%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 11:50:13 AM UTC 2026
% Result : Unsatisfiable 2.93s 0.95s
% Output : CNFRefutation 2.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 11
% Syntax : Number of clauses : 115 ( 12 unt; 35 nHn; 111 RR)
% Number of literals : 368 ( 2 equ; 240 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 : 204 ( 16 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(partitions_exclusive_c_d2,hypothesis,
( ~ d2(X1)
| ~ c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_exclusive_c_d2) ).
cnf(conjecture_1,negated_conjecture,
( ~ c(X2)
| ~ c(X1)
| d1(f(X1,X2))
| d2(f(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_1) ).
cnf(partitions_exclusive_c_d1,hypothesis,
( ~ d1(X1)
| ~ c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_exclusive_c_d1) ).
cnf(conjecture_3,negated_conjecture,
( ~ d2(X2)
| ~ d2(X1)
| c(f(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_3) ).
cnf(f_is_associative,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f_is_associative) ).
cnf(conjecture_2,negated_conjecture,
( ~ d1(X2)
| ~ d1(X1)
| c(f(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conjecture_2) ).
cnf(partitions_union,axiom,
( d2(X1)
| d1(X1)
| c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_union) ).
cnf(partition_d2_not_empty,hypothesis,
d2(a3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_d2_not_empty) ).
cnf(partition_c_not_empty,hypothesis,
c(a1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_c_not_empty) ).
cnf(partitions_exclusive_d1_d2,hypothesis,
( ~ d2(X1)
| ~ d1(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partitions_exclusive_d1_d2) ).
cnf(partition_d1_not_empty,hypothesis,
d1(a2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',partition_d1_not_empty) ).
cnf(c_0_11,hypothesis,
( ~ d2(X1)
| ~ c(X1) ),
inference(fof_simplification,[status(thm)],[partitions_exclusive_c_d2]) ).
cnf(c_0_12,negated_conjecture,
( ~ c(X2)
| ~ c(X1)
| d1(f(X1,X2))
| d2(f(X1,X2)) ),
inference(fof_simplification,[status(thm)],[conjecture_1]) ).
cnf(c_0_13,hypothesis,
( ~ d1(X1)
| ~ c(X1) ),
inference(fof_simplification,[status(thm)],[partitions_exclusive_c_d1]) ).
cnf(c_0_14,hypothesis,
( ~ d2(X1)
| ~ c(X1) ),
c_0_11 ).
cnf(c_0_15,negated_conjecture,
( ~ c(X2)
| ~ c(X1)
| d1(f(X1,X2))
| d2(f(X1,X2)) ),
c_0_12 ).
cnf(c_0_16,hypothesis,
( ~ d1(X1)
| ~ c(X1) ),
c_0_13 ).
cnf(c_0_17,negated_conjecture,
( ~ d2(X2)
| ~ d2(X1)
| c(f(X1,X2)) ),
inference(fof_simplification,[status(thm)],[conjecture_3]) ).
cnf(c_0_18,hypothesis,
( ~ c(X1)
| ~ c(X2)
| ~ c(f(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_16]) ).
cnf(c_0_19,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),X3),
f_is_associative ).
cnf(c_0_20,negated_conjecture,
( ~ d1(X2)
| ~ d1(X1)
| c(f(X1,X2)) ),
inference(fof_simplification,[status(thm)],[conjecture_2]) ).
cnf(c_0_21,negated_conjecture,
( ~ d2(X2)
| ~ d2(X1)
| c(f(X1,X2)) ),
c_0_17 ).
cnf(c_0_22,hypothesis,
( ~ c(X3)
| ~ c(f(X1,X2))
| ~ c(f(X1,f(X2,X3))) ),
inference(spm,[status(thm)],[c_0_18,c_0_19]) ).
cnf(c_0_23,negated_conjecture,
( ~ d1(X2)
| ~ d1(X1)
| c(f(X1,X2)) ),
c_0_20 ).
