%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG012-1 : TPTP v9.2.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n023.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 : Tue May 5 04:03:59 PM UTC 2026
% Result : Unsatisfiable 6.14s 4.44s
% Output : CNFRefutation 6.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 11
% Syntax : Number of clauses : 126 ( 30 unt; 75 nHn; 110 RR)
% Number of literals : 355 ( 2 equ; 115 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 5 ( 2 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 : 121 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
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(conjecture_3,negated_conjecture,
( c(f(X1,X2))
| ~ d2(X1)
| ~ d2(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_3) ).
cnf(partition_c_not_empty,hypothesis,
c(a1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_c_not_empty) ).
cnf(partition_d2_not_empty,hypothesis,
d2(a3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d2_not_empty) ).
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(partitions_union,axiom,
( c(X1)
| d1(X1)
| d2(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_union) ).
cnf(partitions_exclusive_c_d2,hypothesis,
( ~ c(X1)
| ~ d2(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d2) ).
cnf(partitions_exclusive_c_d1,hypothesis,
( ~ c(X1)
| ~ d1(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_c_d1) ).
cnf(conjecture_2,negated_conjecture,
( c(f(X1,X2))
| ~ d1(X1)
| ~ d1(X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conjecture_2) ).
cnf(partitions_exclusive_d1_d2,hypothesis,
( ~ d1(X1)
| ~ d2(X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partitions_exclusive_d1_d2) ).
cnf(partition_d1_not_empty,hypothesis,
d1(a2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',partition_d1_not_empty) ).
cnf(c_0_11,negated_conjecture,
( d2(f(X1,X2))
| d1(f(X1,X2))
| ~ c(X1)
| ~ c(X2) ),
conjecture_1 ).
cnf(c_0_12,negated_conjecture,
( c(f(X1,X2))
| ~ d2(X1)
| ~ d2(X2) ),
conjecture_3 ).
cnf(c_0_13,hypothesis,
c(a1),
partition_c_not_empty ).
cnf(c_0_14,negated_conjecture,
( d2(f(X1,f(X2,X3)))
| d1(f(X1,f(X2,X3)))
| ~ d2(X3)
| ~ d2(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_15,hypothesis,
d2(a3),
partition_d2_not_empty ).
cnf(c_0_16,hypothesis,
( d2(f(X1,a1))
| d1(f(X1,a1))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_13]) ).
cnf(c_0_17,axiom,
f(X1,f(X2,X3)) = f(f(X1,X2),X3),
f_is_associative ).
cnf(c_0_18,hypothesis,
( d2(f(X1,f(X2,a3)))
| d1(f(X1,f(X2,a3)))
| ~ d2(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_15]) ).
cnf(c_0_19,negated_conjecture,
( d2(f(X1,f(X2,a1)))
| d1(f(X1,f(X2,a1)))
| ~ d2(X2)
| ~ d2(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_12]),c_0_17]),c_0_17]) ).
cnf(c_0_20,hypothesis,
( d2(f(X1,f(a3,a3)))
| d1(f(X1,f(a3,a3)))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_18,c_0_15]) ).
cnf(c_0_21,hypothesis,
( d2(f(X1,f(a3,a1)))
| d1(f(X1,f(a3,a1)))
| ~ d2(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_15]) ).
cnf(c_0_22,axiom,
( c(X1)
| d1(X1)
| d2(X1) ),
partitions_union ).
cnf(c_0_23,negated_conjecture,
( d2(f(X1,f(X2,f(a3,a3))))
| d1(f(X1,f(X2,f(a3,a3))))
| ~ d2(X2)
| ~ d2(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_12]),c_0_17]),c_0_17]) ).
cnf(c_0_24,hypothesis,
( ~ c(X1)
| ~ d2(X1) ),
partitions_exclusive_c_d2 ).
cnf(c_0_25,hypothesis,
( d2(f(a3,f(a3,a1)))
| d1(f(a3,f(a3,a1))) ),
inference(spm,[status(thm)],[c_0_21,c_0_15]) ).
