TSTP Solution File: GEO063-3 by CSE---1.6
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE---1.6
% Problem : GEO063-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% Computer : n031.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 : Wed Aug 30 22:42:44 EDT 2023
% Result : Unsatisfiable 0.51s 0.63s
% Output : CNFRefutation 0.51s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO063-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.06/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %s %d
% 0.12/0.33 % Computer : n031.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 29 23:20:11 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof:theBenchmark
% 0.51/0.61 %-------------------------------------------
% 0.51/0.61 % File :CSE---1.6
% 0.51/0.61 % Problem :theBenchmark
% 0.51/0.61 % Transform :cnf
% 0.51/0.61 % Format :tptp:raw
% 0.51/0.61 % Command :java -jar mcs_scs.jar %d %s
% 0.51/0.61
% 0.51/0.61 % Result :Theorem 0.020000s
% 0.51/0.61 % Output :CNFRefutation 0.020000s
% 0.51/0.61 %-------------------------------------------
% 0.51/0.62 %--------------------------------------------------------------------------
% 0.51/0.62 % File : GEO063-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.51/0.62 % Domain : Geometry
% 0.51/0.62 % Problem : Insertion respects congruence in its last two arguments
% 0.51/0.62 % Version : [Qua89] axioms : Augmented.
% 0.51/0.62 % English :
% 0.51/0.62
% 0.51/0.62 % Refs : [SST83] Schwabbauser et al. (1983), Metamathematische Methoden
% 0.51/0.62 % : [Qua89] Quaife (1989), Automated Development of Tarski's Geome
% 0.51/0.62 % Source : [Qua89]
% 0.51/0.62 % Names : I4 [Qua89]
% 0.51/0.62
% 0.51/0.62 % Status : Unsatisfiable
% 0.51/0.62 % Rating : 0.19 v8.1.0, 0.16 v7.5.0, 0.26 v7.4.0, 0.18 v7.3.0, 0.25 v7.1.0, 0.17 v7.0.0, 0.40 v6.3.0, 0.27 v6.2.0, 0.50 v5.5.0, 0.80 v5.3.0, 0.83 v5.2.0, 0.75 v5.1.0, 0.71 v5.0.0, 0.64 v4.1.0, 0.62 v4.0.1, 0.55 v4.0.0, 0.45 v3.7.0, 0.30 v3.5.0, 0.36 v3.4.0, 0.42 v3.3.0, 0.43 v3.2.0, 0.46 v3.1.0, 0.45 v2.7.0, 0.50 v2.6.0, 0.44 v2.5.0, 0.73 v2.4.0, 0.38 v2.3.0, 0.50 v2.2.1, 0.71 v2.2.0, 0.60 v2.1.0, 1.00 v2.0.0
% 0.51/0.62 % Syntax : Number of clauses : 76 ( 27 unt; 15 nHn; 55 RR)
% 0.51/0.62 % Number of literals : 198 ( 43 equ; 113 neg)
% 0.51/0.62 % Maximal clause size : 8 ( 2 avg)
% 0.51/0.62 % Maximal term depth : 3 ( 1 avg)
% 0.51/0.62 % Number of predicates : 3 ( 2 usr; 0 prp; 2-4 aty)
% 0.51/0.62 % Number of functors : 16 ( 16 usr; 9 con; 0-6 aty)
% 0.51/0.62 % Number of variables : 265 ( 14 sgn)
% 0.51/0.62 % SPC : CNF_UNS_RFO_SEQ_NHN
% 0.51/0.62
% 0.51/0.62 % Comments :
% 0.51/0.62 % Bugfixes : v1.2.1 - Clause d12 fixed.
% 0.51/0.62 %--------------------------------------------------------------------------
% 0.51/0.62 %----Include Tarski geometry axioms
% 0.51/0.62 include('Axioms/GEO002-0.ax').
% 0.51/0.62 %----Include definition of reflection
% 0.51/0.62 include('Axioms/GEO002-2.ax').
% 0.51/0.62 %----Include definition of insertion
% 0.51/0.62 include('Axioms/GEO002-3.ax').
% 0.51/0.62 %--------------------------------------------------------------------------
% 0.51/0.62 cnf(d1,axiom,
% 0.51/0.62 equidistant(U,V,U,V) ).
