TSTP Solution File: GRP781-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : GRP781-1 : TPTP v8.1.2. Released v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% Computer : n014.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 00:23:43 EDT 2023
% Result : Unsatisfiable 78.70s 78.75s
% Output : CNFRefutation 78.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 11
% Syntax : Number of formulae : 173 ( 134 unt; 5 typ; 0 def)
% Number of atoms : 202 ( 201 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 70 ( 36 ~; 34 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 3 ( 1 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 470 ( 37 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
m: ( $i * $i ) > $i ).
tff(decl_23,type,
c: ( $i * $i ) > $i ).
tff(decl_24,type,
x: $i ).
tff(decl_25,type,
y: $i ).
tff(decl_26,type,
z: $i ).
cnf(cancellation_001,axiom,
( X2 = X3
| m(X1,X2) != m(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation_001) ).
cnf(commutator,axiom,
m(X1,m(X2,c(X2,X1))) = m(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutator) ).
cnf(associativity,axiom,
m(X1,m(X2,X3)) = m(m(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity) ).
cnf(cancellation,axiom,
( X1 = X3
| m(X1,X2) != m(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cancellation) ).
cnf(assumption,axiom,
m(X1,m(X2,m(X3,m(X2,X1)))) = m(X2,m(X1,m(X3,m(X1,X2)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',assumption) ).
cnf(distributivity,negated_conjecture,
c(m(x,y),z) != m(c(x,z),c(y,z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity) ).
cnf(c_0_6,axiom,
( X2 = X3
| m(X1,X2) != m(X1,X3) ),
cancellation_001 ).
cnf(c_0_7,axiom,
m(X1,m(X2,c(X2,X1))) = m(X2,X1),
commutator ).
cnf(c_0_8,plain,
( X1 = m(X2,c(X2,X3))
| m(X3,X1) != m(X2,X3) ),
inference(spm,[status(thm)],[c_0_6,c_0_7]) ).
cnf(c_0_9,axiom,
m(X1,m(X2,X3)) = m(m(X1,X2),X3),
associativity ).
cnf(c_0_10,plain,
m(X1,c(X1,X1)) = X1,
inference(er,[status(thm)],[c_0_8]) ).
cnf(c_0_11,plain,
m(X1,m(c(X1,X1),X2)) = m(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_12,plain,
( X1 = c(X2,X2)
| m(X2,X1) != X2 ),
inference(spm,[status(thm)],[c_0_6,c_0_10]) ).
cnf(c_0_13,plain,
m(X1,c(c(X1,X1),c(X1,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_10]),c_0_10]) ).
cnf(c_0_14,plain,
c(c(X1,X1),c(X1,X1)) = c(X1,X1),
inference(spm,[status(thm)],[c_0_12,c_0_13]) ).
cnf(c_0_15,plain,
( X1 = X2
| m(X3,m(X4,X1)) != m(X3,m(X4,X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_9]),c_0_9]) ).
cnf(c_0_16,plain,
( X1 = m(X2,m(X3,c(m(X2,X3),X4)))
| m(X4,X1) != m(X2,m(X3,X4)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_9]),c_0_9]) ).
cnf(c_0_17,plain,
m(c(X1,X1),m(c(X1,X1),X2)) = m(c(X1,X1),X2),
inference(spm,[status(thm)],[c_0_11,c_0_14]) ).
cnf(c_0_18,plain,
( X1 = c(X2,X3)
| m(X3,m(X2,X1)) != m(X2,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_7]) ).
cnf(c_0_19,plain,
m(X1,m(X2,c(m(X1,X2),X1))) = m(X2,X1),
inference(er,[status(thm)],[c_0_16]) ).
cnf(c_0_20,plain,
m(c(X1,X1),m(X2,c(X1,X1))) = m(X2,c(X1,X1)),
inference(spm,[status(thm)],[c_0_17,c_0_7]) ).
cnf(c_0_21,plain,
c(m(X1,X2),X1) = c(X2,X1),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_22,axiom,
( X1 = X3
| m(X1,X2) != m(X3,X2) ),
cancellation ).
