TSTP Solution File: ALG012-1 by CSE_E---1.5
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- Process Solution
%------------------------------------------------------------------------------
% File : CSE_E---1.5
% Problem : ALG012-1 : TPTP v8.1.2. Released v2.7.0.
% 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 : Wed Aug 30 16:00:05 EDT 2023
% Result : Unsatisfiable 0.96s 1.03s
% Output : CNFRefutation 0.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 17
% Syntax : Number of formulae : 145 ( 11 unt; 7 typ; 0 def)
% Number of atoms : 499 ( 2 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 716 ( 355 ~; 361 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 4 >; 1 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 280 ( 23 sgn; 0 !; 0 ?; 0 :)
% Comments :
%------------------------------------------------------------------------------
tff(decl_22,type,
f: ( $i * $i ) > $i ).
tff(decl_23,type,
c: $i > $o ).
tff(decl_24,type,
d1: $i > $o ).
tff(decl_25,type,
d2: $i > $o ).
tff(decl_26,type,
a1: $i ).
tff(decl_27,type,
a2: $i ).
tff(decl_28,type,
a3: $i ).
cnf(partitions_exclusive_c_d2,hypothesis,
( ~ c(X1)
| ~ d2(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d2) ).
cnf(conjecture_1,negated_conjecture,
( d2(f(X1,X2))
| d1(f(X1,X2))
| ~ c(X1)
| ~ c(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_1) ).
cnf(partitions_exclusive_c_d1,hypothesis,
( ~ c(X1)
| ~ d1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d1) ).
cnf(conjecture_3,negated_conjecture,
( c(f(X1,X2))
| ~ d2(X1)
| ~ d2(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_3) ).
cnf(f_is_associative,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',f_is_associative) ).
cnf(conjecture_2,negated_conjecture,
( c(f(X1,X2))
| ~ d1(X1)
| ~ d1(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_2) ).
cnf(partitions_union,axiom,
( c(X1)
| d1(X1)
| d2(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_union) ).
cnf(partition_d2_not_empty,hypothesis,
d2(a3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d2_not_empty) ).
cnf(partition_c_not_empty,hypothesis,
c(a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_c_not_empty) ).
cnf(partition_d1_not_empty,hypothesis,
d1(a2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d1_not_empty) ).
cnf(c_0_10,hypothesis,
( ~ c(X1)
| ~ d2(X1) ),
partitions_exclusive_c_d2 ).
cnf(c_0_11,negated_conjecture,
( d2(f(X1,X2))
| d1(f(X1,X2))
| ~ c(X1)
| ~ c(X2) ),
conjecture_1 ).
cnf(c_0_12,hypothesis,
( ~ c(X1)
| ~ d1(X1) ),
partitions_exclusive_c_d1 ).
cnf(c_0_13,negated_conjecture,
( c(f(X1,X2))
| ~ d2(X1)
| ~ d2(X2) ),
conjecture_3 ).
cnf(c_0_14,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),X3),
f_is_associative ).
cnf(c_0_15,hypothesis,
( ~ c(f(X1,X2))
| ~ c(X2)
| ~ c(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_11]),c_0_12]) ).
cnf(c_0_16,negated_conjecture,
( c(f(X1,f(X2,X3)))
| ~ d2(f(X1,X2))
| ~ d2(X3) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,hypothesis,
( ~ d2(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X2,X3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_18,negated_conjecture,
( c(f(X1,X2))
| ~ d1(X1)
| ~ d1(X2) ),
conjecture_2 ).
cnf(c_0_19,axiom,
( c(X1)
| d1(X1)
| d2(X1) ),
partitions_union ).
cnf(c_0_20,negated_conjecture,
( d1(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X2,X3))
| ~ c(X1)
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_17,c_0_11]) ).
cnf(c_0_21,negated_conjecture,
( c(f(X1,f(X2,X3)))
| ~ d1(f(X1,X2))
| ~ d1(X3) ),
inference(spm,[status(thm)],[c_0_18,c_0_14]) ).
cnf(c_0_22,hypothesis,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X2,X3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_17,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( d1(f(X1,X2))
| ~ d2(f(X3,X4))
| ~ d1(f(X2,X3))
| ~ d1(X4)
| ~ c(X1)
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,hypothesis,
( ~ d1(f(X1,X2))
| ~ d1(X3)
| ~ c(f(X2,X3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_15,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X3)
| ~ d2(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_13]) ).
cnf(c_0_26,hypothesis,
d2(a3),
partition_d2_not_empty ).