cnf(c_0_24,negated_conjecture,
( ~ d2(X3)
| ~ d2(f(X1,X2))
| c(f(X1,f(X2,X3))) ),
inference(spm,[status(thm)],[c_0_21,c_0_19]) ).
cnf(c_0_25,hypothesis,
( ~ c(X4)
| ~ c(f(X1,f(X2,X3)))
| ~ c(f(X1,f(X2,f(X3,X4)))) ),
inference(spm,[status(thm)],[c_0_22,c_0_19]) ).
cnf(c_0_26,negated_conjecture,
( ~ d1(X3)
| ~ d1(f(X1,X2))
| c(f(X1,f(X2,X3))) ),
inference(spm,[status(thm)],[c_0_23,c_0_19]) ).
cnf(c_0_27,negated_conjecture,
( ~ c(X2)
| ~ c(f(X3,X1))
| ~ d2(X3)
| ~ d2(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_22,c_0_21]) ).
cnf(c_0_28,axiom,
( d2(X1)
| d1(X1)
| c(X1) ),
partitions_union ).
cnf(c_0_29,negated_conjecture,
( ~ c(X1)
| ~ c(f(X2,X3))
| ~ d2(X3)
| ~ d2(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_24]) ).
cnf(c_0_30,negated_conjecture,
( ~ c(X4)
| ~ c(f(X1,f(X2,X3)))
| ~ d1(f(X3,X4))
| ~ d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_25,c_0_26]) ).
cnf(c_0_31,negated_conjecture,
( ~ c(X2)
| ~ c(f(X3,X1))
| ~ d2(X3)
| c(f(X1,X2))
| d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_32,negated_conjecture,
( ~ c(X2)
| ~ c(X1)
| ~ c(f(X2,X3))
| ~ d2(X3)
| d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_29,c_0_15]) ).
cnf(c_0_33,negated_conjecture,
( ~ c(X4)
| ~ d1(f(X2,X4))
| ~ d1(f(X3,X1))
| ~ d2(X3)
| ~ d2(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_21]) ).
cnf(c_0_34,negated_conjecture,
( ~ c(X2)
| ~ d2(X1)
| ~ d2(X3)
| c(f(X1,X2))
| d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_31,c_0_21]) ).
cnf(c_0_35,hypothesis,
d2(a3),
partition_d2_not_empty ).
cnf(c_0_36,negated_conjecture,
( ~ c(X2)
| ~ c(X1)
| ~ d2(X4)
| ~ d2(f(X2,X3))
| ~ d2(f(X3,X4))
| d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_37,negated_conjecture,
( ~ c(X1)
| ~ c(X2)
| ~ c(X4)
| ~ d1(f(X2,X4))
| ~ d1(f(X3,X1))
| ~ d2(X3)
| d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_33,c_0_15]) ).
cnf(c_0_38,hypothesis,
( ~ c(X2)
| ~ d2(X1)
| c(f(X1,X2))
| d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_34,c_0_35]) ).
cnf(c_0_39,negated_conjecture,
( ~ c(X1)
| ~ c(X2)
| ~ c(f(X3,X1))
| ~ d2(X3)
| d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_40,negated_conjecture,
( ~ c(X4)
| ~ c(X3)
| ~ d2(X2)
| ~ d2(f(X4,X1))
| d1(f(X3,X4))
| d1(f(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_28]),c_0_29]) ).
cnf(c_0_41,hypothesis,
( ~ c(X1)
| ~ c(X2)
| ~ c(X4)
| ~ d1(f(X2,X4))
| ~ d2(X3)
| d1(f(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_38]),c_0_39]) ).
cnf(c_0_42,negated_conjecture,
( ~ c(X3)
| ~ c(X2)
| ~ c(X1)
| ~ d2(X4)
| d1(f(X3,X4))
| d1(f(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_15]),c_0_41]) ).
cnf(c_0_43,hypothesis,
( ~ c(X1)
| ~ c(X3)
| ~ c(X2)
| d1(f(X2,X3))
| d1(f(X1,a3)) ),
inference(spm,[status(thm)],[c_0_42,c_0_35]) ).
