TSTP Solution File: ALG012-1 by E-SAT---3.1.00
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- Process Solution
%------------------------------------------------------------------------------
% File : E-SAT---3.1.00
% Problem : ALG012-1 : TPTP v8.2.0. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E %s %d THM
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon May 20 18:06:27 EDT 2024
% Result : Unsatisfiable 3.80s 0.94s
% Output : CNFRefutation 3.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 10
% Syntax : Number of clauses : 143 ( 11 unt; 39 nHn; 139 RR)
% Number of literals : 513 ( 2 equ; 365 neg)
% Maximal clause size : 7 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% 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 : 288 ( 23 sgn)
% Comments :
%------------------------------------------------------------------------------
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) ),
inference(fof_simplification,[status(thm)],[partitions_exclusive_c_d2]) ).
cnf(c_0_11,negated_conjecture,
( d2(f(X1,X2))
| d1(f(X1,X2))
| ~ c(X1)
| ~ c(X2) ),
inference(fof_simplification,[status(thm)],[conjecture_1]) ).
cnf(c_0_12,hypothesis,
( ~ c(X1)
| ~ d1(X1) ),
inference(fof_simplification,[status(thm)],[partitions_exclusive_c_d1]) ).
cnf(c_0_13,negated_conjecture,
( c(f(X1,X2))
| ~ d2(X1)
| ~ d2(X2) ),
inference(fof_simplification,[status(thm)],[conjecture_3]) ).
cnf(c_0_14,hypothesis,
( ~ c(X1)
| ~ d2(X1) ),
c_0_10 ).
cnf(c_0_15,negated_conjecture,
( d2(f(X1,X2))
| d1(f(X1,X2))
| ~ c(X1)
| ~ c(X2) ),
c_0_11 ).
cnf(c_0_16,hypothesis,
( ~ c(X1)
| ~ d1(X1) ),
c_0_12 ).
cnf(c_0_17,negated_conjecture,
( c(f(X1,X2))
| ~ d2(X1)
| ~ d2(X2) ),
c_0_13 ).
cnf(c_0_18,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),X3),
f_is_associative ).
cnf(c_0_19,hypothesis,
( ~ c(f(X1,X2))
| ~ c(X2)
| ~ c(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_20,negated_conjecture,
( c(f(X1,f(X2,X3)))
| ~ d2(f(X1,X2))
| ~ d2(X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,negated_conjecture,
( c(f(X1,X2))
| ~ d1(X1)
| ~ d1(X2) ),
inference(fof_simplification,[status(thm)],[conjecture_2]) ).
cnf(c_0_22,hypothesis,
( ~ d2(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X2,X3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_23,negated_conjecture,
( c(f(X1,X2))
| ~ d1(X1)
| ~ d1(X2) ),
c_0_21 ).
cnf(c_0_24,axiom,
( c(X1)
| d1(X1)
| d2(X1) ),
partitions_union ).
cnf(c_0_25,negated_conjecture,
( d1(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X2,X3))
| ~ c(X1)
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_22,c_0_15]) ).
cnf(c_0_26,negated_conjecture,
( c(f(X1,f(X2,X3)))
| ~ d1(f(X1,X2))
| ~ d1(X3) ),
inference(spm,[status(thm)],[c_0_23,c_0_18]) ).
cnf(c_0_27,hypothesis,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X2,X3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_24]) ).
cnf(c_0_28,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_25,c_0_26]) ).
cnf(c_0_29,hypothesis,
( ~ d1(f(X1,X2))
| ~ d1(X3)
| ~ c(f(X2,X3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_30,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X3)
| ~ d2(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_17]) ).
cnf(c_0_31,hypothesis,
d2(a3),
partition_d2_not_empty ).
cnf(c_0_32,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_28,c_0_24]),c_0_29]) ).
cnf(c_0_33,hypothesis,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_30,c_0_31]) ).
cnf(c_0_34,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_32,c_0_33]),c_0_25]) ).
cnf(c_0_35,hypothesis,
( ~ c(f(X1,f(X2,X3)))
| ~ c(f(X1,X2))
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_36,hypothesis,
( d1(f(a3,X1))
| d1(f(X2,X3))
| ~ d1(X1)
| ~ c(X2)
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_37,hypothesis,
c(a1),
partition_c_not_empty ).