% 0.51/0.62
% 0.51/0.62 cnf(d2,axiom,
% 0.51/0.62 ( ~ equidistant(U,V,W,X)
% 0.51/0.62 | equidistant(W,X,U,V) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d3,axiom,
% 0.51/0.62 ( ~ equidistant(U,V,W,X)
% 0.51/0.62 | equidistant(V,U,W,X) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d4_1,axiom,
% 0.51/0.62 ( ~ equidistant(U,V,W,X)
% 0.51/0.62 | equidistant(U,V,X,W) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d4_2,axiom,
% 0.51/0.62 ( ~ equidistant(U,V,W,X)
% 0.51/0.62 | equidistant(V,U,X,W) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d4_3,axiom,
% 0.51/0.62 ( ~ equidistant(U,V,W,X)
% 0.51/0.62 | equidistant(W,X,V,U) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d4_4,axiom,
% 0.51/0.62 ( ~ equidistant(U,V,W,X)
% 0.51/0.62 | equidistant(X,W,U,V) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d4_5,axiom,
% 0.51/0.62 ( ~ equidistant(U,V,W,X)
% 0.51/0.62 | equidistant(X,W,V,U) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d5,axiom,
% 0.51/0.62 ( ~ equidistant(U,V,W,X)
% 0.51/0.62 | ~ equidistant(W,X,Y,Z)
% 0.51/0.62 | equidistant(U,V,Y,Z) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(e1,axiom,
% 0.51/0.62 V = extension(U,V,W,W) ).
% 0.51/0.62
% 0.51/0.62 cnf(b0,axiom,
% 0.51/0.62 ( Y != extension(U,V,W,X)
% 0.51/0.62 | between(U,V,Y) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(r2_1,axiom,
% 0.51/0.62 between(U,V,reflection(U,V)) ).
% 0.51/0.62
% 0.51/0.62 cnf(r2_2,axiom,
% 0.51/0.62 equidistant(V,reflection(U,V),U,V) ).
% 0.51/0.62
% 0.51/0.62 cnf(r3_1,axiom,
% 0.51/0.62 ( U != V
% 0.51/0.62 | V = reflection(U,V) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(r3_2,axiom,
% 0.51/0.62 U = reflection(U,U) ).
% 0.51/0.62
% 0.51/0.62 cnf(r4,axiom,
% 0.51/0.62 ( V != reflection(U,V)
% 0.51/0.62 | U = V ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d7,axiom,
% 0.51/0.62 equidistant(U,U,V,V) ).
% 0.51/0.62
% 0.51/0.62 cnf(d8,axiom,
% 0.51/0.62 ( ~ equidistant(U,V,U1,V1)
% 0.51/0.62 | ~ equidistant(V,W,V1,W1)
% 0.51/0.62 | ~ between(U,V,W)
% 0.51/0.62 | ~ between(U1,V1,W1)
% 0.51/0.62 | equidistant(U,W,U1,W1) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d9,axiom,
% 0.51/0.62 ( ~ between(U,V,W)
% 0.51/0.62 | ~ between(U,V,X)
% 0.51/0.62 | ~ equidistant(V,W,V,X)
% 0.51/0.62 | U = V
% 0.51/0.62 | W = X ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d10_1,axiom,
% 0.51/0.62 ( ~ between(U,V,W)
% 0.51/0.62 | U = V
% 0.51/0.62 | W = extension(U,V,V,W) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d10_2,axiom,
% 0.51/0.62 ( ~ equidistant(W,X,Y,Z)
% 0.51/0.62 | extension(U,V,W,X) = extension(U,V,Y,Z)
% 0.51/0.62 | U = V ) ).
% 0.51/0.62
% 0.51/0.62 cnf(d10_3,axiom,
% 0.51/0.62 ( extension(U,V,U,V) = extension(U,V,V,U)
% 0.51/0.62 | U = V ) ).
% 0.51/0.62
% 0.51/0.62 cnf(r5,axiom,
% 0.51/0.62 equidistant(V,U,V,reflection(reflection(U,V),V)) ).
% 0.51/0.62
% 0.51/0.62 cnf(r6,axiom,
% 0.51/0.62 U = reflection(reflection(U,V),V) ).
% 0.51/0.62
% 0.51/0.62 cnf(t3,axiom,
% 0.51/0.62 between(U,V,V) ).
% 0.51/0.62
% 0.51/0.62 cnf(b1,axiom,
% 0.51/0.62 ( ~ between(U,W,X)
% 0.51/0.62 | U != X
% 0.51/0.62 | between(V,W,X) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(t1,axiom,
% 0.51/0.62 ( ~ between(U,V,W)
% 0.51/0.62 | between(W,V,U) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(t2,axiom,
% 0.51/0.62 between(U,U,V) ).