cnf(c_0_44,hypothesis,
c(a1),
partition_c_not_empty ).
cnf(c_0_45,hypothesis,
( ~ c(X2)
| ~ c(X1)
| d1(f(X2,a3))
| d1(f(a1,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_46,hypothesis,
( ~ c(X1)
| d1(f(X1,a3))
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_44]) ).
cnf(c_0_47,negated_conjecture,
( ~ d2(X1)
| ~ d2(X2)
| d1(f(a1,a1))
| d1(f(X1,f(X2,a3))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_21]),c_0_19]) ).
cnf(c_0_48,negated_conjecture,
( ~ d1(X1)
| ~ d1(X2)
| d1(f(a1,a1))
| d1(f(X1,f(X2,a3))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_23]),c_0_19]) ).
cnf(c_0_49,hypothesis,
( ~ c(f(X2,f(X1,a3)))
| ~ d2(X2)
| ~ d2(X1)
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_47]) ).
cnf(c_0_50,negated_conjecture,
( ~ c(X3)
| ~ d2(X1)
| ~ d2(X2)
| d1(f(X3,a3))
| d1(f(a1,f(X1,X2))) ),
inference(spm,[status(thm)],[c_0_45,c_0_21]) ).
cnf(c_0_51,hypothesis,
( ~ c(f(X2,f(X1,a3)))
| ~ d1(X2)
| ~ d1(X1)
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_48]) ).
cnf(c_0_52,negated_conjecture,
( ~ d2(X2)
| ~ d2(X1)
| ~ d2(f(X1,a3))
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_49,c_0_21]) ).
cnf(c_0_53,hypothesis,
( ~ c(X2)
| ~ d2(X1)
| d1(f(X2,a3))
| d1(f(a1,f(X1,a3))) ),
inference(spm,[status(thm)],[c_0_50,c_0_35]) ).
cnf(c_0_54,negated_conjecture,
( ~ d1(X2)
| ~ d1(X1)
| ~ d1(f(X1,a3))
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_51,c_0_23]) ).
cnf(c_0_55,negated_conjecture,
( ~ d2(X2)
| ~ d2(X1)
| c(f(X1,a3))
| d1(f(X1,a3))
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_28]) ).
cnf(c_0_56,hypothesis,
( ~ c(X1)
| d1(f(X1,a3))
| d1(f(a1,f(a3,a3))) ),
inference(spm,[status(thm)],[c_0_53,c_0_35]) ).
cnf(c_0_57,negated_conjecture,
( ~ d1(X3)
| ~ d1(f(X1,X2))
| ~ d1(f(X1,f(X2,a3)))
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_54,c_0_19]) ).
cnf(c_0_58,hypothesis,
( ~ d2(X1)
| c(f(X1,a3))
| d1(f(X1,a3))
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_55,c_0_35]) ).
cnf(c_0_59,hypothesis,
( d1(f(a1,a3))
| d1(f(a1,f(a3,a3))) ),
inference(spm,[status(thm)],[c_0_56,c_0_44]) ).
cnf(c_0_60,hypothesis,
( ~ d2(X1)
| ~ d1(X1) ),
inference(fof_simplification,[status(thm)],[partitions_exclusive_d1_d2]) ).
cnf(c_0_61,negated_conjecture,
( ~ d1(X3)
| ~ d1(f(X2,X1))
| ~ d2(X2)
| ~ d2(X1)
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_57,c_0_47]) ).
cnf(c_0_62,hypothesis,
( c(f(a3,a3))
| d1(f(a1,a1))
| d1(f(a3,a3)) ),
inference(spm,[status(thm)],[c_0_58,c_0_35]) ).
cnf(c_0_63,hypothesis,
( ~ c(f(a1,f(a3,a3)))
| d1(f(a1,a3)) ),
inference(spm,[status(thm)],[c_0_16,c_0_59]) ).
cnf(c_0_64,hypothesis,
( ~ d2(X1)
| ~ d1(X1) ),
c_0_60 ).