cnf(c_0_38,hypothesis,
( ~ c(f(X1,f(X2,f(X3,X4))))
| ~ c(f(X1,f(X2,X3)))
| ~ c(X4) ),
inference(spm,[status(thm)],[c_0_35,c_0_18]) ).
cnf(c_0_39,negated_conjecture,
( ~ d2(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X3,X1))
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_17]) ).
cnf(c_0_40,hypothesis,
( d1(f(a1,X1))
| d1(f(a3,X2))
| ~ d1(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_36,c_0_37]) ).
cnf(c_0_41,negated_conjecture,
( ~ d1(f(X1,X2))
| ~ d1(f(X3,X4))
| ~ c(f(X1,f(X2,X3)))
| ~ c(X4) ),
inference(spm,[status(thm)],[c_0_38,c_0_26]) ).
cnf(c_0_42,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X3,X1))
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_39,c_0_24]) ).
cnf(c_0_43,negated_conjecture,
( d1(f(a1,f(X1,X2)))
| d1(f(a3,X3))
| ~ d2(X2)
| ~ d2(X1)
| ~ d1(X3) ),
inference(spm,[status(thm)],[c_0_40,c_0_17]) ).
cnf(c_0_44,negated_conjecture,
( ~ d2(f(X1,X2))
| ~ d2(X3)
| ~ d1(f(X3,X1))
| ~ d1(f(X2,X4))
| ~ c(X4) ),
inference(spm,[status(thm)],[c_0_41,c_0_17]) ).
cnf(c_0_45,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X3)
| ~ d2(X1)
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_42,c_0_17]) ).
cnf(c_0_46,hypothesis,
( d1(f(a1,f(X1,a3)))
| d1(f(a3,X2))
| ~ d2(X1)
| ~ d1(X2) ),
inference(spm,[status(thm)],[c_0_43,c_0_31]) ).
cnf(c_0_47,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_44,c_0_15]) ).
cnf(c_0_48,hypothesis,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(X1)
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_45,c_0_31]) ).
cnf(c_0_49,negated_conjecture,
( d1(f(X1,X2))
| ~ d2(X3)
| ~ c(f(X3,X1))
| ~ c(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_39,c_0_15]) ).
cnf(c_0_50,hypothesis,
( d1(f(a1,f(a3,a3)))
| d1(f(a3,X1))
| ~ d1(X1) ),
inference(spm,[status(thm)],[c_0_46,c_0_31]) ).
cnf(c_0_51,hypothesis,
d1(a2),
partition_d1_not_empty ).
cnf(c_0_52,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_47,c_0_48]),c_0_49]) ).
cnf(c_0_53,hypothesis,
( d1(f(a1,f(a3,a3)))
| d1(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_50,c_0_51]) ).
cnf(c_0_54,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_52,c_0_53]),c_0_37])]) ).
cnf(c_0_55,hypothesis,
( d1(f(a3,a2))
| d1(f(X1,a1))
| ~ c(f(a3,a3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_54,c_0_31]) ).
cnf(c_0_56,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_55,c_0_17]),c_0_31])]) ).
cnf(c_0_57,hypothesis,
( d1(f(a1,a1))
| d1(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_56,c_0_37]) ).
cnf(c_0_58,negated_conjecture,
( ~ d1(f(X1,X2))
| ~ d1(X3)
| ~ c(f(X3,X1))
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_35,c_0_23]) ).
cnf(c_0_59,hypothesis,
( d1(f(a1,a1))
| ~ c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_57]) ).
cnf(c_0_60,negated_conjecture,
( ~ d1(f(X1,f(X2,X3)))
| ~ d1(X4)
| ~ c(f(X4,f(X1,X2)))
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_58,c_0_18]) ).
cnf(c_0_61,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_52,c_0_59]),c_0_37])]) ).
cnf(c_0_62,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_60,c_0_33]) ).
cnf(c_0_63,hypothesis,
( d1(f(X1,a1))
| ~ c(f(a3,a2))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_61,c_0_31]) ).
cnf(c_0_64,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_62,c_0_23]) ).
cnf(c_0_65,hypothesis,
( d1(f(X1,f(X2,a1)))
| ~ c(f(a3,a2))
| ~ c(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_63,c_0_18]) ).
cnf(c_0_66,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_64,c_0_51]) ).
cnf(c_0_67,hypothesis,
( ~ c(f(X1,f(X2,a1)))
| ~ c(f(a3,a2))
| ~ c(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_65]) ).