% 0.51/0.62
% 0.51/0.62 cnf(b2,axiom,
% 0.51/0.62 ( ~ between(U,V,W)
% 0.51/0.62 | ~ between(V,U,W)
% 0.51/0.62 | U = V ) ).
% 0.51/0.62
% 0.51/0.62 cnf(b3,axiom,
% 0.51/0.62 ( ~ between(U,V,W)
% 0.51/0.62 | ~ between(U,W,V)
% 0.51/0.62 | V = W ) ).
% 0.51/0.62
% 0.51/0.62 cnf(t6_1,axiom,
% 0.51/0.62 ( ~ between(U,V,W)
% 0.51/0.62 | ~ between(V,U,W)
% 0.51/0.62 | U = V
% 0.51/0.62 | V = W ) ).
% 0.51/0.62
% 0.51/0.62 cnf(t6_2,axiom,
% 0.51/0.62 ( ~ between(U,V,W)
% 0.51/0.62 | ~ between(U,W,V)
% 0.51/0.62 | U = V
% 0.51/0.62 | V = W ) ).
% 0.51/0.62
% 0.51/0.62 cnf(b4,axiom,
% 0.51/0.62 ( ~ between(U,V,W)
% 0.51/0.62 | ~ between(V,W,X)
% 0.51/0.62 | between(U,V,W) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(b5,axiom,
% 0.51/0.62 ( ~ between(U,V,W)
% 0.51/0.62 | ~ between(U,W,X)
% 0.51/0.62 | between(V,W,X) ) ).
% 0.51/0.62
% 0.51/0.62 cnf(b6,axiom,
% 0.51/0.62 ( ~ between(U,V,W)
% 0.51/0.62 | ~ between(V,W,X)
% 0.51/0.62 | between(U,W,X)
% 0.51/0.62 | V = W ) ).
% 0.51/0.62
% 0.51/0.62 cnf(b7,axiom,
% 0.51/0.62 ( ~ between(U,V,W)
% 0.51/0.62 | ~ between(V,W,X)
% 0.51/0.62 | between(U,V,X)
% 0.51/0.62 | V = W ) ).
% 0.51/0.62
% 0.51/0.62 cnf(b8,axiom,
% 0.51/0.63 ( ~ between(U,V,X)
% 0.51/0.63 | ~ between(V,W,X)
% 0.51/0.63 | between(U,W,X) ) ).
% 0.51/0.63
% 0.51/0.63 cnf(b9,axiom,
% 0.51/0.63 ( ~ between(U,V,W)
% 0.51/0.63 | ~ between(U,W,X)
% 0.51/0.63 | between(U,V,X) ) ).
% 0.51/0.63
% 0.51/0.63 cnf(e2_1,axiom,
% 0.51/0.63 lower_dimension_point_1 != lower_dimension_point_2 ).
% 0.51/0.63
% 0.51/0.63 cnf(e2_2,axiom,
% 0.51/0.63 lower_dimension_point_2 != lower_dimension_point_3 ).
% 0.51/0.63
% 0.51/0.63 cnf(e2_3,axiom,
% 0.51/0.63 lower_dimension_point_1 != lower_dimension_point_3 ).
% 0.51/0.63
% 0.51/0.63 cnf(e3_1,axiom,
% 0.51/0.63 V != extension(U,V,lower_dimension_point_1,lower_dimension_point_2) ).
% 0.51/0.63
% 0.51/0.63 cnf(e3_2,axiom,
% 0.51/0.63 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)) ).
% 0.51/0.63
% 0.51/0.63 cnf(e3_3,axiom,
% 0.51/0.63 between(U,V,extension(U,V,lower_dimension_point_1,lower_dimension_point_2)) ).
% 0.51/0.63
% 0.51/0.63 cnf(b10,axiom,
% 0.51/0.63 ( ~ between(U,V,W)
% 0.51/0.63 | ~ between(U1,V1,W)
% 0.51/0.63 | ~ between(U,X,U1)
% 0.51/0.63 | between(X,inner_pasch(V1,inner_pasch(U,X,U1,V1,W),U,V,W),W)
% 0.51/0.63 | between(V,inner_pasch(V1,inner_pasch(U,X,U1,V1,W),U,V,W),V1) ) ).