cnf(c_0_27,negated_conjecture,
( d1(f(X1,X2))
| d1(f(X3,X4))
| ~ d1(f(X4,X1))
| ~ d1(X2)
| ~ c(X3)
| ~ c(X4) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_19]),c_0_24]) ).
cnf(c_0_28,hypothesis,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_29,hypothesis,
( d1(f(X1,X2))
| d1(f(X3,X4))
| ~ d2(X3)
| ~ d1(X4)
| ~ c(X1)
| ~ c(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_20]) ).
cnf(c_0_30,hypothesis,
( ~ c(f(X1,f(X2,X3)))
| ~ c(f(X1,X2))
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_15,c_0_14]) ).
cnf(c_0_31,hypothesis,
( d1(f(a3,X1))
| d1(f(X2,X3))
| ~ d1(X1)
| ~ c(X2)
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_29,c_0_26]) ).
cnf(c_0_32,hypothesis,
c(a1),
partition_c_not_empty ).
cnf(c_0_33,hypothesis,
( ~ c(f(X1,f(X2,f(X3,X4))))
| ~ c(f(X1,f(X2,X3)))
| ~ c(X4) ),
inference(spm,[status(thm)],[c_0_30,c_0_14]) ).
cnf(c_0_34,negated_conjecture,
( ~ d2(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X3,X1))
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_13]) ).
cnf(c_0_35,hypothesis,
( d1(f(a1,X1))
| d1(f(a3,X2))
| ~ d1(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_36,negated_conjecture,
( ~ d1(f(X1,X2))
| ~ d1(f(X3,X4))
| ~ c(f(X1,f(X2,X3)))
| ~ c(X4) ),
inference(spm,[status(thm)],[c_0_33,c_0_21]) ).
cnf(c_0_37,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X3,X1))
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_34,c_0_19]) ).
cnf(c_0_38,negated_conjecture,
( d1(f(a1,f(X1,X2)))
| d1(f(a3,X3))
| ~ d2(X2)
| ~ d2(X1)
| ~ d1(X3) ),
inference(spm,[status(thm)],[c_0_35,c_0_13]) ).
cnf(c_0_39,negated_conjecture,
( ~ d2(f(X1,X2))
| ~ d2(X3)
| ~ d1(f(X3,X1))
| ~ d1(f(X2,X4))
| ~ c(X4) ),
inference(spm,[status(thm)],[c_0_36,c_0_13]) ).
cnf(c_0_40,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X3)
| ~ d2(X1)
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_37,c_0_13]) ).
cnf(c_0_41,hypothesis,
( d1(f(a1,f(X1,a3)))
| d1(f(a3,X2))
| ~ d2(X1)
| ~ d1(X2) ),
inference(spm,[status(thm)],[c_0_38,c_0_26]) ).
cnf(c_0_42,negated_conjecture,
( d1(f(X1,X2))
| ~ d2(X3)
| ~ d1(f(X3,X1))
| ~ d1(f(X2,X4))
| ~ c(X4)
| ~ c(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_11]) ).
cnf(c_0_43,hypothesis,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X1)
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_26]) ).
cnf(c_0_44,negated_conjecture,
( d1(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X3,X1))
| ~ c(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_11]) ).
cnf(c_0_45,hypothesis,
( d1(f(a1,f(a3,a3)))
| d1(f(a3,X1))
| ~ d1(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_26]) ).
cnf(c_0_46,hypothesis,
d1(a2),
partition_d1_not_empty ).
cnf(c_0_47,hypothesis,
( d1(f(X1,X2))
| ~ d2(X3)
| ~ d1(f(X2,X4))
| ~ c(X4)
| ~ c(X2)
| ~ c(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_44]) ).
cnf(c_0_48,hypothesis,
( d1(f(a1,f(a3,a3)))
| d1(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_49,hypothesis,
( d1(f(a3,a2))
| d1(f(X1,a1))
| ~ d2(X2)
| ~ c(f(a3,a3))
| ~ c(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_32])]) ).
cnf(c_0_50,hypothesis,
( d1(f(a3,a2))
| d1(f(X1,a1))
| ~ c(f(a3,a3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_49,c_0_26]) ).
cnf(c_0_51,negated_conjecture,
( d1(f(a3,a2))
| d1(f(X1,a1))
| ~ c(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_13]),c_0_26])]) ).
cnf(c_0_52,hypothesis,
( d1(f(a1,a1))
| d1(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_51,c_0_32]) ).
