%------------------------------------------------------------------------------
% File : CSE---1.7
% Problem : GEO065-3 : TPTP v8.2.0. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n032.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 06:03:37 EDT 2024
% Result : Unsatisfiable 0.46s 0.59s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : GEO065-3 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.00/0.08 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.08/0.27 % Computer : n032.cluster.edu
% 0.08/0.27 % Model : x86_64 x86_64
% 0.08/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.27 % Memory : 8042.1875MB
% 0.08/0.27 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.27 % CPULimit : 300
% 0.08/0.27 % WCLimit : 300
% 0.08/0.27 % DateTime : Fri Jun 21 08:15:23 EDT 2024
% 0.08/0.27 % CPUTime :
% 0.11/0.46 start to proof:theBenchmark
% 0.46/0.57 %-------------------------------------------
% 0.46/0.57 % File :CSE---1.7
% 0.46/0.57 % Problem :theBenchmark
% 0.46/0.57 % Transform :cnf
% 0.46/0.57 % Format :tptp:raw
% 0.46/0.57 % Command :java -jar mcs_scs.jar %d %s
% 0.46/0.57
% 0.46/0.57 % Result :Theorem 0.070000s
% 0.46/0.57 % Output :CNFRefutation 0.070000s
% 0.46/0.57 %-------------------------------------------
% 0.46/0.58 %--------------------------------------------------------------------------
% 0.46/0.58 % File : GEO065-3 : TPTP v8.2.0. Bugfixed v1.2.1.
% 0.46/0.58 % Domain : Geometry
% 0.46/0.58 % Problem : Corollary 2 to collinearity
% 0.46/0.58 % Version : [Qua89] axioms : Augmented.
% 0.46/0.58 % English :
% 0.46/0.58
% 0.46/0.58 % Refs : [SST83] Schwabbauser et al. (1983), Metamathematische Methoden
% 0.46/0.58 % : [Qua89] Quaife (1989), Automated Development of Tarski's Geome
% 0.46/0.58 % Source : [Qua89]
% 0.46/0.58 % Names : C2.2 [Qua89]
% 0.46/0.58
% 0.46/0.58 % Status : Unsatisfiable
% 0.46/0.58 % Rating : 0.05 v8.1.0, 0.00 v7.5.0, 0.05 v7.4.0, 0.06 v7.3.0, 0.08 v7.1.0, 0.00 v6.2.0, 0.10 v6.1.0, 0.07 v6.0.0, 0.10 v5.3.0, 0.11 v5.2.0, 0.12 v5.0.0, 0.07 v4.1.0, 0.00 v4.0.1, 0.09 v4.0.0, 0.00 v3.3.0, 0.07 v3.2.0, 0.08 v3.1.0, 0.09 v2.7.0, 0.17 v2.6.0, 0.11 v2.5.0, 0.09 v2.4.0, 0.12 v2.2.1, 0.00 v2.0.0
% 0.46/0.58 % Syntax : Number of clauses : 89 ( 27 unt; 21 nHn; 67 RR)
% 0.46/0.58 % Number of literals : 245 ( 47 equ; 137 neg)
% 0.46/0.58 % Maximal clause size : 8 ( 2 avg)
% 0.46/0.58 % Maximal term depth : 3 ( 1 avg)
% 0.46/0.58 % Number of predicates : 4 ( 3 usr; 0 prp; 2-4 aty)
% 0.46/0.58 % Number of functors : 13 ( 13 usr; 6 con; 0-6 aty)
% 0.46/0.58 % Number of variables : 317 ( 14 sgn)
% 0.46/0.58 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.46/0.58
% 0.46/0.58 % Comments :
% 0.46/0.58 % Bugfixes : v1.2.1 - Clause d12 fixed.
% 0.46/0.58 %--------------------------------------------------------------------------
% 0.46/0.58 %----Include Tarski geometry axioms
% 0.46/0.58 include('Axioms/GEO002-0.ax').
% 0.46/0.58 %----Include definition of colinearity
% 0.46/0.58 include('Axioms/GEO002-1.ax').
% 0.46/0.58 %----Include definition of reflection
% 0.46/0.58 include('Axioms/GEO002-2.ax').
% 0.46/0.58 %----Include definition of insertion
% 0.46/0.58 include('Axioms/GEO002-3.ax').
% 0.46/0.58 %--------------------------------------------------------------------------
% 0.46/0.58 cnf(d1,axiom,
% 0.46/0.58 equidistant(U,V,U,V) ).