cnf(c_0_68,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_41,c_0_66]) ).
cnf(c_0_69,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_52,c_0_63]),c_0_37])]) ).
cnf(c_0_70,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_67,c_0_18]) ).
cnf(c_0_71,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_68,c_0_15]) ).
cnf(c_0_72,hypothesis,
( d1(f(X1,X2))
| ~ c(f(a3,a2))
| ~ c(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_69,c_0_31]) ).
cnf(c_0_73,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_70,c_0_26]) ).
cnf(c_0_74,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_71,c_0_59]),c_0_37])]),c_0_72]) ).
cnf(c_0_75,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_73,c_0_23]) ).
cnf(c_0_76,hypothesis,
( d1(f(a1,X1))
| ~ c(f(a3,a2))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_74,c_0_37]) ).
cnf(c_0_77,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_75,c_0_76]),c_0_37])]) ).
cnf(c_0_78,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_29,c_0_53]),c_0_18]),c_0_37])]) ).
cnf(c_0_79,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_77,c_0_72]),c_0_37])]) ).
cnf(c_0_80,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_78,c_0_17]),c_0_31])]) ).
cnf(c_0_81,hypothesis,
( ~ d1(f(X1,f(X2,X3)))
| ~ d1(f(X1,X2))
| ~ c(f(a3,a2))
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_79,c_0_18]) ).
cnf(c_0_82,negated_conjecture,
( d1(f(a3,a2))
| d1(f(a3,X1))
| c(f(a3,X1))
| ~ d1(X1) ),
inference(spm,[status(thm)],[c_0_80,c_0_24]) ).
cnf(c_0_83,hypothesis,
( ~ d1(f(a1,X1))
| ~ c(f(a3,a2))
| ~ c(f(X1,X2))
| ~ c(X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_76]) ).
cnf(c_0_84,hypothesis,
( d1(f(a3,a2))
| c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_82,c_0_51]) ).
cnf(c_0_85,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_56,c_0_17]),c_0_18]) ).
cnf(c_0_86,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_83,c_0_53]),c_0_18]),c_0_84]) ).
cnf(c_0_87,negated_conjecture,
( c(f(X1,f(X2,f(X3,X4))))
| ~ d1(f(X1,f(X2,X3)))
| ~ d1(X4) ),
inference(spm,[status(thm)],[c_0_26,c_0_18]) ).
cnf(c_0_88,hypothesis,
( d1(f(a3,a2))
| ~ d2(X1)
| ~ d2(X2)
| ~ c(f(X2,f(X1,a1))) ),
inference(spm,[status(thm)],[c_0_16,c_0_85]) ).
cnf(c_0_89,hypothesis,
( d1(f(a3,a2))
| ~ c(f(a1,f(a3,a3))) ),
inference(spm,[status(thm)],[c_0_16,c_0_53]) ).
cnf(c_0_90,negated_conjecture,
( d1(f(a3,a2))
| ~ d1(f(a3,f(a3,X1)))
| ~ d1(X2)
| ~ c(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_86,c_0_87]) ).
cnf(c_0_91,negated_conjecture,
( d1(f(a3,a2))
| ~ d2(f(X1,a1))
| ~ d2(X1)
| ~ d2(X2) ),
inference(spm,[status(thm)],[c_0_88,c_0_17]) ).
cnf(c_0_92,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_77,c_0_76]),c_0_37])]) ).
cnf(c_0_93,negated_conjecture,
( d1(f(a3,a2))
| ~ d2(f(a1,a3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_20]),c_0_31])]) ).
cnf(c_0_94,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_90,c_0_85]),c_0_31])]) ).
cnf(c_0_95,negated_conjecture,
( d1(f(a3,a2))
| d1(f(X1,a1))
| c(f(X1,a1))
| ~ d2(X1)
| ~ d2(X2) ),
inference(spm,[status(thm)],[c_0_91,c_0_24]) ).
cnf(c_0_96,hypothesis,
( ~ d1(f(X1,f(X2,a1)))
| ~ d1(f(X1,X2))
| ~ c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_92,c_0_18]) ).
cnf(c_0_97,negated_conjecture,
( d1(f(a1,a3))
| d1(f(a3,a2))
| c(f(a1,a3)) ),
inference(spm,[status(thm)],[c_0_93,c_0_24]) ).