cnf(c_0_26,hypothesis,
( ~ c(X1)
| ~ d1(X1) ),
partitions_exclusive_c_d1 ).
cnf(c_0_27,negated_conjecture,
( d2(f(X1,f(X2,a1)))
| d1(f(X1,f(X2,a1)))
| d1(X2)
| c(X2)
| ~ d2(X1) ),
inference(spm,[status(thm)],[c_0_19,c_0_22]) ).
cnf(c_0_28,negated_conjecture,
( d2(f(X1,f(X2,f(a3,a3))))
| d1(f(X1,f(X2,f(a3,a3))))
| d1(X2)
| c(X2)
| ~ d2(X1) ),
inference(spm,[status(thm)],[c_0_23,c_0_22]) ).
cnf(c_0_29,hypothesis,
~ c(f(a3,f(a3,a1))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_26]) ).
cnf(c_0_30,hypothesis,
( d2(f(a3,f(X1,a1)))
| d1(f(a3,f(X1,a1)))
| d1(X1)
| c(X1) ),
inference(spm,[status(thm)],[c_0_27,c_0_15]) ).
cnf(c_0_31,hypothesis,
( d2(f(a3,f(X1,f(a3,a3))))
| d1(f(a3,f(X1,f(a3,a3))))
| d1(X1)
| c(X1) ),
inference(spm,[status(thm)],[c_0_28,c_0_15]) ).
cnf(c_0_32,negated_conjecture,
( c(f(X1,X2))
| ~ d1(X1)
| ~ d1(X2) ),
conjecture_2 ).
cnf(c_0_33,negated_conjecture,
~ d2(f(a3,a1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_12]),c_0_15])]) ).
cnf(c_0_34,hypothesis,
( d1(X1)
| c(X1)
| ~ c(f(a3,f(X1,a1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_26]) ).
cnf(c_0_35,hypothesis,
( d1(X1)
| c(X1)
| ~ c(f(a3,f(X1,f(a3,a3)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_31]),c_0_26]) ).
cnf(c_0_36,negated_conjecture,
( d2(f(X1,f(X2,a1)))
| d1(f(X1,f(X2,a1)))
| ~ d1(X2)
| ~ d1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_32]),c_0_17]),c_0_17]) ).
cnf(c_0_37,negated_conjecture,
( d1(f(a3,a1))
| c(f(a3,a1)) ),
inference(spm,[status(thm)],[c_0_33,c_0_22]) ).
cnf(c_0_38,negated_conjecture,
( d2(f(X1,f(X2,X3)))
| d1(f(X1,f(X2,X3)))
| d1(X3)
| c(X3)
| ~ d2(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_14,c_0_22]) ).
cnf(c_0_39,hypothesis,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ c(f(a3,f(X1,f(X2,a1)))) ),
inference(spm,[status(thm)],[c_0_34,c_0_17]) ).
cnf(c_0_40,negated_conjecture,
( c(f(X1,f(X2,X3)))
| ~ d1(f(X1,X2))
| ~ d1(X3) ),
inference(spm,[status(thm)],[c_0_32,c_0_17]) ).
cnf(c_0_41,negated_conjecture,
( d1(X1)
| c(X1)
| ~ d2(f(X1,a1)) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_12]),c_0_15])]) ).
cnf(c_0_42,hypothesis,
( ~ d1(X1)
| ~ d2(X1) ),
partitions_exclusive_d1_d2 ).
cnf(c_0_43,hypothesis,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ c(f(a3,f(X1,f(X2,f(a3,a3))))) ),
inference(spm,[status(thm)],[c_0_35,c_0_17]) ).
cnf(c_0_44,negated_conjecture,
( c(f(X1,f(X2,X3)))
| ~ d2(f(X1,X2))
| ~ d2(X3) ),
inference(spm,[status(thm)],[c_0_12,c_0_17]) ).