cnf(c_0_23,plain,
m(c(X1,X1),X1) = X1,
inference(spm,[status(thm)],[c_0_20,c_0_10]) ).
cnf(c_0_24,plain,
m(X1,m(X2,m(X3,c(X3,m(X1,X2))))) = m(X3,m(X1,X2)),
inference(spm,[status(thm)],[c_0_9,c_0_7]) ).
cnf(c_0_25,plain,
c(m(X1,m(X2,X3)),m(X1,X2)) = c(X3,m(X1,X2)),
inference(spm,[status(thm)],[c_0_21,c_0_9]) ).
cnf(c_0_26,axiom,
m(X1,m(X2,m(X3,m(X2,X1)))) = m(X2,m(X1,m(X3,m(X1,X2)))),
assumption ).
cnf(c_0_27,plain,
m(X1,m(X2,m(c(X2,X1),X3))) = m(X2,m(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_7]),c_0_9]),c_0_9]) ).
cnf(c_0_28,plain,
( X1 = c(X2,X2)
| m(X1,X2) != X2 ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_29,plain,
m(c(X1,X1),m(X1,X2)) = m(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_23]) ).
cnf(c_0_30,plain,
( X1 = m(X2,m(X3,c(X3,m(X4,X2))))
| m(X4,X1) != m(X3,m(X4,X2)) ),
inference(spm,[status(thm)],[c_0_6,c_0_24]) ).
cnf(c_0_31,plain,
c(c(X1,X2),m(X2,X1)) = c(m(X1,X2),m(X2,X1)),
inference(spm,[status(thm)],[c_0_25,c_0_7]) ).
cnf(c_0_32,plain,
m(X1,m(X2,m(c(X1,X2),m(X2,X1)))) = m(X1,m(X2,m(X1,X2))),
inference(spm,[status(thm)],[c_0_26,c_0_27]) ).
cnf(c_0_33,plain,
c(m(X1,X2),m(X1,X2)) = c(X1,X1),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_34,plain,
c(X1,c(X2,X2)) = c(X2,X2),
inference(spm,[status(thm)],[c_0_18,c_0_20]) ).
cnf(c_0_35,plain,
m(X1,m(X2,c(X2,m(X2,X1)))) = m(X2,X1),
inference(er,[status(thm)],[c_0_30]) ).
cnf(c_0_36,plain,
m(X1,m(X2,c(m(X1,X2),m(X2,X1)))) = m(c(X1,X2),m(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_31]),c_0_9]),c_0_27]) ).
cnf(c_0_37,plain,
c(m(c(X1,X2),m(X2,X1)),m(X1,X2)) = c(X1,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_32]),c_0_25]),c_0_33]) ).
cnf(c_0_38,plain,
c(X1,X1) = c(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_20]),c_0_33]),c_0_34]) ).
cnf(c_0_39,plain,
c(X1,m(X1,X2)) = c(X1,X2),
inference(spm,[status(thm)],[c_0_18,c_0_35]) ).
cnf(c_0_40,plain,
m(X1,m(X2,c(c(X1,X2),X1))) = m(X2,m(c(X1,X2),X1)),
inference(spm,[status(thm)],[c_0_27,c_0_7]) ).
cnf(c_0_41,plain,
c(c(m(X1,X2),m(X2,X1)),m(X1,X2)) = c(X1,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_36]),c_0_37]) ).
cnf(c_0_42,plain,
m(X1,c(X2,X2)) = X1,
inference(spm,[status(thm)],[c_0_10,c_0_38]) ).
cnf(c_0_43,plain,
m(c(X1,X1),X2) = X2,
inference(spm,[status(thm)],[c_0_23,c_0_38]) ).
cnf(c_0_44,plain,
c(m(X1,X2),m(X1,m(X2,X3))) = c(m(X1,X2),X3),
inference(spm,[status(thm)],[c_0_39,c_0_9]) ).