% 0.51/0.63
% 0.51/0.63 cnf(d11,axiom,
% 0.51/0.63 ( ~ between(U,V,W)
% 0.51/0.63 | ~ equidistant(U,W,U,W1)
% 0.51/0.63 | ~ equidistant(V,W,V,W1)
% 0.51/0.63 | U = V
% 0.51/0.63 | W = W1 ) ).
% 0.51/0.63
% 0.51/0.63 cnf(d12,axiom,
% 0.51/0.63 ( ~ equidistant(U,V,U1,V1)
% 0.51/0.63 | ~ equidistant(U,W,U1,W1)
% 0.51/0.63 | ~ equidistant(U,X,U1,X1)
% 0.51/0.63 | ~ equidistant(W,X,W1,X1)
% 0.51/0.63 | ~ between(U,V,W)
% 0.51/0.63 | ~ between(U1,V1,W1)
% 0.51/0.63 | equidistant(V,X,V1,X1) ) ).
% 0.51/0.63
% 0.51/0.63 cnf(d13,axiom,
% 0.51/0.63 ( ~ between(U,V,W)
% 0.51/0.63 | ~ between(U1,V1,W1)
% 0.51/0.63 | ~ equidistant(U,V,U1,V1)
% 0.51/0.63 | ~ equidistant(U,W,U1,W1)
% 0.51/0.63 | equidistant(V,W,V1,W1) ) ).
% 0.51/0.63
% 0.51/0.63 cnf(d14,axiom,
% 0.51/0.63 ( ~ equidistant(U,V,U1,V1)
% 0.51/0.63 | ~ equidistant(V,W,V1,W1)
% 0.51/0.63 | ~ equidistant(U,X,U1,X1)
% 0.51/0.63 | ~ equidistant(W,X,W1,X1)
% 0.51/0.63 | ~ between(U,V,W)
% 0.51/0.63 | ~ between(U1,V1,W1)
% 0.51/0.63 | equidistant(V,X,V1,X1) ) ).
% 0.51/0.63
% 0.51/0.63 cnf(d15,axiom,
% 0.51/0.63 ( ~ between(U,V,W)
% 0.51/0.63 | ~ equidistant(U,V,U,X)
% 0.51/0.63 | ~ equidistant(W,V,W,X)
% 0.51/0.63 | V = X ) ).
% 0.51/0.63
% 0.51/0.63 cnf(i2_1,axiom,
% 0.51/0.63 equidistant(U,V,U1,insertion(U1,W1,U,V)) ).
% 0.51/0.63
% 0.51/0.63 cnf(i2_2,axiom,
% 0.51/0.63 ( ~ between(U,V,W)
% 0.51/0.63 | ~ equidistant(U,W,U1,W1)
% 0.51/0.63 | between(U1,insertion(U1,W1,U,V),W1) ) ).
% 0.51/0.63
% 0.51/0.63 cnf(i2_3,axiom,
% 0.51/0.63 ( ~ between(U,V,W)
% 0.51/0.63 | ~ equidistant(U,W,U1,W1)
% 0.51/0.63 | equidistant(V,W,insertion(U1,W1,U,V),W1) ) ).
% 0.51/0.63
% 0.51/0.63 cnf(i3,axiom,
% 0.51/0.63 ( ~ between(U,V,W)
% 0.51/0.63 | V = insertion(U,W,U,V) ) ).
% 0.51/0.63
% 0.51/0.63 cnf(w_to_x_equals_y_to_z,hypothesis,
% 0.51/0.63 equidistant(w,x,y,z) ).
% 0.51/0.63
% 0.51/0.63 cnf(prove_equality_of_insertions,negated_conjecture,
% 0.51/0.63 insertion(u,v,w,x) != insertion(u,v,y,z) ).