% 0.46/0.58
% 0.46/0.58 cnf(d2,axiom,
% 0.46/0.58 ( ~ equidistant(U,V,W,X)
% 0.46/0.58 | equidistant(W,X,U,V) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d3,axiom,
% 0.46/0.58 ( ~ equidistant(U,V,W,X)
% 0.46/0.58 | equidistant(V,U,W,X) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d4_1,axiom,
% 0.46/0.58 ( ~ equidistant(U,V,W,X)
% 0.46/0.58 | equidistant(U,V,X,W) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d4_2,axiom,
% 0.46/0.58 ( ~ equidistant(U,V,W,X)
% 0.46/0.58 | equidistant(V,U,X,W) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d4_3,axiom,
% 0.46/0.58 ( ~ equidistant(U,V,W,X)
% 0.46/0.58 | equidistant(W,X,V,U) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d4_4,axiom,
% 0.46/0.58 ( ~ equidistant(U,V,W,X)
% 0.46/0.58 | equidistant(X,W,U,V) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d4_5,axiom,
% 0.46/0.58 ( ~ equidistant(U,V,W,X)
% 0.46/0.58 | equidistant(X,W,V,U) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d5,axiom,
% 0.46/0.58 ( ~ equidistant(U,V,W,X)
% 0.46/0.58 | ~ equidistant(W,X,Y,Z)
% 0.46/0.58 | equidistant(U,V,Y,Z) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(e1,axiom,
% 0.46/0.58 V = extension(U,V,W,W) ).
% 0.46/0.58
% 0.46/0.58 cnf(b0,axiom,
% 0.46/0.58 ( Y != extension(U,V,W,X)
% 0.46/0.58 | between(U,V,Y) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(r2_1,axiom,
% 0.46/0.58 between(U,V,reflection(U,V)) ).
% 0.46/0.58
% 0.46/0.58 cnf(r2_2,axiom,
% 0.46/0.58 equidistant(V,reflection(U,V),U,V) ).
% 0.46/0.58
% 0.46/0.58 cnf(r3_1,axiom,
% 0.46/0.58 ( U != V
% 0.46/0.58 | V = reflection(U,V) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(r3_2,axiom,
% 0.46/0.58 U = reflection(U,U) ).
% 0.46/0.58
% 0.46/0.58 cnf(r4,axiom,
% 0.46/0.58 ( V != reflection(U,V)
% 0.46/0.58 | U = V ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d7,axiom,
% 0.46/0.58 equidistant(U,U,V,V) ).
% 0.46/0.58
% 0.46/0.58 cnf(d8,axiom,
% 0.46/0.58 ( ~ equidistant(U,V,U1,V1)
% 0.46/0.58 | ~ equidistant(V,W,V1,W1)
% 0.46/0.58 | ~ between(U,V,W)
% 0.46/0.58 | ~ between(U1,V1,W1)
% 0.46/0.58 | equidistant(U,W,U1,W1) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d9,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(U,V,X)
% 0.46/0.58 | ~ equidistant(V,W,V,X)
% 0.46/0.58 | U = V
% 0.46/0.58 | W = X ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d10_1,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | U = V
% 0.46/0.58 | W = extension(U,V,V,W) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d10_2,axiom,
% 0.46/0.58 ( ~ equidistant(W,X,Y,Z)
% 0.46/0.58 | extension(U,V,W,X) = extension(U,V,Y,Z)
% 0.46/0.58 | U = V ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d10_3,axiom,
% 0.46/0.58 ( extension(U,V,U,V) = extension(U,V,V,U)
% 0.46/0.58 | U = V ) ).
% 0.46/0.58
% 0.46/0.58 cnf(r5,axiom,
% 0.46/0.58 equidistant(V,U,V,reflection(reflection(U,V),V)) ).
% 0.46/0.58
% 0.46/0.58 cnf(r6,axiom,
% 0.46/0.58 U = reflection(reflection(U,V),V) ).
% 0.46/0.58
% 0.46/0.58 cnf(t3,axiom,
% 0.46/0.58 between(U,V,V) ).
% 0.46/0.58
% 0.46/0.58 cnf(b1,axiom,
% 0.46/0.58 ( ~ between(U,W,X)
% 0.46/0.58 | U != X
% 0.46/0.58 | between(V,W,X) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(t1,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | between(W,V,U) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(t2,axiom,
% 0.46/0.58 between(U,U,V) ).
% 0.46/0.58
% 0.46/0.58 cnf(b2,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(V,U,W)
% 0.46/0.58 | U = V ) ).
% 0.46/0.58
% 0.46/0.58 cnf(b3,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(U,W,V)
% 0.46/0.58 | V = W ) ).
% 0.46/0.58
% 0.46/0.58 cnf(t6_1,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(V,U,W)
% 0.46/0.58 | U = V
% 0.46/0.58 | V = W ) ).
% 0.46/0.58
% 0.46/0.58 cnf(t6_2,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(U,W,V)
% 0.46/0.58 | U = V
% 0.46/0.58 | V = W ) ).
% 0.46/0.58
% 0.46/0.58 cnf(b4,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(V,W,X)
% 0.46/0.58 | between(U,V,W) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(b5,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(U,W,X)
% 0.46/0.58 | between(V,W,X) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(b6,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(V,W,X)
% 0.46/0.58 | between(U,W,X)
% 0.46/0.58 | V = W ) ).