cnf(c_0_45,plain,
( c(c(X1,X2),X1) = c(X2,X1)
| m(X2,m(c(X1,X2),X1)) != m(X2,X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_40]) ).
cnf(c_0_46,plain,
m(c(m(X1,X2),m(X2,X1)),m(X1,X2)) = m(c(X1,X2),m(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_41]),c_0_42]),c_0_9]),c_0_36]) ).
cnf(c_0_47,plain,
m(X1,m(X2,m(X2,X1))) = m(X2,m(X1,m(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_43]),c_0_43]) ).
cnf(c_0_48,plain,
c(m(X1,X2),c(X2,X1)) = c(m(X1,X2),m(X2,X1)),
inference(spm,[status(thm)],[c_0_44,c_0_7]) ).
cnf(c_0_49,plain,
c(m(X1,X2),m(X2,X1)) = c(X2,X2),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_41]),c_0_9]),c_0_27]),c_0_9]),c_0_47]) ).
cnf(c_0_50,plain,
c(X1,m(X2,c(X2,X1))) = c(X1,m(X2,X1)),
inference(spm,[status(thm)],[c_0_39,c_0_7]) ).
cnf(c_0_51,plain,
c(m(X1,X2),c(X2,X1)) = c(X2,X2),
inference(rw,[status(thm)],[c_0_48,c_0_49]) ).
cnf(c_0_52,plain,
m(X1,m(X2,m(X3,c(m(X2,X3),X1)))) = m(X2,m(X3,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_9]),c_0_9]) ).
cnf(c_0_53,plain,
c(c(X1,X2),m(X1,X2)) = c(X2,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_50,c_0_51]),c_0_42]),c_0_31]),c_0_49]),c_0_9]),c_0_7]) ).
cnf(c_0_54,plain,
( X1 = c(X2,X2)
| m(X3,m(X4,X1)) != m(X3,X4) ),
inference(spm,[status(thm)],[c_0_15,c_0_42]) ).
cnf(c_0_55,plain,
m(X1,m(X2,c(m(X1,c(X1,X2)),X2))) = m(X1,m(c(X1,X2),X2)),
inference(spm,[status(thm)],[c_0_27,c_0_52]) ).
cnf(c_0_56,plain,
c(m(X1,c(X1,X2)),X2) = c(m(X1,X2),X2),
inference(spm,[status(thm)],[c_0_21,c_0_7]) ).
cnf(c_0_57,plain,
m(c(X1,X2),m(X1,X2)) = m(X1,m(X2,c(X1,X2))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_53]),c_0_42]),c_0_9]) ).
cnf(c_0_58,plain,
m(c(X1,X2),m(X2,m(X1,X3))) = m(X1,m(X2,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_51]),c_0_43]),c_0_9]),c_0_9]),c_0_27]) ).
cnf(c_0_59,plain,
m(c(X1,X2),m(X2,X1)) = m(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_49]),c_0_43]) ).
cnf(c_0_60,plain,
( m(c(X1,X2),X3) = c(X4,X4)
| m(X1,m(X2,X3)) != m(X2,X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_27]) ).
cnf(c_0_61,plain,
( X1 = m(X2,c(m(X3,X2),X2))
| m(X3,X1) != m(X3,m(c(X3,X2),X2)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_55]),c_0_56]) ).
cnf(c_0_62,plain,
( X1 = c(m(X2,X3),X4)
| m(X4,m(X2,m(X3,X1))) != m(X2,m(X3,X4)) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_9]),c_0_9]) ).
cnf(c_0_63,plain,
m(X1,m(X2,m(X1,c(X2,X1)))) = m(X2,m(X1,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_21]),c_0_9]),c_0_9]),c_0_58]) ).
cnf(c_0_64,plain,
( X1 = X2
| m(c(X2,X3),m(X3,X1)) != m(X2,X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_59]) ).
cnf(c_0_65,plain,
c(m(X1,m(X2,c(X2,m(X3,X1)))),X3) = c(m(X2,m(X3,X1)),X3),
inference(spm,[status(thm)],[c_0_21,c_0_24]) ).