cnf(c_0_65,negated_conjecture,
( ~ d1(X1)
| c(f(a3,a3))
| d1(f(a1,a1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_35])]) ).
cnf(c_0_66,hypothesis,
d1(a2),
partition_d1_not_empty ).
cnf(c_0_67,negated_conjecture,
~ d2(f(a1,a3)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_63,c_0_24]),c_0_35])]),c_0_64]) ).
cnf(c_0_68,hypothesis,
( c(f(a3,a3))
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_65,c_0_66]) ).
cnf(c_0_69,negated_conjecture,
( ~ c(X1)
| ~ c(f(X2,X3))
| ~ d1(X3)
| ~ d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_18,c_0_26]) ).
cnf(c_0_70,negated_conjecture,
( c(f(a1,a3))
| d1(f(a1,a3)) ),
inference(spm,[status(thm)],[c_0_67,c_0_28]) ).
cnf(c_0_71,hypothesis,
( ~ c(X1)
| ~ d2(X2)
| c(f(a3,a3))
| d1(f(X1,a1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_68]),c_0_44])]) ).
cnf(c_0_72,negated_conjecture,
( ~ c(X4)
| ~ d1(X3)
| ~ d1(f(X3,X4))
| ~ d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_30,c_0_26]) ).
cnf(c_0_73,hypothesis,
( d1(f(a1,a1))
| d1(f(a1,a3)) ),
inference(spm,[status(thm)],[c_0_46,c_0_44]) ).
cnf(c_0_74,negated_conjecture,
( ~ c(f(a3,f(a3,X1)))
| ~ d1(X1)
| d1(f(a1,a3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_59]),c_0_19]),c_0_44])]) ).
cnf(c_0_75,negated_conjecture,
( ~ c(f(X1,X2))
| ~ c(f(X3,X4))
| ~ d1(X4)
| ~ d1(f(X1,f(X2,X3))) ),
inference(spm,[status(thm)],[c_0_69,c_0_19]) ).
cnf(c_0_76,negated_conjecture,
( ~ c(f(a3,X1))
| ~ d1(X1)
| c(f(a1,a3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_70]),c_0_44])]) ).
cnf(c_0_77,hypothesis,
( ~ c(X1)
| c(f(a3,a3))
| d1(f(X1,a1)) ),
inference(spm,[status(thm)],[c_0_71,c_0_35]) ).
cnf(c_0_78,negated_conjecture,
( ~ c(X2)
| ~ d1(X1)
| ~ d1(f(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_72,c_0_73]),c_0_72]) ).
cnf(c_0_79,negated_conjecture,
( ~ d1(X1)
| ~ d2(f(a3,X1))
| d1(f(a1,a3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_21]),c_0_35])]) ).
cnf(c_0_80,negated_conjecture,
( ~ c(f(a3,X1))
| ~ d1(X1)
| d1(f(a1,a3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_75,c_0_59]),c_0_76]) ).
cnf(c_0_81,hypothesis,
( ~ c(X1)
| ~ d2(X2)
| d1(f(X1,a1))
| d1(f(a1,a3)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_59]),c_0_44])]),c_0_77]) ).
cnf(c_0_82,negated_conjecture,
( ~ c(X3)
| ~ d1(f(X1,X2))
| ~ d1(f(X1,f(X2,X3))) ),
inference(spm,[status(thm)],[c_0_78,c_0_19]) ).
cnf(c_0_83,negated_conjecture,
( ~ d1(X1)
| d1(f(a3,X1))
| d1(f(a1,a3)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_79,c_0_28]),c_0_80]) ).
cnf(c_0_84,hypothesis,
( ~ c(X1)
| d1(f(X1,a1))
| d1(f(a1,a3)) ),
inference(spm,[status(thm)],[c_0_81,c_0_35]) ).
cnf(c_0_85,negated_conjecture,
( ~ c(X2)
| ~ d1(f(X1,X2))
| ~ d1(f(a3,X1))
| d1(f(a1,a3)) ),
inference(spm,[status(thm)],[c_0_82,c_0_83]) ).