% 0.46/0.58
% 0.46/0.58 cnf(b7,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(V,W,X)
% 0.46/0.58 | between(U,V,X)
% 0.46/0.58 | V = W ) ).
% 0.46/0.58
% 0.46/0.58 cnf(b8,axiom,
% 0.46/0.58 ( ~ between(U,V,X)
% 0.46/0.58 | ~ between(V,W,X)
% 0.46/0.58 | between(U,W,X) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(b9,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(U,W,X)
% 0.46/0.58 | between(U,V,X) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(e2_1,axiom,
% 0.46/0.58 lower_dimension_point_1 != lower_dimension_point_2 ).
% 0.46/0.58
% 0.46/0.58 cnf(e2_2,axiom,
% 0.46/0.58 lower_dimension_point_2 != lower_dimension_point_3 ).
% 0.46/0.58
% 0.46/0.58 cnf(e2_3,axiom,
% 0.46/0.58 lower_dimension_point_1 != lower_dimension_point_3 ).
% 0.46/0.58
% 0.46/0.58 cnf(e3_1,axiom,
% 0.46/0.58 V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ).
% 0.46/0.58
% 0.46/0.58 cnf(e3_2,axiom,
% 0.46/0.58 equidistant(V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2),X,extension(W,X,lower_dimension_point_1,lower_dimension_point_2)) ).
% 0.46/0.58
% 0.46/0.58 cnf(e3_3,axiom,
% 0.46/0.58 between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)) ).
% 0.46/0.58
% 0.46/0.58 cnf(b10,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(U1,V1,W)
% 0.46/0.58 | ~ between(U,X,U1)
% 0.46/0.58 | between(X,inner_pasch(V1,inner_pasch(U,X,U1,V1,W),U,V,W),W)
% 0.46/0.58 | between(V,inner_pasch(V1,inner_pasch(U,X,U1,V1,W),U,V,W),V1) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d11,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ equidistant(U,W,U,W1)
% 0.46/0.58 | ~ equidistant(V,W,V,W1)
% 0.46/0.58 | U = V
% 0.46/0.58 | W = W1 ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d12,axiom,
% 0.46/0.58 ( ~ equidistant(U,V,U1,V1)
% 0.46/0.58 | ~ equidistant(U,W,U1,W1)
% 0.46/0.58 | ~ equidistant(U,X,U1,X1)
% 0.46/0.58 | ~ equidistant(W,X,W1,X1)
% 0.46/0.58 | ~ between(U,V,W)
% 0.46/0.58 | ~ between(U1,V1,W1)
% 0.46/0.58 | equidistant(V,X,V1,X1) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d13,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ between(U1,V1,W1)
% 0.46/0.58 | ~ equidistant(U,V,U1,V1)
% 0.46/0.58 | ~ equidistant(U,W,U1,W1)
% 0.46/0.58 | equidistant(V,W,V1,W1) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d14,axiom,
% 0.46/0.58 ( ~ equidistant(U,V,U1,V1)
% 0.46/0.58 | ~ equidistant(V,W,V1,W1)
% 0.46/0.58 | ~ equidistant(U,X,U1,X1)
% 0.46/0.58 | ~ equidistant(W,X,W1,X1)
% 0.46/0.58 | ~ between(U,V,W)
% 0.46/0.58 | ~ between(U1,V1,W1)
% 0.46/0.58 | equidistant(V,X,V1,X1) ) ).
% 0.46/0.58
% 0.46/0.58 cnf(d15,axiom,
% 0.46/0.58 ( ~ between(U,V,W)
% 0.46/0.58 | ~ equidistant(U,V,U,X)
% 0.46/0.58 | ~ equidistant(W,V,W,X)
% 0.46/0.58 | V = X ) ).
% 0.46/0.58
% 0.46/0.59 cnf(i2_1,axiom,
% 0.46/0.59 equidistant(U,V,U1,insertion(U1,W1,U,V)) ).
% 0.46/0.59
% 0.46/0.59 cnf(i2_2,axiom,
% 0.46/0.59 ( ~ between(U,V,W)
% 0.46/0.59 | ~ equidistant(U,W,U1,W1)
% 0.46/0.59 | between(U1,insertion(U1,W1,U,V),W1) ) ).
% 0.46/0.59
% 0.46/0.59 cnf(i2_3,axiom,
% 0.46/0.59 ( ~ between(U,V,W)
% 0.46/0.59 | ~ equidistant(U,W,U1,W1)
% 0.46/0.59 | equidistant(V,W,insertion(U1,W1,U,V),W1) ) ).
% 0.46/0.59
% 0.46/0.59 cnf(i3,axiom,
% 0.46/0.59 ( ~ between(U,V,W)
% 0.46/0.59 | V = insertion(U,W,U,V) ) ).
