TSTP Solution File: LAT070-1 by CSE_E---1.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : LAT070-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% Computer : n013.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 05:59:24 EDT 2023
% Result : Unsatisfiable 54.61s 54.66s
% Output : CNFRefutation 54.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 55
% Number of leaves : 6
% Syntax : Number of formulae : 165 ( 161 unt; 4 typ; 0 def)
% Number of atoms : 161 ( 160 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 2 ( 2 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 2 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 2 ( 1 >; 1 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 480 ( 103 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
f: ( $i * $i ) > $i ).
tff(decl_23,type,
a: $i ).
tff(decl_24,type,
b: $i ).
tff(decl_25,type,
c: $i ).
cnf(ol_23A,axiom,
f(f(f(f(X1,X2),f(X2,X3)),X4),f(X2,f(f(X2,f(f(X1,X1),X1)),X3))) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ol_23A) ).
cnf(associativity,negated_conjecture,
f(a,f(f(b,c),f(b,c))) != f(c,f(f(b,a),f(b,a))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity) ).
cnf(c_0_2,axiom,
f(f(f(f(X1,X2),f(X2,X3)),X4),f(X2,f(f(X2,f(f(X1,X1),X1)),X3))) = X2,
ol_23A ).
cnf(c_0_3,plain,
f(X1,f(f(X1,X2),f(f(f(X1,X2),f(f(f(X3,X1),f(X3,X1)),f(X3,X1))),X4))) = f(X1,X2),
inference(spm,[status(thm)],[c_0_2,c_0_2]) ).
cnf(c_0_4,plain,
f(f(X1,X2),f(f(f(X1,X2),f(X2,X3)),X2)) = f(f(X1,X2),f(X2,X3)),
inference(spm,[status(thm)],[c_0_3,c_0_2]) ).
cnf(c_0_5,plain,
f(f(f(f(X1,X2),f(X2,X3)),X2),f(X2,X2)) = X2,
inference(spm,[status(thm)],[c_0_4,c_0_2]) ).
cnf(c_0_6,plain,
f(f(X1,X1),f(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_5]) ).
cnf(c_0_7,plain,
f(f(X1,X2),f(X1,f(f(X1,f(f(X1,X1),X1)),X1))) = X1,
inference(spm,[status(thm)],[c_0_2,c_0_6]) ).
cnf(c_0_8,plain,
f(X1,f(f(X1,X2),f(X1,X2))) = f(X1,X2),
inference(spm,[status(thm)],[c_0_3,c_0_7]) ).
cnf(c_0_9,plain,
f(f(X1,X2),f(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_8,c_0_7]) ).
cnf(c_0_10,plain,
f(X1,f(f(X1,X1),X2)) = f(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_4,c_0_9]),c_0_9]) ).
cnf(c_0_11,plain,
f(f(X1,X1),f(X1,X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_7]),c_0_10]),c_0_10]) ).
cnf(c_0_12,plain,
f(f(f(f(X1,X2),f(X2,X3)),X4),f(X2,X2)) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_2]) ).
cnf(c_0_13,plain,
f(f(X1,X2),f(X2,f(f(X2,f(f(X1,X1),X1)),X3))) = X2,
inference(spm,[status(thm)],[c_0_2,c_0_7]) ).
cnf(c_0_14,plain,
f(f(f(X1,X2),f(X1,X2)),X1) = f(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_7]) ).
cnf(c_0_15,plain,
f(f(X1,X2),f(X2,X2)) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_7]) ).
cnf(c_0_16,plain,
f(f(X1,X2),f(X2,f(f(X1,X1),X1))) = X2,
inference(spm,[status(thm)],[c_0_13,c_0_13]) ).
cnf(c_0_17,plain,
f(f(X1,X1),f(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_18,plain,
f(X1,f(f(X1,X2),f(X1,f(X1,X1)))) = f(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_11]),c_0_9]) ).
cnf(c_0_19,plain,
f(X1,f(X2,f(X1,X1))) = f(X1,X1),
inference(spm,[status(thm)],[c_0_17,c_0_17]) ).
cnf(c_0_20,plain,
f(f(X1,X2),f(X1,f(f(X3,X3),X3))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_18]),c_0_19]),c_0_15]) ).