cnf(c_0_45,negated_conjecture,
( d2(f(X1,f(a3,f(a1,a1))))
| d1(f(X1,f(a3,f(a1,a1))))
| c(f(a3,a1))
| ~ d1(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_17]),c_0_17]) ).
cnf(c_0_46,hypothesis,
d1(a2),
partition_d1_not_empty ).
cnf(c_0_47,hypothesis,
( d2(f(X1,f(a3,X2)))
| d1(f(X1,f(a3,X2)))
| d1(X2)
| c(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_38,c_0_15]) ).
cnf(c_0_48,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d1(f(a3,X1))
| ~ d1(f(X2,a1)) ),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_49,negated_conjecture,
( d1(f(X1,a1))
| d1(X1)
| c(f(X1,a1))
| c(X1) ),
inference(spm,[status(thm)],[c_0_41,c_0_22]) ).
cnf(c_0_50,hypothesis,
~ d1(a3),
inference(spm,[status(thm)],[c_0_42,c_0_15]) ).
cnf(c_0_51,hypothesis,
~ c(a3),
inference(spm,[status(thm)],[c_0_24,c_0_15]) ).
cnf(c_0_52,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d2(f(X2,f(a3,a3)))
| ~ d2(f(a3,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_53,hypothesis,
( d2(f(a1,f(a3,a3)))
| d1(f(a1,f(a3,a3))) ),
inference(spm,[status(thm)],[c_0_20,c_0_13]) ).
cnf(c_0_54,hypothesis,
( d2(f(a2,f(a3,f(a1,a1))))
| d1(f(a2,f(a3,f(a1,a1))))
| c(f(a3,a1)) ),
inference(spm,[status(thm)],[c_0_45,c_0_46]) ).
cnf(c_0_55,hypothesis,
( d2(f(a1,f(a3,X1)))
| d1(f(a1,f(a3,X1)))
| d1(X1)
| c(X1) ),
inference(spm,[status(thm)],[c_0_47,c_0_13]) ).
cnf(c_0_56,negated_conjecture,
( d1(f(a1,X1))
| c(f(a3,a1))
| c(f(a1,X1))
| ~ d1(f(X1,a1)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50]),c_0_51]) ).
cnf(c_0_57,hypothesis,
( d1(f(a1,f(a3,a3)))
| d1(f(X1,a1))
| c(f(X1,a1))
| ~ d2(f(a3,X1)) ),
inference(spm,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_58,hypothesis,
( d2(f(X1,f(a3,a1)))
| d1(f(X1,f(a3,a1)))
| d1(X1)
| c(X1) ),
inference(spm,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_59,hypothesis,
( c(f(a3,a1))
| ~ c(f(a2,f(a3,f(a1,a1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_54]),c_0_26]) ).
cnf(c_0_60,hypothesis,
( d1(X1)
| c(X1)
| ~ c(f(a1,f(a3,X1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_55]),c_0_26]) ).
cnf(c_0_61,negated_conjecture,
( c(f(X1,f(X2,f(X3,X4))))
| ~ d1(f(X1,f(X2,X3)))
| ~ d1(X4) ),
inference(spm,[status(thm)],[c_0_40,c_0_17]) ).
cnf(c_0_62,negated_conjecture,
( d1(f(a1,f(X1,X2)))
| c(f(a1,f(X1,X2)))
| c(f(a3,a1))
| ~ d1(f(X1,f(X2,a1))) ),
inference(spm,[status(thm)],[c_0_56,c_0_17]) ).
cnf(c_0_63,hypothesis,
( d1(f(a3,f(a3,a1)))
| d1(f(a3,f(a1,a1)))
| d1(f(a1,f(a3,a3)))
| c(f(a3,f(a1,a1))) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_58]),c_0_17]),c_0_17]),c_0_50]),c_0_51]) ).
cnf(c_0_64,hypothesis,
~ c(f(a1,f(a3,a3))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_53]),c_0_26]) ).
cnf(c_0_65,negated_conjecture,
( c(f(a3,a1))
| ~ d1(f(a3,f(a1,a1))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_32]),c_0_46])]) ).