cnf(c_0_98,negated_conjecture,
( d1(f(a3,a2))
| ~ d1(f(a1,X1))
| ~ d1(f(X1,X2))
| ~ d1(X2) ),
inference(spm,[status(thm)],[c_0_94,c_0_26]) ).
cnf(c_0_99,negated_conjecture,
( d1(f(a3,a2))
| ~ d1(f(a3,f(a3,X1)))
| ~ d1(f(X1,X2))
| ~ d1(X2) ),
inference(spm,[status(thm)],[c_0_78,c_0_87]) ).
cnf(c_0_100,hypothesis,
( d1(f(a3,a2))
| d1(f(X1,a1))
| c(f(X1,a1))
| ~ d2(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_31]) ).
cnf(c_0_101,hypothesis,
( ~ d1(f(X1,X2))
| ~ c(f(a3,a2))
| ~ c(f(X2,a1))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_96,c_0_72]) ).
cnf(c_0_102,hypothesis,
( ~ d1(f(a1,X1))
| ~ c(f(a3,a2))
| ~ c(f(X1,a1)) ),
inference(spm,[status(thm)],[c_0_96,c_0_76]) ).
cnf(c_0_103,hypothesis,
( d1(f(a1,a3))
| c(f(a1,a3))
| ~ c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_97]) ).
cnf(c_0_104,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_98,c_0_33]),c_0_37])]) ).
cnf(c_0_105,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_99,c_0_85]),c_0_31])]) ).
cnf(c_0_106,hypothesis,
( d1(f(a3,a1))
| d1(f(a3,a2))
| c(f(a3,a1)) ),
inference(spm,[status(thm)],[c_0_100,c_0_31]) ).
cnf(c_0_107,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_101,c_0_18]) ).
cnf(c_0_108,hypothesis,
( c(f(a1,a3))
| ~ c(f(a3,a2))
| ~ c(f(a3,a1)) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]) ).
cnf(c_0_109,negated_conjecture,
( d1(f(a3,a2))
| c(f(a1,X1))
| ~ d2(X1)
| ~ d2(X2)
| ~ d1(f(X2,a1)) ),
inference(spm,[status(thm)],[c_0_104,c_0_85]) ).
cnf(c_0_110,hypothesis,
( d1(f(a3,a2))
| ~ d1(f(X1,a1))
| ~ c(f(a1,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_65]),c_0_84]) ).
cnf(c_0_111,hypothesis,
( d1(f(a3,a1))
| c(f(a3,a1))
| ~ c(f(a3,a2)) ),
inference(spm,[status(thm)],[c_0_16,c_0_106]) ).
cnf(c_0_112,hypothesis,
( d1(f(a3,a2))
| ~ c(f(a3,a1)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_53]),c_0_108]),c_0_84]) ).
cnf(c_0_113,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_109,c_0_48]),c_0_37])]) ).
cnf(c_0_114,hypothesis,
( d1(f(a3,a2))
| ~ c(f(a1,a3)) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_110,c_0_111]),c_0_84]),c_0_112]) ).
cnf(c_0_115,hypothesis,
( d1(f(a3,a2))
| c(f(X1,a1))
| ~ d2(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_31]),c_0_114]) ).
cnf(c_0_116,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_49,c_0_26]),c_0_18]) ).
cnf(c_0_117,hypothesis,
d1(f(a3,a2)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_115,c_0_31]),c_0_112]) ).
cnf(c_0_118,hypothesis,
( ~ d1(f(X1,f(X2,X3)))
| ~ d1(X4)
| ~ c(f(X3,X4))
| ~ c(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_18]) ).
cnf(c_0_119,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_116,c_0_117]),c_0_31])]) ).
cnf(c_0_120,hypothesis,
( ~ d1(X1)
| ~ d1(X2)
| ~ c(f(a2,X2))
| ~ c(f(X3,X1))
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_118,c_0_119]) ).
cnf(c_0_121,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_120,c_0_23]),c_0_51])]) ).
cnf(c_0_122,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_60,c_0_48]) ).
cnf(c_0_123,negated_conjecture,
( ~ d1(f(X1,X2))
| ~ d1(f(X3,X1))
| ~ d1(X4)
| ~ d1(X2)
| ~ c(X3) ),
inference(spm,[status(thm)],[c_0_121,c_0_26]) ).
cnf(c_0_124,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_122,c_0_23]) ).
cnf(c_0_125,hypothesis,
( ~ d1(f(X1,a3))
| ~ d1(X2)
| ~ c(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_117]),c_0_51])]) ).