% 0.46/0.59
% 0.46/0.59 cnf(i4,axiom,
% 0.46/0.59 ( ~ equidistant(W,X,Y,Z)
% 0.46/0.59 | insertion(U,V,W,X) = insertion(U,V,Y,Z) ) ).
% 0.46/0.59
% 0.46/0.59 cnf(b11,axiom,
% 0.46/0.59 ( ~ equidistant(U,V,U1,V1)
% 0.46/0.59 | ~ equidistant(V,W,V1,W1)
% 0.46/0.59 | ~ equidistant(U,W,U1,W1)
% 0.46/0.59 | ~ between(U,V,W)
% 0.46/0.59 | between(U1,V1,W1) ) ).
% 0.46/0.59
% 0.46/0.59 cnf(b12,axiom,
% 0.46/0.59 ( ~ between(U,V,W)
% 0.46/0.59 | ~ between(U,V,X)
% 0.46/0.59 | U = V
% 0.46/0.59 | between(U,W,X)
% 0.46/0.59 | between(U,X,W) ) ).
% 0.46/0.59
% 0.46/0.59 cnf(b13,axiom,
% 0.46/0.59 ( ~ between(U,V,W)
% 0.46/0.59 | ~ between(U,V,X)
% 0.46/0.59 | U = V
% 0.46/0.59 | between(V,W,X)
% 0.46/0.59 | between(V,X,W) ) ).
% 0.46/0.59
% 0.46/0.59 cnf(t7,axiom,
% 0.46/0.59 ( ~ between(U,W,X)
% 0.46/0.59 | ~ between(V,W,X)
% 0.46/0.59 | W = X
% 0.46/0.59 | between(U,V,W)
% 0.46/0.59 | between(V,U,W) ) ).
% 0.46/0.59
% 0.46/0.59 cnf(t9,axiom,
% 0.46/0.59 ( ~ between(U,V,X)
% 0.46/0.59 | ~ between(U,W,X)
% 0.46/0.59 | between(U,V,W)
% 0.46/0.59 | between(U,W,V) ) ).
% 0.46/0.59
% 0.46/0.59 cnf(b14,axiom,
% 0.46/0.59 ( ~ between(U,V,X)
% 0.46/0.59 | ~ between(U,W,X)
% 0.46/0.59 | between(V,W,X)
% 0.46/0.59 | between(W,V,X) ) ).
% 0.46/0.59
% 0.46/0.59 cnf(t8,axiom,
% 0.46/0.59 ( ~ between(U,V,Y)
% 0.46/0.59 | ~ between(V,W,X)
% 0.46/0.59 | ~ between(U,X,Y)
% 0.46/0.59 | between(U,W,Y) ) ).
% 0.46/0.59
% 0.46/0.59 cnf(b15,axiom,
% 0.46/0.59 ( ~ between(U,V,W)
% 0.46/0.59 | ~ equidistant(U,V,U,W)
% 0.46/0.59 | V = W ) ).
% 0.46/0.59
% 0.46/0.59 cnf(w_between_u_and_v,hypothesis,
% 0.46/0.59 between(u,w,v) ).
% 0.46/0.59
% 0.46/0.59 cnf(prove_uvw_colinear,negated_conjecture,
% 0.46/0.59 ~ colinear(u,v,w) ).
% 0.46/0.59
% 0.46/0.59 %--------------------------------------------------------------------------
% 0.46/0.59 %-------------------------------------------
% 0.46/0.59 % Proof found
% 0.46/0.59 % SZS status Theorem for theBenchmark
% 0.46/0.59 % SZS output start Proof
% 0.46/0.59 %ClaNum:124(EqnAxiom:38)
% 0.46/0.59 %VarNum:822(SingletonVarNum:294)
% 0.46/0.59 %MaxLitNum:8
% 0.46/0.59 %MaxfuncDepth:2
% 0.46/0.59 %SharedTerms:14
% 0.46/0.59 %goalClause: 62
% 0.46/0.59 %singleGoalClaCount:1
% 0.46/0.59 [39]P1(a1,a10,a11)
% 0.46/0.59 [56]~E(a8,a6)
% 0.46/0.59 [57]~E(a9,a6)
% 0.46/0.59 [58]~E(a9,a8)
% 0.46/0.59 [59]~P1(a6,a8,a9)
% 0.46/0.59 [60]~P1(a8,a9,a6)
% 0.46/0.59 [61]~P1(a9,a6,a8)
% 0.46/0.59 [62]~P3(a1,a11,a10)
% 0.46/0.59 [40]P1(x401,x402,x402)
% 0.46/0.59 [41]P1(x411,x411,x412)
% 0.46/0.59 [42]P2(x421,x422,x422,x421)
% 0.46/0.59 [43]P2(x431,x432,x431,x432)
% 0.46/0.59 [44]P2(x441,x441,x442,x442)
% 0.46/0.59 [63]~E(f2(x631,x632,a6,a8),x632)
% 0.46/0.59 [53]E(f2(f2(x531,x532,x531,x532),x532,f2(x531,x532,x531,x532),x532),x531)