cnf(c_0_21,plain,
f(X1,X1) = f(X1,f(f(X2,X2),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_20]),c_0_20]) ).
cnf(c_0_22,plain,
f(X1,f(f(X2,X1),f(X2,X1))) = f(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_15]),c_0_10]),c_0_10]) ).
cnf(c_0_23,plain,
f(f(X1,X1),f(f(X2,X2),X2)) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_21]),c_0_10]),c_0_10]) ).
cnf(c_0_24,plain,
f(f(f(X1,X1),X1),f(X2,X2)) = X2,
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_25,plain,
f(X1,f(f(X2,X1),f(X1,f(X1,X1)))) = f(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_9]) ).
cnf(c_0_26,plain,
f(f(f(X1,X1),X1),X2) = f(X2,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_21]),c_0_6]) ).
cnf(c_0_27,plain,
f(f(X1,f(X1,X1)),f(X2,X2)) = X2,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_7]),c_0_10]),c_0_10]) ).
cnf(c_0_28,plain,
f(f(X1,X1),f(X2,f(X2,X2))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_7]),c_0_10]),c_0_10]) ).
cnf(c_0_29,plain,
f(f(X1,X1),X1) = f(X1,f(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_8]) ).
cnf(c_0_30,plain,
f(f(X1,f(X1,X1)),X2) = f(X2,X2),
inference(spm,[status(thm)],[c_0_27,c_0_11]) ).
cnf(c_0_31,plain,
f(f(f(X1,X1),X2),X1) = f(X1,X1),
inference(spm,[status(thm)],[c_0_9,c_0_9]) ).
cnf(c_0_32,plain,
f(X1,f(X2,f(X2,X2))) = f(X1,X1),
inference(spm,[status(thm)],[c_0_28,c_0_11]) ).
cnf(c_0_33,plain,
f(f(X1,f(X1,X1)),X2) = f(X2,f(X3,f(X3,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_20]),c_0_29]) ).
cnf(c_0_34,plain,
f(f(f(X1,f(X1,X1)),f(X2,X3)),X2) = f(X2,X3),
inference(spm,[status(thm)],[c_0_14,c_0_30]) ).
cnf(c_0_35,plain,
f(f(a,f(a,a)),f(f(X1,X2),f(X2,X3))) = f(X2,f(f(X1,X2),f(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_12]),c_0_32]),c_0_33]) ).
cnf(c_0_36,plain,
f(f(f(X1,X2),f(X1,X2)),X2) = f(X1,X2),
inference(spm,[status(thm)],[c_0_11,c_0_15]) ).
cnf(c_0_37,plain,
f(f(X1,f(f(X2,X1),f(X1,X3))),f(X2,X1)) = f(f(X2,X1),f(X1,X3)),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_38,plain,
f(f(f(X1,f(X1,X1)),X2),f(X2,X3)) = X2,
inference(spm,[status(thm)],[c_0_11,c_0_30]) ).
cnf(c_0_39,plain,
f(X1,f(f(X2,f(X2,X2)),f(X3,X1))) = f(X3,X1),
inference(spm,[status(thm)],[c_0_22,c_0_30]) ).
cnf(c_0_40,plain,
f(f(f(X1,f(X1,X1)),f(X2,X3)),X3) = f(X2,X3),
inference(spm,[status(thm)],[c_0_36,c_0_30]) ).
cnf(c_0_41,plain,
f(f(f(X1,X2),f(X1,f(f(X1,X2),X3))),X1) = f(X1,f(f(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,plain,
f(f(X1,X2),f(X1,f(f(X3,X1),f(X1,X2)))) = f(f(X3,X1),f(X1,X2)),
inference(spm,[status(thm)],[c_0_39,c_0_35]) ).
cnf(c_0_43,plain,
f(f(X1,f(f(X2,X1),f(X1,X3))),f(X1,X3)) = f(f(X2,X1),f(X1,X3)),
inference(spm,[status(thm)],[c_0_40,c_0_35]) ).
cnf(c_0_44,plain,
f(f(X1,X2),f(f(X3,f(X3,X3)),X1)) = X1,
inference(spm,[status(thm)],[c_0_9,c_0_30]) ).