cnf(c_0_66,plain,
m(c(X1,X2),c(X2,X1)) = c(X3,X3),
inference(spm,[status(thm)],[c_0_60,c_0_7]) ).
cnf(c_0_67,plain,
m(X1,c(m(X2,X1),X1)) = m(c(X2,X1),X1),
inference(er,[status(thm)],[c_0_61]) ).
cnf(c_0_68,plain,
c(m(X1,X2),X2) = c(X1,X2),
inference(spm,[status(thm)],[c_0_62,c_0_63]) ).
cnf(c_0_69,plain,
( m(X1,X2) = X1
| m(X1,m(X3,X2)) != m(X1,X3) ),
inference(spm,[status(thm)],[c_0_64,c_0_58]) ).
cnf(c_0_70,plain,
c(m(c(X1,X2),X3),c(X2,X1)) = c(X3,c(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_66]),c_0_34]),c_0_42]),c_0_42]) ).
cnf(c_0_71,plain,
m(c(X1,X2),X2) = m(X2,c(X1,X2)),
inference(rw,[status(thm)],[c_0_67,c_0_68]) ).
cnf(c_0_72,plain,
c(m(X1,c(X2,X3)),c(X3,X2)) = c(c(X2,X3),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_66]),c_0_42]),c_0_21]) ).
cnf(c_0_73,plain,
m(c(X1,X2),m(c(X2,X1),X3)) = X3,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_66]),c_0_9]) ).
cnf(c_0_74,plain,
( m(X1,c(X2,X1)) = X1
| m(X2,X1) != m(X1,X2) ),
inference(spm,[status(thm)],[c_0_69,c_0_7]) ).
cnf(c_0_75,plain,
c(c(X1,X2),X2) = c(X2,c(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_72]) ).
cnf(c_0_76,plain,
( X1 = X2
| m(X1,m(X3,c(X3,X2))) != m(X3,X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_7]) ).
cnf(c_0_77,plain,
c(c(X1,X2),m(c(X2,X1),X3)) = c(c(X1,X2),X3),
inference(spm,[status(thm)],[c_0_39,c_0_73]) ).
cnf(c_0_78,plain,
m(X1,c(X1,c(X1,X2))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_71]),c_0_75]) ).
cnf(c_0_79,plain,
( m(X1,X2) = X3
| m(X1,m(X2,m(X4,c(X4,X3)))) != m(X4,X3) ),
inference(spm,[status(thm)],[c_0_76,c_0_9]) ).
cnf(c_0_80,plain,
( c(X1,X1) = c(X2,X3)
| m(X3,X2) != m(X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_42]) ).
cnf(c_0_81,plain,
m(c(c(X1,X2),X3),X3) = m(X3,c(c(X1,X2),X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_73]),c_0_77]),c_0_77]),c_0_9]),c_0_73]) ).
cnf(c_0_82,plain,
( X1 = c(X2,m(X3,X4))
| m(X3,m(X4,m(X2,X1))) != m(X2,m(X3,X4)) ),
inference(spm,[status(thm)],[c_0_18,c_0_9]) ).
cnf(c_0_83,plain,
m(c(X1,X2),X1) = m(X1,c(X1,X2)),
inference(spm,[status(thm)],[c_0_7,c_0_78]) ).
cnf(c_0_84,plain,
( m(X1,X2) = X2
| m(X1,m(X3,X2)) != m(X3,X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_7]) ).
cnf(c_0_85,plain,
c(X1,X1) = c(c(c(X2,X3),X4),X4),
inference(spm,[status(thm)],[c_0_80,c_0_81]) ).
cnf(c_0_86,plain,
( c(X1,m(X2,X3)) = c(X1,X3)
| m(X2,m(X1,X3)) != m(X1,m(X2,X3)) ),
inference(spm,[status(thm)],[c_0_82,c_0_7]) ).
cnf(c_0_87,plain,
m(c(X1,X2),m(X1,X3)) = m(X1,m(c(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_83]),c_0_9]) ).