% 0.51/0.63
% 0.51/0.63 %--------------------------------------------------------------------------
% 0.51/0.63 %-------------------------------------------
% 0.51/0.63 % Proof found
% 0.51/0.63 % SZS status Theorem for theBenchmark
% 0.51/0.63 % SZS output start Proof
% 0.51/0.63 %ClaNum:108(EqnAxiom:35)
% 0.51/0.63 %VarNum:673(SingletonVarNum:242)
% 0.51/0.63 %MaxLitNum:8
% 0.51/0.63 %MaxfuncDepth:2
% 0.51/0.63 %SharedTerms:20
% 0.51/0.63 %goalClause: 60
% 0.51/0.63 %singleGoalClaCount:1
% 0.51/0.63 [38]P2(a1,a12,a13,a14)
% 0.51/0.63 [53]~E(a8,a6)
% 0.51/0.63 [54]~E(a9,a6)
% 0.51/0.63 [55]~E(a9,a8)
% 0.51/0.63 [56]~P1(a6,a8,a9)
% 0.51/0.63 [57]~P1(a8,a9,a6)
% 0.51/0.63 [58]~P1(a9,a6,a8)
% 0.51/0.63 [60]~E(f2(f2(a10,a11,a6,a8),a11,a13,a14),f2(f2(a10,a11,a6,a8),a11,a1,a12))
% 0.51/0.63 [36]P1(x361,x362,x362)
% 0.51/0.63 [37]P1(x371,x371,x372)
% 0.51/0.63 [39]P2(x391,x392,x392,x391)
% 0.51/0.63 [40]P2(x401,x402,x401,x402)
% 0.51/0.63 [41]P2(x411,x411,x412,x412)
% 0.51/0.63 [59]~E(f2(x591,x592,a6,a8),x592)
% 0.51/0.63 [50]E(f2(f2(x501,x502,x501,x502),x502,f2(x501,x502,x501,x502),x502),x501)
% 0.51/0.63 [52]P2(x521,x522,x521,f2(f2(x522,x521,x522,x521),x521,f2(x522,x521,x522,x521),x521))
% 0.51/0.63 [42]E(f2(x421,x422,x423,x423),x422)
% 0.51/0.63 [45]P1(x451,x452,f2(x451,x452,x453,x454))
% 0.51/0.63 [47]P2(x471,f2(x472,x471,x473,x474),x473,x474)
% 0.51/0.63 [49]P2(x491,f2(x492,x491,a6,a8),x493,f2(x494,x493,a6,a8))
% 0.51/0.63 [51]P2(x511,x512,x513,f2(f2(x514,x513,a6,a8),x513,x511,x512))
% 0.51/0.63 [61]~P1(x611,x612,x611)+E(x611,x612)
% 0.51/0.63 [73]~E(x731,x732)+E(f2(x731,x732,x731,x732),x732)
% 0.51/0.63 [76]E(x761,x762)+~E(f2(x762,x761,x762,x761),x761)
% 0.51/0.63 [78]E(x781,x782)+E(f2(x781,x782,x781,x782),f2(x781,x782,x782,x781))
% 0.51/0.63 [62]~P1(x623,x622,x621)+P1(x621,x622,x623)
% 0.51/0.63 [75]~P2(x751,x752,x753,x753)+E(x751,x752)
% 0.51/0.63 [87]~P1(x872,x873,x871)+E(f2(f2(x871,x872,a6,a8),x872,x872,x873),x873)
% 0.51/0.63 [80]~P2(x804,x803,x802,x801)+P2(x801,x802,x803,x804)
% 0.51/0.63 [81]~P2(x813,x814,x812,x811)+P2(x811,x812,x813,x814)
% 0.51/0.63 [82]~P2(x824,x823,x821,x822)+P2(x821,x822,x823,x824)
% 0.51/0.63 [83]~P2(x833,x834,x831,x832)+P2(x831,x832,x833,x834)
% 0.51/0.63 [84]~P2(x842,x841,x844,x843)+P2(x841,x842,x843,x844)
% 0.51/0.63 [85]~P2(x852,x851,x853,x854)+P2(x851,x852,x853,x854)
% 0.51/0.63 [86]~P2(x861,x862,x864,x863)+P2(x861,x862,x863,x864)
% 0.51/0.63 [77]P1(x771,x772,x773)+~E(x773,f2(x771,x772,x774,x775))
% 0.51/0.63 [64]~P1(x643,x641,x642)+E(x641,x642)+~P1(x643,x642,x641)
% 0.51/0.63 [65]~P1(x651,x652,x653)+E(x651,x652)+~P1(x652,x651,x653)
% 0.51/0.63 [74]~P1(x741,x742,x743)+E(x741,x742)+E(f2(x741,x742,x742,x743),x743)