cnf(c_0_45,plain,
f(f(f(X1,X2),f(X2,X3)),X2) = f(X2,f(f(X1,X2),f(X2,X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_42]) ).
cnf(c_0_46,plain,
f(f(f(X1,X2),f(f(X3,f(X1,X2)),X1)),X1) = f(f(X3,f(X1,X2)),X1),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,plain,
f(f(f(X1,f(X1,X1)),X2),f(X3,X2)) = X2,
inference(spm,[status(thm)],[c_0_17,c_0_30]) ).
cnf(c_0_48,plain,
f(f(f(X1,X2),f(X3,X2)),X2) = f(X2,f(f(X1,X2),f(X3,X2))),
inference(spm,[status(thm)],[c_0_45,c_0_22]) ).
cnf(c_0_49,plain,
f(X1,f(f(X1,f(f(X2,X1),X3)),f(X2,X1))) = f(X1,f(f(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_4,c_0_17]) ).
cnf(c_0_50,plain,
f(f(f(X1,X2),f(X2,X1)),X1) = f(X2,X1),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_51,plain,
f(f(f(X1,X2),f(X3,X1)),X1) = f(X1,f(f(X1,X2),f(X3,X1))),
inference(spm,[status(thm)],[c_0_48,c_0_34]) ).
cnf(c_0_52,plain,
f(X1,f(f(X1,X2),f(X2,X1))) = f(X1,X2),
inference(spm,[status(thm)],[c_0_49,c_0_7]) ).
cnf(c_0_53,plain,
f(X1,X2) = f(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_50,c_0_51]),c_0_52]) ).
cnf(c_0_54,plain,
f(X1,f(f(X2,f(X2,X2)),f(X1,X3))) = f(X1,X3),
inference(spm,[status(thm)],[c_0_8,c_0_30]) ).
cnf(c_0_55,plain,
f(f(f(f(X1,X2),f(X1,X3)),X4),f(X1,X1)) = X1,
inference(spm,[status(thm)],[c_0_12,c_0_14]) ).
cnf(c_0_56,plain,
f(X1,f(f(X2,X1),f(X1,X2))) = f(X1,X2),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_57,plain,
f(f(X1,X1),f(f(f(X2,X1),f(X1,X3)),X4)) = X1,
inference(spm,[status(thm)],[c_0_14,c_0_2]) ).
cnf(c_0_58,plain,
f(f(X1,X2),f(X2,f(f(X1,X2),f(X2,X3)))) = f(f(X1,X2),f(X2,X3)),
inference(spm,[status(thm)],[c_0_54,c_0_35]) ).
cnf(c_0_59,plain,
f(f(f(f(X1,f(X1,X1)),f(X2,X3)),X4),f(X2,X2)) = X2,
inference(spm,[status(thm)],[c_0_55,c_0_30]) ).
cnf(c_0_60,plain,
f(f(a,f(a,a)),f(f(X1,X2),f(X2,X1))) = f(X2,X1),
inference(spm,[status(thm)],[c_0_35,c_0_56]) ).
cnf(c_0_61,plain,
f(f(X1,X1),f(f(f(X1,X2),f(X1,X3)),X4)) = X1,
inference(spm,[status(thm)],[c_0_57,c_0_14]) ).
cnf(c_0_62,plain,
f(X1,f(f(X2,X1),f(X1,f(f(X2,X1),X3)))) = f(X1,f(f(X2,X1),X3)),
inference(spm,[status(thm)],[c_0_58,c_0_47]) ).
cnf(c_0_63,plain,
f(f(f(X1,X2),X3),f(f(X2,X1),f(X2,X1))) = f(X2,X1),
inference(spm,[status(thm)],[c_0_59,c_0_60]) ).
cnf(c_0_64,plain,
f(f(X1,X1),f(X2,f(f(X1,X3),f(X1,X4)))) = X1,
inference(spm,[status(thm)],[c_0_61,c_0_22]) ).
cnf(c_0_65,plain,
f(X1,f(f(f(X2,X3),X1),f(X1,f(X3,X2)))) = f(X1,f(X3,X2)),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_66,plain,
f(X1,f(f(X1,X2),f(f(X3,X3),X3))) = f(X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_20]) ).