cnf(c_0_88,plain,
m(X1,m(X2,c(m(X1,X2),X2))) = m(X1,m(c(X1,X2),X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_7]),c_0_9]),c_0_27]),c_0_9]) ).
cnf(c_0_89,plain,
( m(c(X1,X2),X3) = X3
| m(c(X2,X1),X3) != X3 ),
inference(spm,[status(thm)],[c_0_84,c_0_73]) ).
cnf(c_0_90,plain,
m(c(X1,c(c(X2,X3),X1)),X4) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_85]),c_0_43]) ).
cnf(c_0_91,plain,
c(c(c(X1,X2),X3),X3) = c(X3,c(X3,c(X1,X2))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_81]),c_0_72]) ).
cnf(c_0_92,plain,
c(c(X1,X2),m(X1,X3)) = c(c(X1,X2),X3),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_93,plain,
m(c(X1,X2),m(X2,X3)) = m(X2,m(c(X1,X2),X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_71]),c_0_9]) ).
cnf(c_0_94,plain,
c(m(X1,c(m(X2,X1),X1)),X2) = c(m(c(X2,X1),X1),X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_88]),c_0_21]) ).
cnf(c_0_95,plain,
m(c(X1,c(X1,c(X2,X3))),X4) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_90]),c_0_91]) ).
cnf(c_0_96,plain,
m(c(c(X1,X2),X3),m(X1,X3)) = m(X1,m(X3,c(c(X1,X2),X3))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_92]),c_0_9]) ).
cnf(c_0_97,plain,
c(m(X1,c(X1,X2)),X2) = c(X1,X2),
inference(rw,[status(thm)],[c_0_56,c_0_68]) ).
cnf(c_0_98,plain,
c(X1,m(c(X2,X1),X3)) = c(X1,X3),
inference(spm,[status(thm)],[c_0_86,c_0_93]) ).
cnf(c_0_99,plain,
m(X1,m(c(m(X2,X1),X1),X2)) = m(X2,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_59,c_0_55]),c_0_56]),c_0_94]),c_0_59]),c_0_9]),c_0_59]),c_0_9]),c_0_56]) ).
cnf(c_0_100,plain,
m(c(X1,c(X2,X3)),X1) = m(X1,c(X1,c(X2,X3))),
inference(spm,[status(thm)],[c_0_59,c_0_95]) ).
cnf(c_0_101,plain,
c(X1,m(X2,c(c(X1,X3),X2))) = c(X1,X2),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_96]),c_0_71]),c_0_71])]) ).
cnf(c_0_102,plain,
c(X1,c(X2,X3)) = c(c(X3,X2),X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_97,c_0_72]),c_0_9]),c_0_7]),c_0_70]) ).
cnf(c_0_103,plain,
c(X1,m(X2,c(X2,c(X3,X1)))) = c(X1,m(X2,c(X3,X1))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_68]),c_0_100]) ).
cnf(c_0_104,plain,
c(c(X1,X2),m(X2,X3)) = c(c(X1,X2),X3),
inference(spm,[status(thm)],[c_0_86,c_0_93]) ).
cnf(c_0_105,plain,
c(X1,m(X2,c(X3,X1))) = c(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_102]),c_0_103]) ).
cnf(c_0_106,plain,
( X1 = m(c(X2,X3),X4)
| m(X3,m(X2,X1)) != m(X2,m(X3,X4)) ),
inference(spm,[status(thm)],[c_0_15,c_0_27]) ).
cnf(c_0_107,plain,
c(c(X1,X2),m(c(X3,X1),X4)) = c(c(X1,X2),X4),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_105]),c_0_9]),c_0_104]) ).
cnf(c_0_108,plain,
c(c(X1,X2),m(X3,c(X3,X1))) = c(c(X1,X2),m(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_92,c_0_99]),c_0_68]),c_0_83]) ).
cnf(c_0_109,plain,
c(m(X1,X2),c(X3,X1)) = c(c(X1,X3),X2),
inference(spm,[status(thm)],[c_0_102,c_0_92]) ).