cnf(c_0_86,negated_conjecture,
( ~ d2(X1)
| ~ d2(X2)
| d1(f(a1,a3))
| d1(f(X1,f(X2,a1))) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_21]),c_0_19]) ).
cnf(c_0_87,hypothesis,
( ~ c(f(a1,a3))
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_73]) ).
cnf(c_0_88,negated_conjecture,
( ~ c(X2)
| ~ d1(f(X1,f(a1,X2)))
| ~ d2(X1)
| d1(f(a1,a3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_85,c_0_86]),c_0_19]),c_0_35])]) ).
cnf(c_0_89,hypothesis,
( ~ c(X1)
| ~ c(f(a1,a3))
| ~ d2(X2)
| d1(f(X1,a1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_87]),c_0_44])]) ).
cnf(c_0_90,negated_conjecture,
( ~ c(X2)
| ~ c(X1)
| ~ d1(X4)
| ~ d1(f(X2,X3))
| ~ d2(f(X3,X4))
| d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_32,c_0_26]) ).
cnf(c_0_91,negated_conjecture,
( ~ c(X1)
| ~ d1(f(a1,X1))
| d1(f(a1,a3)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_83]),c_0_35])]) ).
cnf(c_0_92,hypothesis,
( ~ c(X1)
| ~ c(f(a1,a3))
| d1(f(X1,a1)) ),
inference(spm,[status(thm)],[c_0_89,c_0_35]) ).
cnf(c_0_93,negated_conjecture,
( ~ c(f(a3,X1))
| ~ d1(X1)
| d1(f(a1,a1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_73]),c_0_44])]) ).
cnf(c_0_94,negated_conjecture,
( ~ c(X4)
| ~ c(X3)
| ~ d1(X2)
| ~ d1(f(X4,X1))
| d1(f(X3,X4))
| d1(f(X1,X2)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_28]),c_0_69]) ).
cnf(c_0_95,hypothesis,
d1(f(a1,a3)),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_91,c_0_92]),c_0_44])]),c_0_70]) ).
cnf(c_0_96,negated_conjecture,
( ~ d1(X2)
| ~ d1(f(X1,X2))
| ~ d1(f(a3,X1))
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_93,c_0_26]) ).
cnf(c_0_97,negated_conjecture,
( ~ c(X1)
| ~ d1(X2)
| d1(f(a3,X2))
| d1(f(X1,a1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_94,c_0_95]),c_0_44])]) ).
cnf(c_0_98,negated_conjecture,
( ~ d1(X2)
| ~ d1(f(X1,f(a3,X2)))
| ~ d2(X1)
| d1(f(a1,a1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_47]),c_0_19]),c_0_35])]) ).
cnf(c_0_99,hypothesis,
( ~ d1(X1)
| d1(f(a3,X1))
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_97,c_0_44]) ).
cnf(c_0_100,negated_conjecture,
( ~ d1(X1)
| d1(f(a1,a1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_98,c_0_99]),c_0_35])]),c_0_99]) ).
cnf(c_0_101,hypothesis,
d1(f(a1,a1)),
inference(spm,[status(thm)],[c_0_100,c_0_66]) ).
cnf(c_0_102,negated_conjecture,
( ~ c(f(a1,X1))
| ~ d1(X1) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_69,c_0_101]),c_0_44])]) ).
cnf(c_0_103,hypothesis,
( ~ c(X1)
| ~ d2(X2)
| d1(f(X1,a1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_101]),c_0_44])]) ).
cnf(c_0_104,negated_conjecture,
( ~ d1(X2)
| ~ d1(f(X1,X2))
| ~ d1(f(a1,X1)) ),
inference(spm,[status(thm)],[c_0_102,c_0_26]) ).
cnf(c_0_105,hypothesis,
( ~ c(X1)
| d1(f(X1,a1)) ),
inference(spm,[status(thm)],[c_0_103,c_0_35]) ).