% 0.46/0.59 [55]P2(x551,x552,x551,f2(f2(x552,x551,x552,x551),x551,f2(x552,x551,x552,x551),x551))
% 0.46/0.59 [45]E(f2(x451,x452,x453,x453),x452)
% 0.46/0.59 [48]P1(x481,x482,f2(x481,x482,x483,x484))
% 0.46/0.59 [50]P2(x501,f2(x502,x501,x503,x504),x503,x504)
% 0.46/0.59 [52]P2(x521,f2(x522,x521,a6,a8),x523,f2(x524,x523,a6,a8))
% 0.46/0.59 [54]P2(x541,x542,x543,f2(f2(x544,x543,a6,a8),x543,x541,x542))
% 0.46/0.59 [64]~P1(x641,x642,x641)+E(x641,x642)
% 0.46/0.59 [80]~E(x801,x802)+E(f2(x801,x802,x801,x802),x802)
% 0.46/0.59 [89]E(x891,x892)+~E(f2(x892,x891,x892,x891),x891)
% 0.46/0.59 [92]E(x921,x922)+E(f2(x921,x922,x921,x922),f2(x921,x922,x922,x921))
% 0.46/0.59 [65]~P1(x653,x652,x651)+P1(x651,x652,x653)
% 0.46/0.59 [66]~P1(x662,x663,x661)+P3(x661,x662,x663)
% 0.46/0.59 [67]~P1(x673,x671,x672)+P3(x671,x672,x673)
% 0.46/0.59 [68]~P1(x681,x682,x683)+P3(x681,x682,x683)
% 0.46/0.59 [88]~P2(x881,x882,x883,x883)+E(x881,x882)
% 0.46/0.59 [101]~P1(x1012,x1013,x1011)+E(f2(f2(x1011,x1012,a6,a8),x1012,x1012,x1013),x1013)
% 0.46/0.59 [94]~P2(x944,x943,x942,x941)+P2(x941,x942,x943,x944)
% 0.46/0.59 [95]~P2(x953,x954,x952,x951)+P2(x951,x952,x953,x954)
% 0.46/0.59 [96]~P2(x964,x963,x961,x962)+P2(x961,x962,x963,x964)
% 0.46/0.59 [97]~P2(x973,x974,x971,x972)+P2(x971,x972,x973,x974)
% 0.46/0.59 [98]~P2(x982,x981,x984,x983)+P2(x981,x982,x983,x984)
% 0.46/0.59 [99]~P2(x992,x991,x993,x994)+P2(x991,x992,x993,x994)
% 0.46/0.59 [100]~P2(x1001,x1002,x1004,x1003)+P2(x1001,x1002,x1003,x1004)
% 0.46/0.59 [90]P1(x901,x902,x903)+~E(x903,f2(x901,x902,x904,x905))
% 0.46/0.59 [111]~P2(x1113,x1114,x1115,x1116)+E(f2(f2(x1111,x1112,a6,a8),x1112,x1113,x1114),f2(f2(x1111,x1112,a6,a8),x1112,x1115,x1116))
% 0.46/0.59 [70]~P1(x703,x701,x702)+E(x701,x702)+~P1(x703,x702,x701)
% 0.46/0.59 [71]~P1(x711,x712,x713)+E(x711,x712)+~P1(x712,x711,x713)
% 0.46/0.59 [91]~P2(x913,x911,x913,x912)+E(x911,x912)+~P1(x913,x911,x912)
% 0.46/0.59 [87]~P1(x871,x872,x873)+E(x871,x872)+E(f2(x871,x872,x872,x873),x873)
% 0.46/0.59 [69]~P1(x694,x692,x693)+P1(x691,x692,x693)+~E(x694,x693)
% 0.46/0.59 [74]~P1(x744,x741,x742)+P1(x741,x742,x743)+~P1(x744,x742,x743)
% 0.46/0.59 [75]~P1(x751,x754,x753)+P1(x751,x752,x753)+~P1(x754,x752,x753)
% 0.46/0.59 [76]~P1(x761,x762,x764)+P1(x761,x762,x763)+~P1(x761,x764,x763)
% 0.46/0.59 [117]~P1(x1175,x1171,x1174)+~P1(x1172,x1173,x1174)+P1(x1171,f7(x1172,x1173,x1174,x1171,x1175),x1172)
% 0.46/0.59 [118]~P1(x1185,x1184,x1183)+~P1(x1182,x1181,x1183)+P1(x1181,f7(x1182,x1181,x1183,x1184,x1185),x1185)
% 0.46/0.59 [115]~P2(x1153,x1155,x1151,x1152)+~P1(x1153,x1154,x1155)+P1(x1151,f2(f2(x1152,x1151,a6,a8),x1151,x1153,x1154),x1152)
% 0.46/0.59 [116]~P1(x1165,x1161,x1162)+~P2(x1165,x1162,x1164,x1163)+P2(x1161,x1162,f2(f2(x1163,x1164,a6,a8),x1164,x1165,x1161),x1163)