% 0.51/0.63 [63]~P1(x634,x632,x633)+P1(x631,x632,x633)+~E(x634,x633)
% 0.51/0.63 [68]~P1(x684,x681,x682)+P1(x681,x682,x683)+~P1(x684,x682,x683)
% 0.51/0.63 [69]~P1(x691,x694,x693)+P1(x691,x692,x693)+~P1(x694,x692,x693)
% 0.51/0.63 [70]~P1(x701,x702,x704)+P1(x701,x702,x703)+~P1(x701,x704,x703)
% 0.51/0.63 [101]~P1(x1015,x1011,x1014)+~P1(x1012,x1013,x1014)+P1(x1011,f7(x1012,x1013,x1014,x1011,x1015),x1012)
% 0.51/0.63 [102]~P1(x1025,x1024,x1023)+~P1(x1022,x1021,x1023)+P1(x1021,f7(x1022,x1021,x1023,x1024,x1025),x1025)
% 0.51/0.63 [99]~P2(x993,x995,x991,x992)+~P1(x993,x994,x995)+P1(x991,f2(f2(x992,x991,a6,a8),x991,x993,x994),x992)
% 0.51/0.63 [100]~P1(x1005,x1001,x1002)+~P2(x1005,x1002,x1004,x1003)+P2(x1001,x1002,f2(f2(x1003,x1004,a6,a8),x1004,x1005,x1001),x1003)
% 0.51/0.63 [91]~P2(x915,x916,x911,x912)+P2(x911,x912,x913,x914)+~P2(x915,x916,x913,x914)
% 0.51/0.63 [92]~P2(x921,x922,x925,x926)+P2(x921,x922,x923,x924)+~P2(x925,x926,x923,x924)
% 0.51/0.63 [90]~P2(x903,x904,x905,x906)+E(x901,x902)+E(f2(x901,x902,x903,x904),f2(x901,x902,x905,x906))
% 0.51/0.63 [71]~P1(x711,x712,x714)+~P1(x713,x711,x712)+E(x711,x712)+P1(x713,x712,x714)
% 0.51/0.63 [72]~P1(x721,x722,x724)+~P1(x723,x721,x722)+E(x721,x722)+P1(x723,x721,x724)
% 0.51/0.63 [88]~P2(x884,x881,x884,x882)+~P2(x883,x881,x883,x882)+E(x881,x882)+~P1(x883,x881,x884)
% 0.51/0.63 [103]~P1(x1034,x1032,x1033)+~P1(x1031,x1032,x1035)+E(x1031,x1032)+P1(x1031,x1033,f3(x1031,x1034,x1032,x1033,x1035))
% 0.51/0.63 [104]~P1(x1043,x1042,x1044)+~P1(x1041,x1042,x1045)+E(x1041,x1042)+P1(x1041,x1043,f4(x1041,x1043,x1042,x1044,x1045))
% 0.51/0.63 [105]~P1(x1053,x1052,x1054)+~P1(x1051,x1052,x1055)+E(x1051,x1052)+P1(f4(x1051,x1053,x1052,x1054,x1055),x1055,f3(x1051,x1053,x1052,x1054,x1055))
% 0.51/0.63 [79]~P1(x793,x794,x792)+~P1(x793,x794,x791)+~P2(x794,x791,x794,x792)+E(x791,x792)+E(x793,x794)
% 0.51/0.63 [89]~P1(x893,x894,x891)+~P2(x894,x891,x894,x892)+~P2(x893,x891,x893,x892)+E(x891,x892)+E(x893,x894)
% 0.51/0.63 [93]~P2(x936,x932,x935,x934)+~P2(x936,x931,x935,x933)+P2(x931,x932,x933,x934)+~P1(x935,x933,x934)+~P1(x936,x931,x932)
% 0.51/0.63 [94]~P2(x946,x942,x945,x944)+~P2(x941,x946,x943,x945)+P2(x941,x942,x943,x944)+~P1(x943,x945,x944)+~P1(x941,x946,x942)
% 0.51/0.63 [106]~P1(x1063,x1064,x1065)+~P1(x1062,x1063,x1065)+~P2(x1062,x1065,x1062,x1066)+~P2(x1062,x1063,x1062,x1061)+P1(x1061,f5(x1062,x1063,x1061,x1064,x1065,x1066),x1066)
% 0.51/0.63 [107]~P1(x1073,x1072,x1075)+~P1(x1071,x1073,x1075)+~P2(x1071,x1075,x1071,x1076)+~P2(x1071,x1073,x1071,x1074)+P2(x1071,x1072,x1071,f5(x1071,x1073,x1074,x1072,x1075,x1076))