cnf(c_0_106,hypothesis,
( ~ d1(X1)
| ~ d1(f(a3,X1)) ),
inference(spm,[status(thm)],[c_0_104,c_0_95]) ).
cnf(c_0_107,hypothesis,
( ~ c(f(X1,X2))
| d1(f(X1,f(X2,a1))) ),
inference(spm,[status(thm)],[c_0_105,c_0_19]) ).
cnf(c_0_108,hypothesis,
( ~ c(X1)
| ~ c(X2)
| ~ d2(X3)
| d1(f(X1,X2)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_105]),c_0_44])]) ).
cnf(c_0_109,hypothesis,
( ~ c(f(a3,X1))
| ~ d1(f(X1,a1)) ),
inference(spm,[status(thm)],[c_0_106,c_0_107]) ).
cnf(c_0_110,hypothesis,
( ~ c(X1)
| ~ c(X2)
| d1(f(X1,X2)) ),
inference(spm,[status(thm)],[c_0_108,c_0_35]) ).
cnf(c_0_111,hypothesis,
( ~ c(f(a3,X1))
| ~ d2(X1)
| c(f(X1,a1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_38]),c_0_44])]) ).
cnf(c_0_112,hypothesis,
( ~ c(X1)
| ~ c(f(a3,X1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_110]),c_0_44])]) ).
cnf(c_0_113,negated_conjecture,
( ~ d2(X1)
| c(f(X1,a1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_21]),c_0_35])]) ).
cnf(c_0_114,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_113]),c_0_44]),c_0_35])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ALG012-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.37 % Computer : n002.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 12:55:17 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_E /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.15/0.44 Running first-order theorem proving
% 0.15/0.44 Running: /export/starexec/sandbox2/solver/bin/eprover --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.93/0.95 % Version: 3.5.1
% 2.93/0.95 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.93/0.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.93/0.95 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.93/0.95 % Starting new_bool_3 with 300s (1) cores
% 2.93/0.95 % Starting new_bool_1 with 300s (1) cores
% 2.93/0.95 % Starting sh5l with 300s (1) cores
% 2.93/0.95 % G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with pid 3327863 completed with status 0
% 2.93/0.95 % Result found by G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN
% 2.93/0.95 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.93/0.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.93/0.95 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.93/0.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.93/0.95 % No SInE strategy applied
% 2.93/0.95 % Search class: FGHSF-FFSS22-SFFFFFNN
% 2.93/0.95 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.93/0.95 % Starting SubtermCWHack with 136s (1) cores
% 2.93/0.95 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 151s (1) cores
% 2.93/0.95 % Starting G-E--_208_C18_F1_SE_CS_SP_PS_S5PRR_S0Y with 136s (1) cores
% 2.93/0.95 % Starting new_bool_3 with 136s (1) cores
% 2.93/0.95 % Starting new_bool_1 with 136s (1) cores
% 2.93/0.95 % SubtermCWHack with pid 3327866 completed with status 0
% 2.93/0.95 % Result found by SubtermCWHack
% 2.93/0.95 % Preprocessing class: FSMSSMSSSSSNFFN.
% 2.93/0.95 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 2.93/0.95 % Starting G-E--_208_C18_F1_SE_CS_SOS_SP_PS_S5PRR_RG_S04AN with 1500s (5) cores
% 2.93/0.95 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 2.93/0.95 % No SInE strategy applied
% 2.93/0.95 % Search class: FGHSF-FFSS22-SFFFFFNN
% 2.93/0.95 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 2.93/0.95 % Starting SubtermCWHack with 136s (1) cores
% 2.93/0.95 % Preprocessing time : 0.002 s
% 2.93/0.95
% 2.93/0.95 % Proof found!