cnf(c_0_53,negated_conjecture,
( ~ d1(f(X1,X2))
| ~ d1(X3)
| ~ c(f(X3,X1))
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_30,c_0_18]) ).
cnf(c_0_54,hypothesis,
( d1(f(a1,a1))
| ~ c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_52]) ).
cnf(c_0_55,negated_conjecture,
( ~ d1(f(X1,f(X2,X3)))
| ~ d1(X4)
| ~ c(f(X4,f(X1,X2)))
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_14]) ).
cnf(c_0_56,hypothesis,
( d1(f(X1,a1))
| ~ d2(X2)
| ~ c(f(a3,a2))
| ~ c(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_54]),c_0_32])]) ).
cnf(c_0_57,negated_conjecture,
( c(f(X1,f(X2,X3)))
| ~ d2(f(X2,X3))
| ~ d1(X4)
| ~ c(f(X4,f(X1,X2)))
| ~ c(X3)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_55,c_0_28]) ).
cnf(c_0_58,hypothesis,
( d1(f(X1,a1))
| ~ c(f(a3,a2))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_56,c_0_26]) ).
cnf(c_0_59,negated_conjecture,
( c(f(X1,f(X2,X3)))
| ~ d2(f(X2,X3))
| ~ d1(f(X1,X2))
| ~ d1(X4)
| ~ c(X3)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_57,c_0_18]) ).
cnf(c_0_60,hypothesis,
( d1(f(X1,f(X2,a1)))
| ~ c(f(a3,a2))
| ~ c(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_58,c_0_14]) ).
cnf(c_0_61,hypothesis,
( c(f(X1,f(X2,X3)))
| ~ d2(f(X2,X3))
| ~ d1(f(X1,X2))
| ~ c(X3)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_59,c_0_46]) ).
cnf(c_0_62,hypothesis,
( ~ c(f(X1,f(X2,a1)))
| ~ c(f(a3,a2))
| ~ c(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_60]) ).
cnf(c_0_63,negated_conjecture,
( ~ d2(f(X1,X2))
| ~ d1(f(X3,X1))
| ~ d1(f(X2,X4))
| ~ c(X4)
| ~ c(X2)
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_61]) ).
cnf(c_0_64,hypothesis,
( d1(f(X1,X2))
| ~ d2(X3)
| ~ c(f(a3,a2))
| ~ c(X2)
| ~ c(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_58]),c_0_32])]) ).
cnf(c_0_65,hypothesis,
( ~ c(f(X1,f(X2,f(X3,a1))))
| ~ c(f(X1,f(X2,X3)))
| ~ c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_62,c_0_14]) ).
cnf(c_0_66,negated_conjecture,
( d1(f(X1,X2))
| ~ d1(f(X3,X1))
| ~ d1(f(X2,X4))
| ~ c(X4)
| ~ c(X2)
| ~ c(X3)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_63,c_0_11]) ).
cnf(c_0_67,hypothesis,
( d1(f(X1,X2))
| ~ c(f(a3,a2))
| ~ c(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_64,c_0_26]) ).
cnf(c_0_68,negated_conjecture,
( ~ d1(f(X1,a1))
| ~ d1(f(X2,X3))
| ~ c(f(X2,f(X3,X1)))
| ~ c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_65,c_0_21]) ).
cnf(c_0_69,negated_conjecture,
( d1(f(a1,X1))
| ~ c(f(a3,a2))
| ~ c(X2)
| ~ c(X1) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_54]),c_0_32])]),c_0_67]) ).
cnf(c_0_70,negated_conjecture,
( ~ d1(f(X1,a1))
| ~ d1(f(X2,X3))
| ~ d1(f(X3,X1))
| ~ d1(X2)
| ~ c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_68,c_0_18]) ).
cnf(c_0_71,hypothesis,
( d1(f(a1,X1))
| ~ c(f(a3,a2))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_32]) ).
cnf(c_0_72,hypothesis,
( ~ d1(f(X1,a1))
| ~ d1(f(X2,X1))
| ~ d1(X2)
| ~ c(f(a3,a2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_32])]) ).
cnf(c_0_73,hypothesis,
( d1(f(a3,a2))
| ~ d1(X1)
| ~ c(f(a3,f(a3,X1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_48]),c_0_14]),c_0_32])]) ).
cnf(c_0_74,hypothesis,
( ~ d1(f(X1,X2))
| ~ d1(X1)
| ~ c(f(a3,a2))
| ~ c(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_67]),c_0_32])]) ).