cnf(c_0_67,plain,
f(f(X1,X2),f(f(X3,f(X3,X3)),X2)) = X2,
inference(spm,[status(thm)],[c_0_15,c_0_30]) ).
cnf(c_0_68,plain,
f(f(X1,f(X2,f(X2,X2))),X1) = f(X1,f(X1,f(X2,f(X2,X2)))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_20]),c_0_29]),c_0_29]) ).
cnf(c_0_69,plain,
f(f(X1,X1),f(X2,f(f(X3,f(X3,X3)),f(X1,X4)))) = X1,
inference(spm,[status(thm)],[c_0_64,c_0_30]) ).
cnf(c_0_70,plain,
f(f(f(f(X1,X2),f(X3,X2)),X4),f(X2,X2)) = X2,
inference(spm,[status(thm)],[c_0_12,c_0_22]) ).
cnf(c_0_71,plain,
f(f(X1,X2),f(X2,f(f(X3,X2),f(X1,X2)))) = f(f(X3,X2),f(X1,X2)),
inference(spm,[status(thm)],[c_0_42,c_0_22]) ).
cnf(c_0_72,plain,
f(X1,f(f(f(X2,X3),X1),f(f(X3,X2),X1))) = f(f(X3,X2),X1),
inference(spm,[status(thm)],[c_0_65,c_0_53]) ).
cnf(c_0_73,plain,
f(X1,f(X1,f(X2,f(X2,X2)))) = f(X2,f(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_29]),c_0_29]),c_0_20]),c_0_68]) ).
cnf(c_0_74,plain,
f(f(f(X1,f(X1,X1)),X2),X2) = f(X2,f(f(X1,f(X1,X1)),X2)),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_75,plain,
f(X1,f(f(X1,X2),f(X1,f(X3,f(X1,X2))))) = f(X1,f(X3,f(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_44]),c_0_53]),c_0_53]) ).
cnf(c_0_76,plain,
f(f(f(X1,X2),f(X1,X2)),f(X3,f(X2,X1))) = f(X1,X2),
inference(spm,[status(thm)],[c_0_69,c_0_60]) ).
cnf(c_0_77,plain,
f(f(f(f(X1,X2),f(X3,f(X3,X3))),X4),f(X2,X2)) = X2,
inference(spm,[status(thm)],[c_0_70,c_0_32]) ).
cnf(c_0_78,plain,
f(f(f(X1,X2),X3),f(f(X2,X1),X3)) = f(f(a,f(a,a)),f(f(X2,X1),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_72]),c_0_32]),c_0_53]) ).
cnf(c_0_79,plain,
f(X1,f(X2,f(f(X3,f(X3,X3)),X1))) = f(f(X3,f(X3,X3)),X1),
inference(spm,[status(thm)],[c_0_19,c_0_30]) ).
cnf(c_0_80,plain,
f(X1,f(f(X2,f(X2,X2)),X1)) = f(X2,f(X2,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_14]),c_0_29]),c_0_47]),c_0_74]) ).
cnf(c_0_81,plain,
f(X1,f(f(f(X2,f(X2,X2)),X1),X3)) = f(f(X2,f(X2,X2)),X1),
inference(spm,[status(thm)],[c_0_10,c_0_30]) ).
cnf(c_0_82,plain,
f(X1,f(f(X1,f(X2,X3)),f(X1,f(X3,X2)))) = f(X1,f(X3,X2)),
inference(spm,[status(thm)],[c_0_75,c_0_76]) ).
cnf(c_0_83,plain,
f(X1,f(f(X1,f(X2,X3)),f(f(X3,X2),X1))) = f(X1,f(X2,X3)),
inference(spm,[status(thm)],[c_0_65,c_0_53]) ).
cnf(c_0_84,plain,
f(f(X1,X2),f(f(a,f(a,a)),f(f(X1,X1),X3))) = f(f(X1,X1),X3),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_77,c_0_10]),c_0_28]),c_0_78]) ).
cnf(c_0_85,plain,
f(f(f(X1,X2),f(X2,X1)),f(X3,f(X2,X1))) = f(X2,X1),
inference(spm,[status(thm)],[c_0_79,c_0_60]) ).
