 [102]P7(x1023,x1022,x1024)+~E(x1021,x1022)+~P7(x1023,x1021,x1024)
% 0.56/0.94 [103]P7(x1033,x1034,x1032)+~E(x1031,x1032)+~P7(x1033,x1034,x1031)
% 0.56/0.94 [104]P8(x1042,x1043,x1044)+~E(x1041,x1042)+~P8(x1041,x1043,x1044)
% 0.56/0.94 [105]P8(x1053,x1052,x1054)+~E(x1051,x1052)+~P8(x1053,x1051,x1054)
% 0.56/0.94 [106]P8(x1063,x1064,x1062)+~E(x1061,x1062)+~P8(x1063,x1064,x1061)
% 0.56/0.94 [107]~P4(x1071)+P4(x1072)+~E(x1071,x1072)
% 0.56/0.94 [108]~P3(x1081)+P3(x1082)+~E(x1081,x1082)
% 0.56/0.94
% 0.56/0.94 %-------------------------------------------
% 0.56/0.94 cnf(219,plain,
% 0.56/0.94 (P4(a6)),
% 0.56/0.94 inference(scs_inference,[],[114,127])).
% 0.56/0.94 cnf(221,plain,
% 0.56/0.94 (P5(a6,a6,x2211)),
% 0.56/0.94 inference(scs_inference,[],[113,114,127,126,139])).
% 0.56/0.94 cnf(227,plain,
% 0.56/0.94 (P8(a6,a6,a6)),
% 0.56/0.94 inference(scs_inference,[],[113,114,124,127,126,139,137,135,155])).
% 0.56/0.94 cnf(229,plain,
% 0.56/0.94 (P7(a6,a6,a6)),
% 0.56/0.94 inference(scs_inference,[],[113,114,124,127,126,139,137,135,155,154])).
% 0.56/0.94 cnf(237,plain,
% 0.56/0.94 (P6(a33,a5,a34,a36)),
% 0.56/0.94 inference(scs_inference,[],[111,112,113,114,124,119,117,127,126,139,137,135,155,154,153,152,151,190])).
% 0.56/0.94 cnf(243,plain,
% 0.56/0.94 (P2(f11(a5),f2(f2(a5,a1),a1))),
% 0.56/0.94 inference(scs_inference,[],[111,112,113,114,124,119,117,118,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149])).
% 0.56/0.94 cnf(247,plain,
% 0.56/0.94 (E(f3(f39(a1,x2471),a6),x2471)),
% 0.56/0.94 inference(scs_inference,[],[111,112,113,114,124,119,117,118,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133])).
% 0.56/0.94 cnf(253,plain,
% 0.56/0.94 (~E(a6,x2531)+P3(x2531)),
% 0.56/0.94 inference(scs_inference,[],[111,112,113,114,124,119,117,118,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133,128,150,108])).
% 0.56/0.94 cnf(254,plain,
% 0.56/0.94 (~P5(a7,a6,f3(f39(a1,a6),a6))),
% 0.56/0.94 inference(scs_inference,[],[111,112,113,114,124,119,117,118,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133,128,150,108,96])).
% 0.56/0.94 cnf(256,plain,
% 0.56/0.94 (~E(a6,a7)),
% 0.56/0.94 inference(scs_inference,[],[111,112,113,114,124,119,117,118,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133,128,150,108,96,95,94])).
% 0.56/0.94 cnf(260,plain,
% 0.56/0.94 (P9(f3(a8,a7))),
% 0.56/0.94 inference(scs_inference,[],[111,112,113,114,115,124,119,117,118,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133,128,150,108,96,95,94,91,140,131])).
% 0.56/0.94 cnf(264,plain,
% 0.56/0.94 (P2(f3(a34,f30(a36,a34,a5,a33,a34,a36)),a5)),
% 0.56/0.94 inference(scs_inference,[],[111,112,113,114,115,124,119,117,118,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133,128,150,108,96,95,94,91,140,131,129,160])).
% 0.56/0.94 cnf(266,plain,
% 0.56/0.94 (~P9(f3(a36,f3(a34,f30(a36,a34,a5,a33,a34,a36))))),
% 0.56/0.94 inference(scs_inference,[],[111,112,113,114,115,124,119,117,118,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133,128,150,108,96,95,94,91,140,131,129,160,147])).
% 0.56/0.94 cnf(282,plain,
% 0.56/0.94 (~P9(f3(f3(a10,a7),a7))),
% 0.56/0.94 inference(scs_inference,[],[111,112,113,114,115,124,119,117,118,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133,128,150,108,96,95,94,91,140,131,129,160,147,189,188,187,186,185,184,143,171])).
% 0.56/0.94 cnf(296,plain,
% 0.56/0.94 (~P9(f3(f11(a5),a35))),
% 0.56/0.94 inference(scs_inference,[],[111,112,113,114,115,124,119,117,118,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133,128,150,108,96,95,94,91,140,131,129,160,147,189,188,187,186,185,184,143,171,159,158,156,192,176,161,180])).
% 0.56/0.94 cnf(298,plain,
% 0.56/0.94 (P9(f3(f12(a1),a8))),
% 0.56/0.94 inference(scs_inference,[],[111,112,109,113,114,115,124,119,117,118,116,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133,128,150,108,96,95,94,91,140,131,129,160,147,189,188,187,186,185,184,143,171,159,158,156,192,176,161,180,179])).
% 0.56/0.94 cnf(302,plain,
% 0.56/0.94 (~P9(f3(f3(f19(a33,a5),a34),a35))),
% 0.56/0.94 inference(scs_inference,[],[111,112,109,113,114,115,124,119,117,118,116,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133,128,150,108,96,95,94,91,140,131,129,160,147,189,188,187,186,185,184,143,171,159,158,156,192,176,161,180,179,201,213,194])).
% 0.56/0.94 cnf(304,plain,
% 0.56/0.94 (E(a6,f3(f39(a1,a6),a6))),
% 0.56/0.94 inference(scs_inference,[],[111,112,109,113,114,115,124,119,117,118,116,125,123,127,126,139,137,135,155,154,153,152,151,190,207,195,149,148,133,128,150,108,96,95,94,91,140,131,129,160,147,189,188,187,186,185,184,143,171,159,158,156,192,176,161,180,179,201,213,194,2])).
% 0.56/0.94 cnf(474,plain,
% 0.56/0.94 ($false),
% 0.56/0.94 inference(scs_inference,[],[111,110,116,109,125,118,119,117,115,113,114,247,243,266,302,282,296,298,256,260,304,264,221,254,219,227,229,237,253,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,107,178,166,218,135,129,188,187,184,155,154,152,180,2,105,104,101,95,92,140,160,189,186,185,153,151,157,183,181,213]),
% 0.56/0.94 ['proof']).
% 0.56/0.94 % SZS output end Proof
% 0.56/0.94 % Total time :0.200000s
%------------------------------------------------------------------------------