% 0.46/0.59 [105]~P2(x1055,x1056,x1051,x1052)+P2(x1051,x1052,x1053,x1054)+~P2(x1055,x1056,x1053,x1054)
% 0.46/0.59 [106]~P2(x1061,x1062,x1065,x1066)+P2(x1061,x1062,x1063,x1064)+~P2(x1065,x1066,x1063,x1064)
% 0.46/0.59 [104]~P2(x1043,x1044,x1045,x1046)+E(x1041,x1042)+E(f2(x1041,x1042,x1043,x1044),f2(x1041,x1042,x1045,x1046))
% 0.46/0.59 [79]P1(x793,x791,x792)+P1(x792,x793,x791)+~P3(x792,x793,x791)+P1(x791,x792,x793)
% 0.46/0.59 [77]~P1(x771,x772,x774)+~P1(x773,x771,x772)+E(x771,x772)+P1(x773,x772,x774)
% 0.46/0.59 [78]~P1(x781,x782,x784)+~P1(x783,x781,x782)+E(x781,x782)+P1(x783,x781,x784)
% 0.46/0.59 [81]P1(x812,x811,x813)+~P1(x814,x812,x813)+P1(x811,x812,x813)+~P1(x814,x811,x813)
% 0.46/0.59 [82]P1(x821,x823,x822)+~P1(x821,x823,x824)+P1(x821,x822,x823)+~P1(x821,x822,x824)
% 0.46/0.59 [102]~P2(x1024,x1021,x1024,x1022)+~P2(x1023,x1021,x1023,x1022)+E(x1021,x1022)+~P1(x1023,x1021,x1024)
% 0.46/0.59 [86]~P1(x861,x865,x863)+~P1(x861,x864,x863)+P1(x861,x862,x863)+~P1(x864,x862,x865)
% 0.46/0.59 [119]~P1(x1194,x1192,x1193)+~P1(x1191,x1192,x1195)+E(x1191,x1192)+P1(x1191,x1193,f3(x1191,x1194,x1192,x1193,x1195))
% 0.46/0.59 [120]~P1(x1203,x1202,x1204)+~P1(x1201,x1202,x1205)+E(x1201,x1202)+P1(x1201,x1203,f4(x1201,x1203,x1202,x1204,x1205))
% 0.46/0.59 [121]~P1(x1213,x1212,x1214)+~P1(x1211,x1212,x1215)+E(x1211,x1212)+P1(f4(x1211,x1213,x1212,x1214,x1215),x1215,f3(x1211,x1213,x1212,x1214,x1215))
% 0.46/0.59 [83]P1(x834,x833,x831)+~P1(x833,x831,x832)+~P1(x834,x831,x832)+E(x831,x832)+P1(x833,x834,x831)
% 0.46/0.59 [84]P1(x842,x844,x843)+~P1(x841,x842,x843)+~P1(x841,x842,x844)+E(x841,x842)+P1(x842,x843,x844)
% 0.46/0.59 [85]P1(x851,x854,x853)+~P1(x851,x852,x853)+~P1(x851,x852,x854)+E(x851,x852)+P1(x851,x853,x854)
% 0.46/0.59 [93]~P1(x933,x934,x932)+~P1(x933,x934,x931)+~P2(x934,x931,x934,x932)+E(x931,x932)+E(x933,x934)
% 0.46/0.59 [103]~P1(x1033,x1034,x1031)+~P2(x1034,x1031,x1034,x1032)+~P2(x1033,x1031,x1033,x1032)+E(x1031,x1032)+E(x1033,x1034)
% 0.46/0.59 [107]~P2(x1076,x1072,x1075,x1074)+~P2(x1076,x1071,x1075,x1073)+P2(x1071,x1072,x1073,x1074)+~P1(x1075,x1073,x1074)+~P1(x1076,x1071,x1072)
% 0.46/0.59 [108]~P2(x1086,x1082,x1085,x1084)+~P2(x1081,x1086,x1083,x1085)+P2(x1081,x1082,x1083,x1084)+~P1(x1083,x1085,x1084)+~P1(x1081,x1086,x1082)
% 0.46/0.59 [109]~P2(x1095,x1096,x1092,x1093)+~P2(x1094,x1096,x1091,x1093)+~P2(x1094,x1095,x1091,x1092)+P1(x1091,x1092,x1093)+~P1(x1094,x1095,x1096)
% 0.46/0.59 [122]~P1(x1223,x1224,x1225)+~P1(x1222,x1223,x1225)+~P2(x1222,x1225,x1222,x1226)+~P2(x1222,x1223,x1222,x1221)+P1(x1221,f5(x1222,x1223,x1221,x1224,x1225,x1226),x1226)
% 0.46/0.59 [123]~P1(x1233,x1232,x1235)+~P1(x1231,x1233,x1235)+~P2(x1231,x1235,x1231,x1236)+~P2(x1231,x1233,x1231,x1234)+P2(x1231,x1232,x1231,f5(x1231,x1233,x1234,x1232,x1235,x1236))