cnf(c_0_75,negated_conjecture,
( d1(f(a3,a2))
| ~ d2(f(a3,X1))
| ~ d1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_13]),c_0_26])]) ).
cnf(c_0_76,hypothesis,
( ~ d1(f(X1,f(X2,X3)))
| ~ d1(f(X1,X2))
| ~ c(f(a3,a2))
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_74,c_0_14]) ).
cnf(c_0_77,negated_conjecture,
( d1(f(a3,a2))
| d1(f(a3,X1))
| c(f(a3,X1))
| ~ d1(X1) ),
inference(spm,[status(thm)],[c_0_75,c_0_19]) ).
cnf(c_0_78,hypothesis,
( ~ d1(f(a1,X1))
| ~ c(f(a3,a2))
| ~ c(f(X1,X2))
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_71]) ).
cnf(c_0_79,hypothesis,
( d1(f(a3,a2))
| c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_77,c_0_46]) ).
cnf(c_0_80,negated_conjecture,
( d1(f(X1,f(X2,a1)))
| d1(f(a3,a2))
| ~ d2(X2)
| ~ d2(X1) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_13]),c_0_14]) ).
cnf(c_0_81,hypothesis,
( d1(f(a3,a2))
| ~ c(f(a3,f(a3,X1)))
| ~ c(X1) ),
inference(csr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_48]),c_0_14]),c_0_79]) ).
cnf(c_0_82,negated_conjecture,
( c(f(X1,f(X2,f(X3,X4))))
| ~ d1(f(X1,f(X2,X3)))
| ~ d1(X4) ),
inference(spm,[status(thm)],[c_0_21,c_0_14]) ).
cnf(c_0_83,hypothesis,
( d1(f(a3,a2))
| ~ d2(X1)
| ~ d2(X2)
| ~ c(f(X2,f(X1,a1))) ),
inference(spm,[status(thm)],[c_0_12,c_0_80]) ).
cnf(c_0_84,hypothesis,
( d1(f(a3,a2))
| ~ c(f(a1,f(a3,a3))) ),
inference(spm,[status(thm)],[c_0_12,c_0_48]) ).
cnf(c_0_85,negated_conjecture,
( d1(f(a3,a2))
| ~ d1(f(a3,f(a3,X1)))
| ~ d1(X2)
| ~ c(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_81,c_0_82]) ).
cnf(c_0_86,negated_conjecture,
( d1(f(a3,a2))
| ~ d2(f(X1,a1))
| ~ d2(X1)
| ~ d2(X2) ),
inference(spm,[status(thm)],[c_0_83,c_0_13]) ).
cnf(c_0_87,hypothesis,
( ~ d1(f(X1,a1))
| ~ d1(X1)
| ~ c(f(a3,a2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_71]),c_0_32])]) ).
cnf(c_0_88,negated_conjecture,
( d1(f(a3,a2))
| ~ d2(f(a1,a3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_16]),c_0_26])]) ).
cnf(c_0_89,negated_conjecture,
( d1(f(a3,a2))
| ~ d1(X1)
| ~ c(f(a1,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_80]),c_0_26])]) ).
cnf(c_0_90,negated_conjecture,
( d1(f(a3,a2))
| d1(f(X1,a1))
| c(f(X1,a1))
| ~ d2(X1)
| ~ d2(X2) ),
inference(spm,[status(thm)],[c_0_86,c_0_19]) ).
cnf(c_0_91,hypothesis,
( ~ d1(f(X1,f(X2,a1)))
| ~ d1(f(X1,X2))
| ~ c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_87,c_0_14]) ).
cnf(c_0_92,negated_conjecture,
( d1(f(a1,a3))
| d1(f(a3,a2))
| c(f(a1,a3)) ),
inference(spm,[status(thm)],[c_0_88,c_0_19]) ).
cnf(c_0_93,negated_conjecture,
( d1(f(a3,a2))
| ~ d1(f(a1,X1))
| ~ d1(f(X1,X2))
| ~ d1(X2) ),
inference(spm,[status(thm)],[c_0_89,c_0_21]) ).
cnf(c_0_94,negated_conjecture,
( d1(f(a3,a2))
| ~ d1(f(a3,f(a3,X1)))
| ~ d1(f(X1,X2))
| ~ d1(X2) ),
inference(spm,[status(thm)],[c_0_73,c_0_82]) ).
cnf(c_0_95,hypothesis,
( d1(f(a3,a2))
| d1(f(X1,a1))
| c(f(X1,a1))
| ~ d2(X1) ),
inference(spm,[status(thm)],[c_0_90,c_0_26]) ).