cnf(c_0_110,plain,
c(c(m(X1,c(X2,X3)),X3),X4) = c(X4,c(X3,X1)),
inference(spm,[status(thm)],[c_0_102,c_0_105]) ).
cnf(c_0_111,plain,
( m(c(X1,X2),X1) = X1
| m(X1,X2) != m(X2,X1) ),
inference(spm,[status(thm)],[c_0_84,c_0_59]) ).
cnf(c_0_112,plain,
( X1 = m(c(X2,X3),m(X4,m(X3,X2)))
| m(X3,m(X2,X1)) != m(X3,m(X2,m(X4,m(X2,X3)))) ),
inference(spm,[status(thm)],[c_0_106,c_0_26]) ).
cnf(c_0_113,plain,
c(c(X1,X2),m(X3,X1)) = c(c(X1,X2),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_83]),c_0_108]) ).
cnf(c_0_114,plain,
c(c(X1,X2),m(c(X3,X2),X4)) = c(X4,c(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_105]),c_0_9]),c_0_109]),c_0_110]) ).
cnf(c_0_115,plain,
c(c(X1,X2),m(X3,c(X3,X2))) = c(c(X1,X2),m(X3,X2)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_99]),c_0_68]),c_0_83]) ).
cnf(c_0_116,plain,
c(X1,m(X2,X1)) = c(X1,X2),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_83]),c_0_50]) ).
cnf(c_0_117,plain,
c(X1,m(c(X2,X3),c(X3,X2))) = m(c(X2,X3),c(X3,X2)),
inference(spm,[status(thm)],[c_0_34,c_0_66]) ).
cnf(c_0_118,plain,
c(X1,m(c(X1,X2),X3)) = c(X1,X3),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_119,plain,
m(X1,c(X1,c(X2,X1))) = X1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_71]),c_0_100]) ).
cnf(c_0_120,plain,
m(c(X1,X2),m(X3,m(X2,X1))) = m(X3,m(X1,X2)),
inference(er,[status(thm)],[c_0_112]) ).
cnf(c_0_121,plain,
c(m(X1,X2),c(X1,X2)) = c(X1,X1),
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_56,c_0_51]),c_0_42]),c_0_48]),c_0_49]),c_0_9]),c_0_7]) ).
cnf(c_0_122,plain,
c(c(X1,X2),m(X3,m(X4,X1))) = c(c(X1,X2),m(X3,X4)),
inference(spm,[status(thm)],[c_0_113,c_0_9]) ).
cnf(c_0_123,plain,
c(c(X1,X2),m(X3,X2)) = c(X3,c(X2,X1)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_83]),c_0_115]) ).
cnf(c_0_124,plain,
( X1 = m(X2,X3)
| m(X1,X4) != m(X2,m(X3,X4)) ),
inference(spm,[status(thm)],[c_0_22,c_0_9]) ).
cnf(c_0_125,plain,
c(X1,m(X2,c(X2,X1))) = c(X1,X2),
inference(rw,[status(thm)],[c_0_50,c_0_116]) ).
cnf(c_0_126,plain,
m(c(X1,X2),c(X2,X1)) = c(X1,c(X2,X1)),
inference(spm,[status(thm)],[c_0_117,c_0_118]) ).
cnf(c_0_127,plain,
m(X1,c(X2,c(X3,X2))) = X1,
inference(spm,[status(thm)],[c_0_69,c_0_119]) ).
cnf(c_0_128,plain,
c(X1,m(X2,c(X2,c(X1,X3)))) = c(X1,m(X2,c(X1,X3))),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_99]),c_0_68]),c_0_100]) ).
cnf(c_0_129,plain,
c(X1,c(X2,X3)) = c(X2,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[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_86,c_0_120]),c_0_102]),c_0_121]),c_0_93]),c_0_83]),c_0_7])]),c_0_122]),c_0_123]) ).