% 0.46/0.59 [124]~P1(x1244,x1242,x1245)+~P1(x1243,x1241,x1244)+~P1(x1243,x1246,x1245)+P1(x1241,f7(x1242,f7(x1243,x1241,x1244,x1242,x1245),x1243,x1246,x1245),x1245)+P1(x1246,f7(x1242,f7(x1243,x1241,x1244,x1242,x1245),x1243,x1246,x1245),x1242)
% 0.46/0.59 [110]P1(x1105,x1103,x1104)+P1(x1104,x1105,x1103)+~P2(x1103,x1101,x1103,x1102)+~P2(x1105,x1101,x1105,x1102)+~P2(x1104,x1101,x1104,x1102)+E(x1101,x1102)+P1(x1103,x1104,x1105)
% 0.46/0.59 [112]~P2(x1128,x1122,x1126,x1124)+~P2(x1121,x1128,x1123,x1126)+~P2(x1127,x1122,x1125,x1124)+~P2(x1127,x1121,x1125,x1123)+P2(x1121,x1122,x1123,x1124)+~P1(x1125,x1123,x1126)+~P1(x1127,x1121,x1128)
% 0.46/0.59 [113]~P2(x1138,x1132,x1136,x1134)+~P2(x1137,x1132,x1135,x1134)+~P2(x1137,x1138,x1135,x1136)+~P2(x1137,x1131,x1135,x1133)+P2(x1131,x1132,x1133,x1134)+~P1(x1135,x1133,x1136)+~P1(x1137,x1131,x1138)
% 0.46/0.59 [114]~P1(x1141,x1142,x1143)+~P2(x1142,x1144,x1148,x1146)+~P2(x1142,x1143,x1148,x1145)+~P2(x1141,x1144,x1147,x1146)+~P2(x1141,x1142,x1147,x1148)+E(x1141,x1142)+P2(x1143,x1144,x1145,x1146)+~P1(x1147,x1148,x1145)
% 0.46/0.59 %EqnAxiom
% 0.46/0.59 [1]E(x11,x11)
% 0.46/0.59 [2]E(x22,x21)+~E(x21,x22)
% 0.46/0.59 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.46/0.59 [4]~E(x41,x42)+E(f2(x41,x43,x44,x45),f2(x42,x43,x44,x45))
% 0.46/0.59 [5]~E(x51,x52)+E(f2(x53,x51,x54,x55),f2(x53,x52,x54,x55))
% 0.46/0.59 [6]~E(x61,x62)+E(f2(x63,x64,x61,x65),f2(x63,x64,x62,x65))
% 0.46/0.59 [7]~E(x71,x72)+E(f2(x73,x74,x75,x71),f2(x73,x74,x75,x72))
% 0.46/0.59 [8]~E(x81,x82)+E(f7(x81,x83,x84,x85,x86),f7(x82,x83,x84,x85,x86))
% 0.46/0.59 [9]~E(x91,x92)+E(f7(x93,x91,x94,x95,x96),f7(x93,x92,x94,x95,x96))
% 0.46/0.59 [10]~E(x101,x102)+E(f7(x103,x104,x101,x105,x106),f7(x103,x104,x102,x105,x106))
% 0.46/0.59 [11]~E(x111,x112)+E(f7(x113,x114,x115,x111,x116),f7(x113,x114,x115,x112,x116))
% 0.46/0.59 [12]~E(x121,x122)+E(f7(x123,x124,x125,x126,x121),f7(x123,x124,x125,x126,x122))
% 0.46/0.59 [13]~E(x131,x132)+E(f3(x131,x133,x134,x135,x136),f3(x132,x133,x134,x135,x136))
% 0.46/0.59 [14]~E(x141,x142)+E(f3(x143,x141,x144,x145,x146),f3(x143,x142,x144,x145,x146))
% 0.46/0.59 [15]~E(x151,x152)+E(f3(x153,x154,x151,x155,x156),f3(x153,x154,x152,x155,x156))
% 0.46/0.59 [16]~E(x161,x162)+E(f3(x163,x164,x165,x161,x166),f3(x163,x164,x165,x162,x166))
% 0.46/0.59 [17]~E(x171,x172)+E(f3(x173,x174,x175,x176,x171),f3(x173,x174,x175,x176,x172))
% 0.46/0.59 [18]~E(x181,x182)+E(f4(x181,x183,x184,x185,x186),f4(x182,x183,x184,x185,x186))
% 0.46/0.59 [19]~E(x191,x192)+E(f4(x193,x191,x194,x195,x196),f4(x193,x192,x194,x195,x196))
% 0.46/0.59 [20]~E(x201,x202)+E(f4(x203,x204,x201,x205,x206),f4(x203,x204,x202,x205,x206))
% 0.46/0.59 [21]~E(x211,x212)+E(f4(x213,x214,x215,x211,x216),f4(x213,x214,x215,x212,x216))
% 0.46/0.59 [22]~E(x221,x222)+E(f4(x223,x224,x225,x226,x221),f4(x223,x224,x225,x226,x222))