cnf(c_0_126,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_124,c_0_51]) ).
cnf(c_0_127,hypothesis,
( c(f(X1,a3))
| ~ d1(X2)
| ~ c(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_125,c_0_33]),c_0_31])]) ).
cnf(c_0_128,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_41,c_0_126]) ).
cnf(c_0_129,hypothesis,
( c(f(X1,a3))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_127,c_0_51]) ).
cnf(c_0_130,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_44,c_0_24]) ).
cnf(c_0_131,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_128,c_0_117]),c_0_31])]) ).
cnf(c_0_132,negated_conjecture,
( d1(f(X1,X2))
| ~ c(X1)
| ~ c(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_129]),c_0_31])]) ).
cnf(c_0_133,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_130,c_0_117]),c_0_31])]) ).
cnf(c_0_134,negated_conjecture,
( ~ c(f(a2,X1))
| ~ c(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_131,c_0_132]) ).
cnf(c_0_135,negated_conjecture,
( ~ d1(f(X1,X2))
| ~ d1(f(X3,X4))
| ~ d1(X3)
| ~ c(X4) ),
inference(spm,[status(thm)],[c_0_41,c_0_26]) ).
cnf(c_0_136,hypothesis,
( d1(f(a1,a1))
| d1(f(a3,X1))
| ~ d1(X1) ),
inference(spm,[status(thm)],[c_0_40,c_0_37]) ).
cnf(c_0_137,negated_conjecture,
( d1(f(a2,X1))
| ~ c(X2)
| ~ c(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_133,c_0_132]),c_0_134]) ).
cnf(c_0_138,negated_conjecture,
( ~ d1(f(X1,X2))
| ~ d1(X1)
| ~ d1(X3)
| ~ c(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_135,c_0_136]),c_0_135]) ).
cnf(c_0_139,hypothesis,
( d1(f(a2,X1))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_137,c_0_37]) ).
cnf(c_0_140,negated_conjecture,
( ~ d1(X1)
| ~ c(X2) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_138,c_0_139]),c_0_51])]) ).
cnf(c_0_141,hypothesis,
~ c(X1),
inference(spm,[status(thm)],[c_0_140,c_0_51]) ).
cnf(c_0_142,hypothesis,
$false,
inference(sr,[status(thm)],[c_0_37,c_0_141]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : ALG012-1 : TPTP v8.2.0. Released v2.7.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n006.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 : Sat May 18 22:39:53 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.20/0.47 Running first-order model finding
% 0.20/0.47 Running: /export/starexec/sandbox/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --satauto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.80/0.94 # Version: 3.1.0
% 3.80/0.94 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.80/0.94 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.80/0.94 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.80/0.94 # Starting new_bool_3 with 300s (1) cores
% 3.80/0.94 # Starting new_bool_1 with 300s (1) cores
% 3.80/0.94 # Starting sh5l with 300s (1) cores
% 3.80/0.94 # G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 4160 completed with status 0
% 3.80/0.94 # Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 3.80/0.94 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.80/0.94 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.80/0.94 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.80/0.94 # No SInE strategy applied
% 3.80/0.94 # Search class: FGHSF-FFSS22-SFFFFFNN
% 3.80/0.94 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.80/0.94 # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 3.80/0.94 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 3.80/0.94 # Starting new_bool_3 with 136s (1) cores
% 3.80/0.94 # Starting new_bool_1 with 136s (1) cores
% 3.80/0.94 # Starting sh5l with 136s (1) cores
% 3.80/0.94 # SAT001_MinMin_p005000_rr_RG with pid 4164 completed with status 0
% 3.80/0.94 # Result found by SAT001_MinMin_p005000_rr_RG
% 3.80/0.94 # Preprocessing class: FSMSSMSSSSSNFFN.
% 3.80/0.94 # Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 3.80/0.94 # Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 3.80/0.94 # No SInE strategy applied
% 3.80/0.94 # Search class: FGHSF-FFSS22-SFFFFFNN
% 3.80/0.94 # Scheduled 6 strats onto 5 cores with 1500 seconds (1500 total)
% 3.80/0.94 # Starting SAT001_MinMin_p005000_rr_RG with 811s (1) cores
% 3.80/0.94 # Preprocessing time : 0.001 s
% 3.80/0.94 # Presaturation interreduction done
% 3.80/0.94
% 3.80/0.94 # Proof found!