cnf(c_0_96,hypothesis,
( ~ d1(f(X1,X2))
| ~ c(f(a3,a2))
| ~ c(f(X2,a1))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_91,c_0_67]) ).
cnf(c_0_97,hypothesis,
( ~ d1(f(a1,X1))
| ~ c(f(a3,a2))
| ~ c(f(X1,a1)) ),
inference(spm,[status(thm)],[c_0_91,c_0_71]) ).
cnf(c_0_98,hypothesis,
( d1(f(a1,a3))
| c(f(a1,a3))
| ~ c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_92]) ).
cnf(c_0_99,hypothesis,
( d1(f(a3,a2))
| c(f(a1,X1))
| ~ d2(X1)
| ~ d1(f(X1,X2))
| ~ d1(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_93,c_0_28]),c_0_32])]) ).
cnf(c_0_100,negated_conjecture,
( d1(f(a3,a2))
| ~ d1(f(a1,X1))
| ~ d1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_80]),c_0_26])]) ).
cnf(c_0_101,hypothesis,
( d1(f(a3,a1))
| d1(f(a3,a2))
| c(f(a3,a1)) ),
inference(spm,[status(thm)],[c_0_95,c_0_26]) ).
cnf(c_0_102,hypothesis,
( ~ d1(f(X1,f(X2,X3)))
| ~ c(f(a3,a2))
| ~ c(f(X3,a1))
| ~ c(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_96,c_0_14]) ).
cnf(c_0_103,hypothesis,
( c(f(a1,a3))
| ~ c(f(a3,a2))
| ~ c(f(a3,a1)) ),
inference(spm,[status(thm)],[c_0_97,c_0_98]) ).
cnf(c_0_104,negated_conjecture,
( d1(f(a3,a2))
| c(f(a1,X1))
| ~ d2(X1)
| ~ d2(X2)
| ~ d1(f(X2,a1)) ),
inference(spm,[status(thm)],[c_0_99,c_0_80]) ).
cnf(c_0_105,hypothesis,
( d1(f(a3,a2))
| ~ d1(f(X1,a1))
| ~ c(f(a1,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_100,c_0_60]),c_0_79]) ).
cnf(c_0_106,hypothesis,
( d1(f(a3,a1))
| c(f(a3,a1))
| ~ c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_12,c_0_101]) ).
cnf(c_0_107,hypothesis,
( d1(f(a3,a2))
| ~ c(f(a3,a1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_102,c_0_48]),c_0_103]),c_0_79]) ).
cnf(c_0_108,hypothesis,
( d1(f(a3,a2))
| c(f(X1,a1))
| c(f(a1,X2))
| ~ d2(X2)
| ~ d2(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_104,c_0_43]),c_0_32])]) ).
cnf(c_0_109,hypothesis,
( d1(f(a3,a2))
| ~ c(f(a1,a3)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_106]),c_0_79]),c_0_107]) ).
cnf(c_0_110,hypothesis,
( d1(f(a3,a2))
| c(f(X1,a1))
| ~ d2(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_108,c_0_26]),c_0_109]) ).
cnf(c_0_111,negated_conjecture,
( d1(f(X1,f(X2,X3)))
| ~ d2(X4)
| ~ d1(f(X4,X1))
| ~ d1(X2)
| ~ c(f(X1,X2))
| ~ c(X3) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_21]),c_0_14]) ).
cnf(c_0_112,hypothesis,
d1(f(a3,a2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_26]),c_0_107]) ).
cnf(c_0_113,hypothesis,
( ~ d1(f(X1,f(X2,X3)))
| ~ d1(X4)
| ~ c(f(X3,X4))
| ~ c(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_24,c_0_14]) ).
cnf(c_0_114,negated_conjecture,
( d1(f(a2,f(X1,X2)))
| ~ d1(X1)
| ~ c(f(a2,X1))
| ~ c(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_26])]) ).
cnf(c_0_115,hypothesis,
( ~ d1(X1)
| ~ d1(X2)
| ~ c(f(a2,X2))
| ~ c(f(X3,X1))
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_113,c_0_114]) ).
cnf(c_0_116,negated_conjecture,
( ~ d1(X1)
| ~ d1(X2)
| ~ c(f(X3,X1))
| ~ c(X3) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_18]),c_0_46])]) ).