% 0.46/0.59 [23]~E(x231,x232)+E(f5(x231,x233,x234,x235,x236,x237),f5(x232,x233,x234,x235,x236,x237))
% 0.46/0.59 [24]~E(x241,x242)+E(f5(x243,x241,x244,x245,x246,x247),f5(x243,x242,x244,x245,x246,x247))
% 0.46/0.59 [25]~E(x251,x252)+E(f5(x253,x254,x251,x255,x256,x257),f5(x253,x254,x252,x255,x256,x257))
% 0.46/0.59 [26]~E(x261,x262)+E(f5(x263,x264,x265,x261,x266,x267),f5(x263,x264,x265,x262,x266,x267))
% 0.46/0.59 [27]~E(x271,x272)+E(f5(x273,x274,x275,x276,x271,x277),f5(x273,x274,x275,x276,x272,x277))
% 0.46/0.59 [28]~E(x281,x282)+E(f5(x283,x284,x285,x286,x287,x281),f5(x283,x284,x285,x286,x287,x282))
% 0.46/0.59 [29]P1(x292,x293,x294)+~E(x291,x292)+~P1(x291,x293,x294)
% 0.46/0.59 [30]P1(x303,x302,x304)+~E(x301,x302)+~P1(x303,x301,x304)
% 0.46/0.59 [31]P1(x313,x314,x312)+~E(x311,x312)+~P1(x313,x314,x311)
% 0.46/0.59 [32]P2(x322,x323,x324,x325)+~E(x321,x322)+~P2(x321,x323,x324,x325)
% 0.46/0.59 [33]P2(x333,x332,x334,x335)+~E(x331,x332)+~P2(x333,x331,x334,x335)
% 0.46/0.59 [34]P2(x343,x344,x342,x345)+~E(x341,x342)+~P2(x343,x344,x341,x345)
% 0.46/0.59 [35]P2(x353,x354,x355,x352)+~E(x351,x352)+~P2(x353,x354,x355,x351)
% 0.46/0.59 [36]P3(x362,x363,x364)+~E(x361,x362)+~P3(x361,x363,x364)
% 0.46/0.59 [37]P3(x373,x372,x374)+~E(x371,x372)+~P3(x373,x371,x374)
% 0.46/0.59 [38]P3(x383,x384,x382)+~E(x381,x382)+~P3(x383,x384,x381)
% 0.46/0.59
% 0.46/0.59 %-------------------------------------------
% 0.46/0.60 cnf(128,plain,
% 0.46/0.60 (~P1(a11,a10,a1)),
% 0.46/0.60 inference(scs_inference,[],[62,66])).
% 0.46/0.60 cnf(137,plain,
% 0.46/0.60 (E(f2(x1371,x1372,x1373,x1373),x1372)),
% 0.46/0.60 inference(rename_variables,[],[45])).
% 0.46/0.60 cnf(142,plain,
% 0.46/0.60 (~E(f2(x1421,x1422,a6,a8),x1422)),
% 0.46/0.60 inference(rename_variables,[],[63])).
% 0.46/0.60 cnf(157,plain,
% 0.46/0.60 (P1(x1571,x1572,f2(x1571,x1572,x1573,x1574))),
% 0.46/0.60 inference(rename_variables,[],[48])).
% 0.46/0.60 cnf(164,plain,
% 0.46/0.60 (P1(x1641,x1641,x1642)),
% 0.46/0.60 inference(rename_variables,[],[41])).
% 0.46/0.60 cnf(167,plain,
% 0.46/0.60 (P1(x1671,x1672,x1672)),
% 0.46/0.60 inference(rename_variables,[],[40])).
% 0.46/0.60 cnf(174,plain,
% 0.46/0.60 (P2(x1741,x1742,x1742,x1741)),
% 0.46/0.60 inference(rename_variables,[],[42])).
% 0.46/0.60 cnf(180,plain,
% 0.46/0.60 (~P2(a6,a8,x1801,x1801)),
% 0.46/0.60 inference(scs_inference,[],[62,39,40,167,41,164,48,157,42,174,50,52,45,137,63,142,56,59,53,66,67,68,65,90,64,80,88,89,94,95,96,2,74,76,70,71,91,105,106,116])).
% 0.46/0.60 cnf(235,plain,
% 0.46/0.60 ($false),
% 0.46/0.60 inference(scs_inference,[],[128,39,180,99,65]),
% 0.46/0.60 ['proof']).
% 0.46/0.60 % SZS output end Proof
% 0.46/0.60 % Total time :0.070000s
%------------------------------------------------------------------------------