cnf(c_0_130,plain,
( X1 = m(X2,X3)
| m(X1,m(X4,m(X4,X3))) != m(X2,m(X4,m(X3,m(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_124,c_0_47]) ).
cnf(c_0_131,plain,
m(X1,m(c(X2,X3),c(X3,X2))) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_66]) ).
cnf(c_0_132,plain,
c(X1,m(X2,c(X1,X3))) = c(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_125]),c_0_9]),c_0_126]),c_0_127]),c_0_128]) ).
cnf(c_0_133,plain,
m(X1,m(X2,m(X3,m(X4,c(X4,m(c(X1,X2),X3)))))) = m(X2,m(X1,m(X4,m(c(X1,X2),X3)))),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_134,plain,
m(X1,c(X2,c(X3,X4))) = X1,
inference(spm,[status(thm)],[c_0_42,c_0_129]) ).
cnf(c_0_135,plain,
m(c(X1,c(X2,X3)),X4) = X4,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_129]),c_0_43]) ).
cnf(c_0_136,plain,
( X1 = m(X2,c(X3,X4))
| m(X1,c(X4,X3)) != X2 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_73]),c_0_131]),c_0_131]) ).
cnf(c_0_137,plain,
m(X1,c(X2,c(c(X2,X3),X4))) = X1,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_127,c_0_113]),c_0_109]),c_0_102]) ).
cnf(c_0_138,plain,
c(c(m(X1,c(X2,X3)),X2),X4) = c(X4,c(X2,X1)),
inference(spm,[status(thm)],[c_0_102,c_0_132]) ).
cnf(c_0_139,plain,
( m(c(X1,X2),X3) = c(X1,m(X4,X2))
| m(X4,m(X1,m(X2,X3))) != m(X1,m(X4,X2)) ),
inference(spm,[status(thm)],[c_0_82,c_0_27]) ).
cnf(c_0_140,plain,
m(X1,m(X2,m(X3,c(X2,X1)))) = m(X2,m(X1,X3)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_135]),c_0_134]) ).
cnf(c_0_141,plain,
m(X1,c(X2,c(X3,c(X2,X4)))) = X1,
inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_136,c_0_137])]),c_0_102]) ).
cnf(c_0_142,plain,
m(c(c(X1,X2),X3),X1) = m(X1,c(c(X1,X2),X3)),
inference(spm,[status(thm)],[c_0_7,c_0_137]) ).
cnf(c_0_143,plain,
c(c(X1,X2),m(c(X2,X3),X4)) = c(X4,c(X2,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_132]),c_0_9]),c_0_109]),c_0_138]) ).
cnf(c_0_144,plain,
m(X1,m(X2,m(X3,m(c(m(X2,X3),X1),X4)))) = m(X2,m(X3,m(X1,X4))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_9]),c_0_9]) ).
cnf(c_0_145,plain,
m(c(X1,X2),m(X3,c(X2,X1))) = X3,
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_73]),c_0_9]),c_0_73]),c_0_9]),c_0_134]) ).
cnf(c_0_146,plain,
m(c(X1,X2),c(X1,X3)) = c(X1,m(X3,X2)),
inference(spm,[status(thm)],[c_0_139,c_0_140]) ).
cnf(c_0_147,plain,
m(c(X1,c(X2,X3)),X2) = m(X2,c(X1,c(X2,X3))),
inference(spm,[status(thm)],[c_0_7,c_0_141]) ).
cnf(c_0_148,plain,
m(c(X1,c(X2,X3)),X3) = m(X3,c(X1,c(X2,X3))),
inference(spm,[status(thm)],[c_0_142,c_0_143]) ).
cnf(c_0_149,plain,
( m(X1,m(c(m(X2,X1),X3),X4)) = c(X2,X3)
| m(X2,m(X1,m(X3,X4))) != m(X2,X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_144]) ).
cnf(c_0_150,plain,
c(X1,m(X2,m(c(X2,X1),X3))) = c(X1,m(X2,m(X1,X3))),
inference(spm,[status(thm)],[c_0_39,c_0_27]) ).