cnf(c_0_86,plain,
f(f(X1,X2),f(f(X2,X1),f(X1,X2))) = f(a,f(a,a)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_80,c_0_60]),c_0_53]) ).
cnf(c_0_87,plain,
f(f(f(X1,X2),f(X2,X1)),f(f(X2,X1),X3)) = f(X2,X1),
inference(spm,[status(thm)],[c_0_81,c_0_60]) ).
cnf(c_0_88,plain,
f(f(X1,X2),f(X2,f(f(X1,X2),f(X3,X2)))) = f(f(X1,X2),f(X3,X2)),
inference(spm,[status(thm)],[c_0_58,c_0_22]) ).
cnf(c_0_89,plain,
f(X1,f(X2,X3)) = f(f(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_53]),c_0_83]) ).
cnf(c_0_90,plain,
f(f(f(X1,X1),X2),f(f(X1,X3),f(X1,X3))) = f(X1,X3),
inference(spm,[status(thm)],[c_0_9,c_0_84]) ).
cnf(c_0_91,plain,
f(f(a,f(a,a)),f(X1,X2)) = f(f(X2,X1),f(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_85]),c_0_86]) ).
cnf(c_0_92,plain,
f(f(X1,X2),f(X3,f(f(X1,X2),f(X2,X1)))) = f(f(X1,X2),f(X2,X1)),
inference(spm,[status(thm)],[c_0_85,c_0_87]) ).
cnf(c_0_93,plain,
f(f(X1,X2),f(f(f(X1,X2),f(X1,X3)),X1)) = f(f(X1,X2),f(X1,X3)),
inference(spm,[status(thm)],[c_0_4,c_0_14]) ).
cnf(c_0_94,plain,
f(f(f(X1,X2),f(X1,X3)),X1) = f(X1,f(f(X1,X2),f(X1,X3))),
inference(spm,[status(thm)],[c_0_45,c_0_14]) ).
cnf(c_0_95,plain,
f(f(X1,X2),f(X2,f(f(X3,X2),f(X2,X1)))) = f(f(X3,X2),f(X2,X1)),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_96,plain,
f(X1,f(f(f(X2,X2),X1),f(X1,f(X2,X3)))) = f(X1,f(X2,X3)),
inference(spm,[status(thm)],[c_0_62,c_0_90]) ).
cnf(c_0_97,plain,
f(f(X1,X2),f(X2,X1)) = f(f(a,f(a,a)),f(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_76,c_0_91]),c_0_67]),c_0_92]) ).
cnf(c_0_98,plain,
f(f(X1,X2),f(X1,f(f(X1,X2),f(X1,X3)))) = f(f(X1,X2),f(X1,X3)),
inference(rw,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_99,plain,
f(f(f(X1,X1),X2),f(X2,f(X1,X3))) = f(f(a,f(a,a)),f(f(X1,X3),X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_96]),c_0_97]) ).
cnf(c_0_100,plain,
f(f(X1,X2),f(X1,f(f(X1,X3),f(X2,X1)))) = f(f(X1,X3),f(X2,X1)),
inference(spm,[status(thm)],[c_0_98,c_0_89]) ).
cnf(c_0_101,plain,
f(f(X1,X2),f(f(f(X2,X3),f(X2,X3)),X1)) = f(f(a,f(a,a)),f(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_44]),c_0_53]) ).
cnf(c_0_102,plain,
f(f(X1,X2),f(X2,f(f(X1,X3),f(X1,X3)))) = f(f(a,f(a,a)),f(X1,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_101]),c_0_39]),c_0_53]) ).
cnf(c_0_103,plain,
f(X1,f(f(X2,X1),f(X1,f(X3,f(X2,X1))))) = f(X1,f(X3,f(X2,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_67]),c_0_53]),c_0_53]) ).
cnf(c_0_104,plain,
f(f(X1,X2),f(X2,f(f(X3,X1),f(X1,X4)))) = f(f(a,f(a,a)),f(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_35]),c_0_67]) ).
cnf(c_0_105,plain,
f(X1,f(f(X2,X3),f(X3,X1))) = f(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_103,c_0_104]),c_0_39]) ).
cnf(c_0_106,plain,
f(X1,f(X2,f(f(X2,X3),X1))) = f(f(X2,X3),X1),
inference(spm,[status(thm)],[c_0_105,c_0_38]) ).