% 0.51/0.63 [108]~P1(x1084,x1082,x1085)+~P1(x1083,x1081,x1084)+~P1(x1083,x1086,x1085)+P1(x1081,f7(x1082,f7(x1083,x1081,x1084,x1082,x1085),x1083,x1086,x1085),x1085)+P1(x1086,f7(x1082,f7(x1083,x1081,x1084,x1082,x1085),x1083,x1086,x1085),x1082)
% 0.51/0.63 [95]P1(x955,x953,x954)+P1(x954,x955,x953)+~P2(x953,x951,x953,x952)+~P2(x955,x951,x955,x952)+~P2(x954,x951,x954,x952)+E(x951,x952)+P1(x953,x954,x955)
% 0.51/0.63 [96]~P2(x968,x962,x966,x964)+~P2(x961,x968,x963,x966)+~P2(x967,x962,x965,x964)+~P2(x967,x961,x965,x963)+P2(x961,x962,x963,x964)+~P1(x965,x963,x966)+~P1(x967,x961,x968)
% 0.51/0.63 [97]~P2(x978,x972,x976,x974)+~P2(x977,x972,x975,x974)+~P2(x977,x978,x975,x976)+~P2(x977,x971,x975,x973)+P2(x971,x972,x973,x974)+~P1(x975,x973,x976)+~P1(x977,x971,x978)
% 0.51/0.63 [98]~P1(x981,x982,x983)+~P2(x982,x984,x988,x986)+~P2(x982,x983,x988,x985)+~P2(x981,x984,x987,x986)+~P2(x981,x982,x987,x988)+E(x981,x982)+P2(x983,x984,x985,x986)+~P1(x987,x988,x985)
% 0.51/0.63 %EqnAxiom
% 0.51/0.63 [1]E(x11,x11)
% 0.51/0.63 [2]E(x22,x21)+~E(x21,x22)
% 0.51/0.63 [3]E(x31,x33)+~E(x31,x32)+~E(x32,x33)
% 0.51/0.63 [4]~E(x41,x42)+E(f2(x41,x43,x44,x45),f2(x42,x43,x44,x45))
% 0.51/0.63 [5]~E(x51,x52)+E(f2(x53,x51,x54,x55),f2(x53,x52,x54,x55))
% 0.51/0.63 [6]~E(x61,x62)+E(f2(x63,x64,x61,x65),f2(x63,x64,x62,x65))
% 0.51/0.63 [7]~E(x71,x72)+E(f2(x73,x74,x75,x71),f2(x73,x74,x75,x72))
% 0.51/0.63 [8]~E(x81,x82)+E(f7(x81,x83,x84,x85,x86),f7(x82,x83,x84,x85,x86))
% 0.51/0.63 [9]~E(x91,x92)+E(f7(x93,x91,x94,x95,x96),f7(x93,x92,x94,x95,x96))
% 0.51/0.63 [10]~E(x101,x102)+E(f7(x103,x104,x101,x105,x106),f7(x103,x104,x102,x105,x106))
% 0.51/0.63 [11]~E(x111,x112)+E(f7(x113,x114,x115,x111,x116),f7(x113,x114,x115,x112,x116))
% 0.51/0.63 [12]~E(x121,x122)+E(f7(x123,x124,x125,x126,x121),f7(x123,x124,x125,x126,x122))
% 0.51/0.63 [13]~E(x131,x132)+E(f3(x131,x133,x134,x135,x136),f3(x132,x133,x134,x135,x136))
% 0.51/0.63 [14]~E(x141,x142)+E(f3(x143,x141,x144,x145,x146),f3(x143,x142,x144,x145,x146))
% 0.51/0.63 [15]~E(x151,x152)+E(f3(x153,x154,x151,x155,x156),f3(x153,x154,x152,x155,x156))
% 0.51/0.63 [16]~E(x161,x162)+E(f3(x163,x164,x165,x161,x166),f3(x163,x164,x165,x162,x166))
% 0.51/0.63 [17]~E(x171,x172)+E(f3(x173,x174,x175,x176,x171),f3(x173,x174,x175,x176,x172))
% 0.51/0.63 [18]~E(x181,x182)+E(f4(x181,x183,x184,x185,x186),f4(x182,x183,x184,x185,x186))
% 0.51/0.63 [19]~E(x191,x192)+E(f4(x193,x191,x194,x195,x196),f4(x193,x192,x194,x195,x196))
% 0.51/0.63 [20]~E(x201,x202)+E(f4(x203,x204,x201,x205,x206),f4(x203,x204,x202,x205,x206))
% 0.51/0.63 [21]~E(x211,x212)+E(f4(x213,x214,x215,x211,x216),f4(x213,x214,x215,x212,x216))
% 0.51/0.63 [22]~E(x221,x222)+E(f4(x223,x224,x225,x226,x221),f4(x223,x224,x225,x226,x222))
% 0.51/0.63 [23]~E(x231,x232)+E(f5(x231,x233,x234,x235,x236,x237),f5(x232,x233,x234,x235,x236,x237))