cnf(c_0_151,plain,
m(c(X1,X2),c(X2,m(X1,X3))) = c(X2,X3),
inference(spm,[status(thm)],[c_0_145,c_0_146]) ).
cnf(c_0_152,plain,
m(c(X1,X2),X3) = m(X3,c(X1,X2)),
inference(spm,[status(thm)],[c_0_99,c_0_135]) ).
cnf(c_0_153,plain,
c(m(X1,m(X2,X3)),X3) = c(m(X1,X2),X3),
inference(spm,[status(thm)],[c_0_68,c_0_9]) ).
cnf(c_0_154,plain,
m(X1,m(X2,m(X3,m(X4,m(X2,X1))))) = m(X2,m(X1,m(X3,m(X4,m(X1,X2))))),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_9]),c_0_9]) ).
cnf(c_0_155,plain,
m(X1,m(X2,m(X3,c(X3,c(X1,X2))))) = m(X2,m(X1,m(X3,c(X1,X2)))),
inference(spm,[status(thm)],[c_0_27,c_0_7]) ).
cnf(c_0_156,plain,
m(c(X1,c(X2,X3)),m(X2,X4)) = m(X2,m(c(X1,c(X2,X3)),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_147]),c_0_9]) ).
cnf(c_0_157,plain,
m(c(X1,c(X2,X3)),m(X3,X4)) = m(X3,m(c(X1,c(X2,X3)),X4)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_148]),c_0_9]) ).
cnf(c_0_158,plain,
c(m(X1,c(X2,X3)),X4) = c(X1,X4),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_149,c_0_145]),c_0_145]) ).
cnf(c_0_159,plain,
c(X1,m(X2,m(X1,X3))) = c(X1,m(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_87]),c_0_150]) ).
cnf(c_0_160,plain,
m(c(X1,X2),c(m(X3,X2),X1)) = c(X3,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_145,c_0_151]),c_0_152]) ).
cnf(c_0_161,plain,
c(m(X1,m(X2,m(X3,X4))),X4) = c(m(X1,m(X2,X3)),X4),
inference(spm,[status(thm)],[c_0_153,c_0_9]) ).
cnf(c_0_162,plain,
m(X1,m(X2,m(X3,m(X1,c(X3,X2))))) = m(X1,m(X3,m(X2,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(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_154,c_0_155]),c_0_83]),c_0_134]),c_0_156]),c_0_157]),c_0_83]),c_0_134]),c_0_87]),c_0_157]),c_0_156]),c_0_57]),c_0_134]) ).
cnf(c_0_163,plain,
c(X1,m(X2,c(X3,X4))) = c(X1,X2),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_158]),c_0_159]),c_0_158]) ).
cnf(c_0_164,negated_conjecture,
c(m(x,y),z) != m(c(x,z),c(y,z)),
distributivity ).
cnf(c_0_165,plain,
m(c(X1,X2),c(X3,X2)) = c(m(X3,X1),X2),
inference(spm,[status(thm)],[c_0_73,c_0_160]) ).
cnf(c_0_166,plain,
c(m(X1,X2),X3) = c(m(X2,X1),X3),
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_161,c_0_162]),c_0_163]),c_0_21]),c_0_153]),c_0_163]),c_0_21]) ).
cnf(c_0_167,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_164,c_0_165]),c_0_166])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP781-1 : TPTP v8.1.2. Released v5.4.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34 % Computer : n014.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue Aug 29 00:28:15 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.21/0.57 start to proof: theBenchmark
% 78.70/78.75 % Version : CSE_E---1.5
% 78.70/78.75 % Problem : theBenchmark.p
% 78.70/78.75 % Proof found
% 78.70/78.75 % SZS status Theorem for theBenchmark.p
% 78.70/78.75 % SZS output start Proof
% See solution above
% 78.70/78.76 % Total time : 78.173000 s
% 78.70/78.76 % SZS output end Proof
% 78.70/78.76 % Total time : 78.179000 s
%------------------------------------------------------------------------------