cnf(c_0_107,plain,
f(X1,f(X2,f(f(X3,X2),X1))) = f(f(X3,X2),X1),
inference(spm,[status(thm)],[c_0_105,c_0_47]) ).
cnf(c_0_108,plain,
f(X1,f(f(X2,X3),f(f(f(X2,X2),X4),X1))) = f(f(f(X2,X2),X4),X1),
inference(spm,[status(thm)],[c_0_106,c_0_84]) ).
cnf(c_0_109,plain,
f(f(f(f(X1,X2),X3),X4),f(f(f(X2,X1),X3),X4)) = f(f(a,f(a,a)),f(f(f(X2,X1),X3),X4)),
inference(spm,[status(thm)],[c_0_78,c_0_89]) ).
cnf(c_0_110,plain,
f(f(a,f(a,a)),f(f(f(X1,X1),X2),X3)) = f(f(X1,X3),f(f(f(X1,X1),X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_108]),c_0_109]) ).
cnf(c_0_111,plain,
f(X1,f(f(X2,X1),f(X1,f(f(X1,X2),X3)))) = f(X1,f(f(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_103,c_0_89]) ).
cnf(c_0_112,plain,
f(X1,f(f(X1,X2),f(X3,X2))) = f(X2,X1),
inference(spm,[status(thm)],[c_0_105,c_0_89]) ).
cnf(c_0_113,plain,
f(f(X1,f(X2,X3)),f(f(f(X1,X1),X2),f(X2,X3))) = f(X2,f(f(f(X1,X1),X2),f(X2,X3))),
inference(spm,[status(thm)],[c_0_35,c_0_110]) ).
cnf(c_0_114,plain,
f(X1,f(f(X1,X2),f(X2,X3))) = f(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_104]),c_0_39]) ).
cnf(c_0_115,plain,
f(f(X1,X2),f(f(f(X1,X2),f(X3,X1)),X1)) = f(f(X1,X2),f(X3,X1)),
inference(spm,[status(thm)],[c_0_93,c_0_22]) ).
cnf(c_0_116,plain,
f(X1,f(X2,f(f(f(X1,X1),X2),f(X2,X3)))) = f(f(X2,X3),X1),
inference(spm,[status(thm)],[c_0_112,c_0_113]) ).
cnf(c_0_117,plain,
f(X1,f(f(X2,X3),f(X1,X2))) = f(X2,X1),
inference(spm,[status(thm)],[c_0_114,c_0_53]) ).
cnf(c_0_118,plain,
f(f(X1,X2),f(f(f(X1,X2),f(X2,X1)),X3)) = f(f(X1,X2),f(X2,X1)),
inference(spm,[status(thm)],[c_0_87,c_0_87]) ).
cnf(c_0_119,plain,
f(X1,f(f(X2,f(X2,X2)),f(X3,f(X3,X3)))) = f(X2,f(X2,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_27]),c_0_29]) ).
cnf(c_0_120,plain,
f(f(f(X1,X2),f(X2,X1)),f(f(X1,X2),X3)) = f(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_52]),c_0_115]),c_0_51]),c_0_52]),c_0_51]),c_0_52]) ).
cnf(c_0_121,plain,
f(X1,f(f(X2,X3),f(X2,f(f(X1,X1),f(X2,X3))))) = f(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_44]),c_0_53]) ).
cnf(c_0_122,plain,
f(X1,f(f(f(X2,X2),X3),f(X1,f(X2,X4)))) = f(f(X2,X4),X1),
inference(spm,[status(thm)],[c_0_117,c_0_84]) ).
cnf(c_0_123,plain,
f(f(X1,X2),f(X3,f(X3,X3))) = f(f(X1,X2),f(X2,X1)),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_124,plain,
f(X1,f(f(X2,X3),f(X1,X3))) = f(X1,X3),
inference(spm,[status(thm)],[c_0_105,c_0_53]) ).
cnf(c_0_125,plain,
f(f(f(X1,X2),f(X2,X1)),f(f(X1,X1),X3)) = f(X1,X2),
inference(spm,[status(thm)],[c_0_120,c_0_84]) ).