cnf(c_0_117,negated_conjecture,
( c(f(X1,f(X2,X3)))
| ~ d2(X1)
| ~ d1(X4)
| ~ c(f(X4,f(X1,X2)))
| ~ c(f(X2,X3))
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_43]) ).
cnf(c_0_118,negated_conjecture,
( ~ d1(f(X1,X2))
| ~ d1(f(X3,X1))
| ~ d1(X4)
| ~ d1(X2)
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_116,c_0_21]) ).
cnf(c_0_119,negated_conjecture,
( c(f(X1,f(X2,X3)))
| ~ d2(X1)
| ~ d1(f(X1,X2))
| ~ d1(X4)
| ~ c(f(X2,X3))
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_117,c_0_18]) ).
cnf(c_0_120,hypothesis,
( ~ d1(f(X1,a3))
| ~ d1(X2)
| ~ c(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_118,c_0_112]),c_0_46])]) ).
cnf(c_0_121,hypothesis,
( c(f(X1,f(X2,X3)))
| ~ d2(X1)
| ~ d1(f(X1,X2))
| ~ c(f(X2,X3))
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_119,c_0_46]) ).
cnf(c_0_122,hypothesis,
( c(f(X1,a3))
| ~ d1(X2)
| ~ c(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_28]),c_0_26])]) ).
cnf(c_0_123,negated_conjecture,
( ~ d2(X1)
| ~ d1(f(X1,X2))
| ~ d1(f(X3,X4))
| ~ c(f(X2,X3))
| ~ c(X4)
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_36,c_0_121]) ).
cnf(c_0_124,hypothesis,
( c(f(X1,a3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_122,c_0_46]) ).
cnf(c_0_125,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X3)
| ~ d1(f(X3,X1))
| ~ d1(f(X2,X4))
| ~ c(X4) ),
inference(spm,[status(thm)],[c_0_39,c_0_19]) ).
cnf(c_0_126,negated_conjecture,
( ~ d1(f(X1,X2))
| ~ c(f(a2,X1))
| ~ c(X2)
| ~ c(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_112]),c_0_26])]) ).
cnf(c_0_127,negated_conjecture,
( d1(f(X1,X2))
| ~ c(X1)
| ~ c(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_124]),c_0_26])]) ).
cnf(c_0_128,negated_conjecture,
( d1(f(a2,X1))
| c(f(a2,X1))
| ~ d1(f(X1,X2))
| ~ c(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_112]),c_0_26])]) ).
cnf(c_0_129,negated_conjecture,
( ~ c(f(a2,X1))
| ~ c(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_126,c_0_127]) ).
cnf(c_0_130,negated_conjecture,
( ~ d1(f(X1,X2))
| ~ d1(f(X3,X4))
| ~ d1(X3)
| ~ c(X4) ),
inference(spm,[status(thm)],[c_0_36,c_0_21]) ).
cnf(c_0_131,hypothesis,
( d1(f(a1,a1))
| d1(f(a3,X1))
| ~ d1(X1) ),
inference(spm,[status(thm)],[c_0_35,c_0_32]) ).
cnf(c_0_132,negated_conjecture,
( d1(f(a2,X1))
| ~ c(X2)
| ~ c(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_128,c_0_127]),c_0_129]) ).
cnf(c_0_133,negated_conjecture,
( ~ d1(f(X1,X2))
| ~ d1(X1)
| ~ d1(X3)
| ~ c(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_130,c_0_131]),c_0_130]) ).
cnf(c_0_134,hypothesis,
( d1(f(a2,X1))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_132,c_0_32]) ).
cnf(c_0_135,negated_conjecture,
( ~ d1(X1)
| ~ c(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_134]),c_0_46])]) ).
cnf(c_0_136,hypothesis,
~ c(X1),
inference(spm,[status(thm)],[c_0_135,c_0_46]) ).
cnf(c_0_137,hypothesis,
$false,
inference(sr,[status(thm)],[c_0_32,c_0_136]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG012-1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13 % Command : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.17/0.34 % Computer : n013.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Mon Aug 28 02:38:17 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.19/0.56 start to proof: theBenchmark
% 0.96/1.03 % Version : CSE_E---1.5
% 0.96/1.03 % Problem : theBenchmark.p
% 0.96/1.03 % Proof found
% 0.96/1.03 % SZS status Theorem for theBenchmark.p
% 0.96/1.03 % SZS output start Proof
% See solution above
% 0.96/1.04 % Total time : 0.462000 s
% 0.96/1.04 % SZS output end Proof
% 0.96/1.04 % Total time : 0.464000 s
%------------------------------------------------------------------------------