% 2.93/0.95 % SZS status Unsatisfiable
% 2.93/0.95 % SZS output start CNFRefutation
% See solution above
% 2.93/0.95 % Parsed axioms : 11
% 2.93/0.95 % Removed by relevancy pruning/SinE : 0
% 2.93/0.95 % Initial clauses : 11
% 2.93/0.95 % Removed in clause preprocessing : 0
% 2.93/0.95 % Initial clauses in saturation : 11
% 2.93/0.95 % Processed clauses : 2148
% 2.93/0.95 % ...of these trivial : 0
% 2.93/0.95 % ...subsumed : 1466
% 2.93/0.95 % ...remaining for further processing : 682
% 2.93/0.95 % Other redundant clauses eliminated : 0
% 2.93/0.95 % Clauses deleted for lack of memory : 0
% 2.93/0.95 % Backward-subsumed : 307
% 2.93/0.95 % Backward-rewritten : 44
% 2.93/0.95 % Generated clauses : 10793
% 2.93/0.95 % ...of the previous two non-redundant : 10652
% 2.93/0.95 % ...aggressively subsumed : 0
% 2.93/0.95 % Contextual simplify-reflections : 45
% 2.93/0.95 % Paramodulations : 10793
% 2.93/0.95 % Factorizations : 0
% 2.93/0.95 % NegExts : 0
% 2.93/0.95 % Equation resolutions : 0
% 2.93/0.95 % Disequality decompositions : 0
% 2.93/0.95 % Total rewrite steps : 4865
% 2.93/0.95 % ...of those cached : 4667
% 2.93/0.95 % Propositional unsat checks : 0
% 2.93/0.95 % Propositional check models : 0
% 2.93/0.95 % Propositional check unsatisfiable : 0
% 2.93/0.95 % Propositional clauses : 0
% 2.93/0.95 % Propositional clauses after purity: 0
% 2.93/0.95 % Propositional unsat core size : 0
% 2.93/0.95 % Propositional preprocessing time : 0.000
% 2.93/0.95 % Propositional encoding time : 0.000
% 2.93/0.95 % Propositional solver time : 0.000
% 2.93/0.95 % Success case prop preproc time : 0.000
% 2.93/0.95 % Success case prop encoding time : 0.000
% 2.93/0.95 % Success case prop solver time : 0.000
% 2.93/0.95 % Current number of processed clauses : 331
% 2.93/0.95 % Positive orientable unit clauses : 6
% 2.93/0.95 % Positive unorientable unit clauses: 0
% 2.93/0.95 % Negative unit clauses : 12
% 2.93/0.95 % Non-unit-clauses : 313
% 2.93/0.95 % Current number of unprocessed clauses: 8009
% 2.93/0.95 % ...number of literals in the above : 53077
% 2.93/0.95 % Current number of archived formulas : 0
% 2.93/0.95 % Current number of archived clauses : 351
% 2.93/0.95 % Clause-clause subsumption calls (NU) : 78209
% 2.93/0.95 % Rec. Clause-clause subsumption calls : 23044
% 2.93/0.95 % Non-unit clause-clause subsumptions : 1011
% 2.93/0.95 % Unit Clause-clause subsumption calls : 2402
% 2.93/0.95 % Rewrite failures with RHS unbound : 0
% 2.93/0.95 % BW rewrite match attempts : 2
% 2.93/0.95 % BW rewrite match successes : 2
% 2.93/0.95 % Condensation attempts : 0
% 2.93/0.95 % Condensation successes : 0
% 2.93/0.95 % Termbank termtop insertions : 211682
% 2.93/0.95 % Search garbage collected termcells : 18
% 2.93/0.95
% 2.93/0.95 % -------------------------------------------------
% 2.93/0.95 % User time : 0.449 s
% 2.93/0.95 % System time : 0.015 s
% 2.93/0.95 % Total time : 0.464 s
% 2.93/0.95 % Maximum resident set size: 3380 pages
% 2.93/0.95
% 2.93/0.95 % -------------------------------------------------
% 2.93/0.95 % User time : 1.988 s
% 2.93/0.95 % System time : 0.073 s
% 2.93/0.95 % Total time : 2.061 s
% 2.93/0.95 % Maximum resident set size: 4864 pages
% 2.93/0.95 % E exiting
%------------------------------------------------------------------------------