cnf(c_0_126,plain,
f(X1,f(X2,f(X3,f(X3,X3)))) = f(f(X2,f(X4,f(X4,X4))),X1),
inference(spm,[status(thm)],[c_0_89,c_0_33]) ).
cnf(c_0_127,plain,
f(f(X1,X1),f(f(X2,f(X1,X3)),f(a,f(a,a)))) = f(X2,f(X1,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123]) ).
cnf(c_0_128,plain,
f(X1,f(f(X2,f(X2,X2)),X3)) = f(f(X3,X3),X1),
inference(spm,[status(thm)],[c_0_89,c_0_32]) ).
cnf(c_0_129,plain,
f(X1,f(f(f(X2,X3),X4),f(X1,f(X3,X2)))) = f(X1,f(X3,X2)),
inference(spm,[status(thm)],[c_0_124,c_0_89]) ).
cnf(c_0_130,plain,
f(f(f(X1,X2),f(X2,X1)),f(X3,f(X1,X1))) = f(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_125]),c_0_118]),c_0_85]) ).
cnf(c_0_131,plain,
f(f(f(X1,f(X2,X3)),f(X4,f(X4,X4))),f(X2,X2)) = f(X1,f(X2,X2)),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_132,plain,
f(X1,f(f(f(X2,f(X2,X2)),X3),X4)) = f(f(f(X3,X3),X4),X1),
inference(spm,[status(thm)],[c_0_89,c_0_128]) ).
cnf(c_0_133,plain,
f(X1,f(f(f(X2,X2),X3),f(X1,f(X4,X2)))) = f(X1,f(X4,X2)),
inference(spm,[status(thm)],[c_0_129,c_0_84]) ).
cnf(c_0_134,plain,
f(f(f(X1,X2),f(X2,X3)),f(X4,f(X2,X2))) = f(X2,f(f(X1,X2),f(X2,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_35]),c_0_38]),c_0_45]) ).
cnf(c_0_135,plain,
f(X1,f(f(a,f(a,a)),f(f(f(X1,X1),X2),X3))) = f(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_132]),c_0_47]),c_0_47]),c_0_33]),c_0_53]) ).
cnf(c_0_136,plain,
f(f(f(X1,f(X2,X3)),X4),f(f(X1,f(X3,X2)),X4)) = f(f(a,f(a,a)),f(f(X1,f(X3,X2)),X4)),
inference(spm,[status(thm)],[c_0_78,c_0_89]) ).
cnf(c_0_137,plain,
f(f(X1,X1),f(f(X2,f(X3,X1)),f(X2,f(X3,X1)))) = f(X2,f(X1,X1)),
inference(spm,[status(thm)],[c_0_121,c_0_133]) ).
cnf(c_0_138,plain,
f(f(f(X1,X1),X2),f(f(X3,X1),f(X1,X4))) = f(X1,f(f(X3,X1),f(X1,X4))),
inference(spm,[status(thm)],[c_0_89,c_0_134]) ).
cnf(c_0_139,plain,
f(X1,f(f(X2,X1),f(X3,f(X3,X3)))) = f(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_29]) ).
cnf(c_0_140,plain,
f(X1,f(f(X2,X3),f(f(f(X1,X1),X4),X3))) = f(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_124]),c_0_135]),c_0_53]) ).
cnf(c_0_141,plain,
f(f(f(X1,f(X2,X3)),X4),f(X4,f(f(X3,X2),X1))) = f(f(a,f(a,a)),f(X4,f(f(X3,X2),X1))),
inference(spm,[status(thm)],[c_0_136,c_0_89]) ).
cnf(c_0_142,plain,
f(f(X1,X2),f(f(X3,X4),f(X4,f(X2,X1)))) = f(X4,f(X2,X1)),
inference(spm,[status(thm)],[c_0_124,c_0_89]) ).
cnf(c_0_143,plain,
f(X1,f(f(a,f(a,a)),f(X2,f(X3,f(X1,X1))))) = f(X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_131,c_0_137]),c_0_6]),c_0_6]),c_0_33]),c_0_53]) ).
cnf(c_0_144,plain,
f(f(f(X1,X1),X2),f(f(X3,X1),f(X4,f(X4,X4)))) = f(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_119]),c_0_139]) ).