% 0.51/0.63 [24]~E(x241,x242)+E(f5(x243,x241,x244,x245,x246,x247),f5(x243,x242,x244,x245,x246,x247))
% 0.51/0.63 [25]~E(x251,x252)+E(f5(x253,x254,x251,x255,x256,x257),f5(x253,x254,x252,x255,x256,x257))
% 0.51/0.63 [26]~E(x261,x262)+E(f5(x263,x264,x265,x261,x266,x267),f5(x263,x264,x265,x262,x266,x267))
% 0.51/0.63 [27]~E(x271,x272)+E(f5(x273,x274,x275,x276,x271,x277),f5(x273,x274,x275,x276,x272,x277))
% 0.51/0.63 [28]~E(x281,x282)+E(f5(x283,x284,x285,x286,x287,x281),f5(x283,x284,x285,x286,x287,x282))
% 0.51/0.63 [29]P1(x292,x293,x294)+~E(x291,x292)+~P1(x291,x293,x294)
% 0.51/0.63 [30]P1(x303,x302,x304)+~E(x301,x302)+~P1(x303,x301,x304)
% 0.51/0.63 [31]P1(x313,x314,x312)+~E(x311,x312)+~P1(x313,x314,x311)
% 0.51/0.63 [32]P2(x322,x323,x324,x325)+~E(x321,x322)+~P2(x321,x323,x324,x325)
% 0.51/0.63 [33]P2(x333,x332,x334,x335)+~E(x331,x332)+~P2(x333,x331,x334,x335)
% 0.51/0.63 [34]P2(x343,x344,x342,x345)+~E(x341,x342)+~P2(x343,x344,x341,x345)
% 0.51/0.63 [35]P2(x353,x354,x355,x352)+~E(x351,x352)+~P2(x353,x354,x355,x351)
% 0.51/0.63
% 0.51/0.63 %-------------------------------------------
% 0.51/0.63 cnf(117,plain,
% 0.51/0.63 (E(f2(x1171,x1172,x1173,x1173),x1172)),
% 0.51/0.63 inference(rename_variables,[],[42])).
% 0.51/0.63 cnf(120,plain,
% 0.51/0.63 (~E(f2(x1201,x1202,a6,a8),x1202)),
% 0.51/0.63 inference(rename_variables,[],[59])).
% 0.51/0.63 cnf(123,plain,
% 0.51/0.63 (P2(x1231,x1232,x1231,x1232)),
% 0.51/0.63 inference(rename_variables,[],[40])).
% 0.51/0.63 cnf(127,plain,
% 0.51/0.63 (P2(x1271,f2(x1272,x1271,a6,a8),x1273,f2(x1274,x1273,a6,a8))),
% 0.51/0.63 inference(rename_variables,[],[49])).
% 0.51/0.63 cnf(129,plain,
% 0.51/0.63 (P2(x1291,x1292,x1292,x1291)),
% 0.51/0.63 inference(rename_variables,[],[39])).
% 0.51/0.63 cnf(131,plain,
% 0.51/0.63 (P1(x1311,x1312,x1312)),
% 0.51/0.63 inference(rename_variables,[],[36])).
% 0.51/0.63 cnf(133,plain,
% 0.51/0.63 (P1(x1331,x1332,f2(x1331,x1332,x1333,x1334))),
% 0.51/0.63 inference(rename_variables,[],[45])).
% 0.51/0.63 cnf(137,plain,
% 0.51/0.63 (~E(f2(x1371,x1372,a6,a8),x1372)),
% 0.51/0.63 inference(rename_variables,[],[59])).
% 0.51/0.63 cnf(139,plain,
% 0.51/0.63 (P2(x1391,x1392,x1392,x1391)),
% 0.51/0.63 inference(rename_variables,[],[39])).
% 0.51/0.63 cnf(160,plain,
% 0.51/0.63 ($false),
% 0.51/0.63 inference(scs_inference,[],[60,39,129,139,40,123,36,131,37,38,53,56,47,45,133,42,117,59,120,137,49,127,2,75,62,61,77,73,35,34,33,32,31,30,29,3,92,91,65,64,90,86,85,84,83]),
% 0.51/0.63 ['proof']).
% 0.51/0.63 % SZS output end Proof
% 0.51/0.63 % Total time :0.020000s
%------------------------------------------------------------------------------