% 3.80/0.94 # SZS status Unsatisfiable
% 3.80/0.94 # SZS output start CNFRefutation
% See solution above
% 3.80/0.94 # Parsed axioms : 11
% 3.80/0.94 # Removed by relevancy pruning/SinE : 0
% 3.80/0.94 # Initial clauses : 11
% 3.80/0.94 # Removed in clause preprocessing : 0
% 3.80/0.94 # Initial clauses in saturation : 11
% 3.80/0.94 # Processed clauses : 4315
% 3.80/0.94 # ...of these trivial : 0
% 3.80/0.94 # ...subsumed : 3006
% 3.80/0.94 # ...remaining for further processing : 1309
% 3.80/0.94 # Other redundant clauses eliminated : 0
% 3.80/0.94 # Clauses deleted for lack of memory : 0
% 3.80/0.94 # Backward-subsumed : 1190
% 3.80/0.94 # Backward-rewritten : 62
% 3.80/0.94 # Generated clauses : 21333
% 3.80/0.94 # ...of the previous two non-redundant : 21160
% 3.80/0.94 # ...aggressively subsumed : 0
% 3.80/0.94 # Contextual simplify-reflections : 56
% 3.80/0.94 # Paramodulations : 21331
% 3.80/0.94 # Factorizations : 0
% 3.80/0.94 # NegExts : 0
% 3.80/0.94 # Equation resolutions : 0
% 3.80/0.94 # Disequality decompositions : 0
% 3.80/0.94 # Total rewrite steps : 8977
% 3.80/0.94 # ...of those cached : 8793
% 3.80/0.94 # Propositional unsat checks : 0
% 3.80/0.94 # Propositional check models : 0
% 3.80/0.94 # Propositional check unsatisfiable : 0
% 3.80/0.94 # Propositional clauses : 0
% 3.80/0.94 # Propositional clauses after purity: 0
% 3.80/0.94 # Propositional unsat core size : 0
% 3.80/0.94 # Propositional preprocessing time : 0.000
% 3.80/0.94 # Propositional encoding time : 0.000
% 3.80/0.94 # Propositional solver time : 0.000
% 3.80/0.94 # Success case prop preproc time : 0.000
% 3.80/0.94 # Success case prop encoding time : 0.000
% 3.80/0.94 # Success case prop solver time : 0.000
% 3.80/0.94 # Current number of processed clauses : 44
% 3.80/0.94 # Positive orientable unit clauses : 4
% 3.80/0.94 # Positive unorientable unit clauses: 0
% 3.80/0.94 # Negative unit clauses : 4
% 3.80/0.94 # Non-unit-clauses : 36
% 3.80/0.94 # Current number of unprocessed clauses: 15714
% 3.80/0.94 # ...number of literals in the above : 113965
% 3.80/0.94 # Current number of archived formulas : 0
% 3.80/0.94 # Current number of archived clauses : 1265
% 3.80/0.94 # Clause-clause subsumption calls (NU) : 281516
% 3.80/0.94 # Rec. Clause-clause subsumption calls : 57955
% 3.80/0.94 # Non-unit clause-clause subsumptions : 2856
% 3.80/0.94 # Unit Clause-clause subsumption calls : 1938
% 3.80/0.94 # Rewrite failures with RHS unbound : 0
% 3.80/0.94 # BW rewrite match attempts : 1
% 3.80/0.94 # BW rewrite match successes : 1
% 3.80/0.94 # Condensation attempts : 0
% 3.80/0.94 # Condensation successes : 0
% 3.80/0.94 # Termbank termtop insertions : 450487
% 3.80/0.94 # Search garbage collected termcells : 18
% 3.80/0.94
% 3.80/0.94 # -------------------------------------------------
% 3.80/0.94 # User time : 0.450 s
% 3.80/0.94 # System time : 0.012 s
% 3.80/0.94 # Total time : 0.462 s
% 3.80/0.94 # Maximum resident set size: 1652 pages
% 3.80/0.94
% 3.80/0.94 # -------------------------------------------------
% 3.80/0.94 # User time : 2.242 s
% 3.80/0.94 # System time : 0.035 s
% 3.80/0.94 # Total time : 2.277 s
% 3.80/0.94 # Maximum resident set size: 1692 pages
% 3.80/0.94 % E---3.1 exiting
%------------------------------------------------------------------------------