cnf(c_0_145,plain,
f(f(X1,X1),f(f(X2,X3),f(f(X1,X4),X3))) = f(X3,f(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_140,c_0_141]),c_0_9]),c_0_9]),c_0_9]),c_0_9]),c_0_27]),c_0_9]),c_0_9]) ).
cnf(c_0_146,plain,
f(X1,f(f(X2,X3),f(X3,f(X4,f(X1,X1))))) = f(X3,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_142]),c_0_143]),c_0_53]) ).
cnf(c_0_147,plain,
f(f(X1,X1),f(f(f(X2,X1),f(X3,X1)),X4)) = X1,
inference(spm,[status(thm)],[c_0_57,c_0_22]) ).
cnf(c_0_148,plain,
f(f(X1,X1),f(f(X2,X3),f(f(X4,X1),X3))) = f(X3,f(X1,X1)),
inference(spm,[status(thm)],[c_0_140,c_0_144]) ).
cnf(c_0_149,plain,
f(f(f(X1,X2),f(f(X3,X4),X2)),f(X3,X3)) = f(X2,f(X3,X3)),
inference(spm,[status(thm)],[c_0_53,c_0_145]) ).
cnf(c_0_150,plain,
f(X1,f(f(X2,f(X3,f(X1,X1))),f(X2,X4))) = f(X2,X1),
inference(spm,[status(thm)],[c_0_146,c_0_89]) ).
cnf(c_0_151,plain,
f(f(f(X1,f(X1,X1)),X2),f(f(f(X2,X3),f(X2,X4)),X5)) = X2,
inference(spm,[status(thm)],[c_0_61,c_0_30]) ).
cnf(c_0_152,plain,
f(X1,f(f(X2,f(f(X1,X1),X3)),f(X4,X2))) = f(X2,X1),
inference(spm,[status(thm)],[c_0_140,c_0_89]) ).
cnf(c_0_153,plain,
f(X1,f(f(f(f(X2,X3),f(X4,X3)),X5),f(X3,X1))) = f(X3,X1),
inference(spm,[status(thm)],[c_0_107,c_0_147]) ).
cnf(c_0_154,plain,
f(f(X1,X1),f(X2,f(f(X3,X1),f(X4,X2)))) = f(f(X4,X2),f(X1,X1)),
inference(spm,[status(thm)],[c_0_148,c_0_47]) ).
cnf(c_0_155,plain,
f(f(f(X1,X2),f(X3,X2)),f(f(X4,X3),f(X4,X3))) = f(X2,f(f(X4,X3),f(X4,X3))),
inference(spm,[status(thm)],[c_0_149,c_0_67]) ).
cnf(c_0_156,plain,
f(f(f(X1,X2),f(X1,X3)),f(f(X4,X1),f(X4,X5))) = f(X4,f(f(X1,X2),f(X1,X3))),
inference(spm,[status(thm)],[c_0_150,c_0_151]) ).
cnf(c_0_157,plain,
f(f(f(X1,X2),f(X3,X2)),f(f(X2,X4),f(X5,X4))) = f(X4,f(f(X1,X2),f(X3,X2))),
inference(spm,[status(thm)],[c_0_152,c_0_153]) ).
cnf(c_0_158,negated_conjecture,
f(a,f(f(b,c),f(b,c))) != f(c,f(f(b,a),f(b,a))),
associativity ).
cnf(c_0_159,plain,
f(X1,f(f(X2,X3),f(X2,X3))) = f(X3,f(f(X1,X2),f(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_19]),c_0_156]),c_0_157]) ).
cnf(c_0_160,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_158,c_0_159]),c_0_159]),c_0_53]),c_0_53])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT070-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Aug 24 08:28:32 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.19/0.55 start to proof: theBenchmark
% 54.61/54.66 % Version : CSE_E---1.5
% 54.61/54.66 % Problem : theBenchmark.p
% 54.61/54.66 % Proof found
% 54.61/54.66 % SZS status Theorem for theBenchmark.p
% 54.61/54.66 % SZS output start Proof
% See solution above
% 54.61/54.68 % Total time : 54.112000 s
% 54.61/54.68 % SZS output end Proof
% 54.61/54.68 % Total time : 54.117000 s
%------------------------------------------------------------------------------