cnf(c_0_66,negated_conjecture,
( d2(f(X1,f(X2,a1)))
| d1(f(X1,f(X2,a1)))
| d1(X1)
| d1(X2)
| c(X1)
| c(X2) ),
inference(spm,[status(thm)],[c_0_27,c_0_22]) ).
cnf(c_0_67,negated_conjecture,
( d2(f(a3,f(a1,f(a3,f(a1,a1)))))
| d1(f(a3,f(a1,f(a3,f(a1,a1)))))
| c(f(a3,a1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_37]),c_0_17]),c_0_17]) ).
cnf(c_0_68,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d1(f(a1,f(a3,X1)))
| ~ d1(X2) ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_69,negated_conjecture,
( d1(f(a1,f(a3,a3)))
| c(f(a3,f(a1,a1)))
| c(f(a3,a1)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_64]),c_0_65]) ).
cnf(c_0_70,hypothesis,
( d1(X1)
| d1(X2)
| c(X1)
| c(X2)
| ~ c(f(X2,f(X1,a1))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_66]),c_0_26]) ).
cnf(c_0_71,hypothesis,
( c(f(a3,a1))
| ~ c(f(a3,f(a1,f(a3,f(a1,a1))))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_67]),c_0_26]) ).
cnf(c_0_72,negated_conjecture,
( c(f(X1,f(X2,f(X3,X4))))
| ~ d2(f(X1,f(X2,X3)))
| ~ d2(X4) ),
inference(spm,[status(thm)],[c_0_44,c_0_17]) ).
cnf(c_0_73,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d1(f(X2,f(a3,a3)))
| ~ d1(f(a3,X1)) ),
inference(spm,[status(thm)],[c_0_43,c_0_40]) ).
cnf(c_0_74,negated_conjecture,
( d1(f(a3,X1))
| c(f(a3,f(a1,a1)))
| c(f(a3,a1))
| c(f(a3,X1))
| ~ d1(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_69]) ).
cnf(c_0_75,hypothesis,
( d1(f(X1,X2))
| d1(X3)
| c(f(X1,X2))
| c(X3)
| ~ c(f(X3,f(X1,f(X2,a1)))) ),
inference(spm,[status(thm)],[c_0_70,c_0_17]) ).
cnf(c_0_76,negated_conjecture,
( c(f(a3,a1))
| ~ d2(f(a3,f(a1,a3)))
| ~ d2(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_77,hypothesis,
( d2(f(a1,a1))
| d1(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_16,c_0_13]) ).
cnf(c_0_78,negated_conjecture,
( d1(f(X1,a1))
| c(f(a3,f(a1,a1)))
| c(f(a3,a1))
| c(f(X1,a1))
| ~ d1(f(a3,X1)) ),
inference(spm,[status(thm)],[c_0_73,c_0_69]) ).
cnf(c_0_79,negated_conjecture,
( d1(f(a3,f(a3,a1)))
| c(f(a3,f(a1,a1)))
| c(f(a3,a1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_74,c_0_37]),c_0_29]) ).
cnf(c_0_80,negated_conjecture,
( d1(f(X1,X2))
| d1(X3)
| c(f(X1,X2))
| c(X3)
| ~ d1(f(X2,a1))
| ~ d1(f(X3,X1)) ),
inference(spm,[status(thm)],[c_0_75,c_0_40]) ).
cnf(c_0_81,negated_conjecture,
( d1(f(a3,f(a1,a3)))
| c(f(a3,f(a1,a3)))
| c(f(a3,a1))
| ~ d2(f(a1,a1)) ),
inference(spm,[status(thm)],[c_0_76,c_0_22]) ).
cnf(c_0_82,hypothesis,
~ c(f(a1,a1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_77]),c_0_26]) ).
cnf(c_0_83,negated_conjecture,
( c(f(a3,f(a1,a1)))
| c(f(a3,a1)) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_78,c_0_79]),c_0_17]),c_0_17])]),c_0_65]) ).
cnf(c_0_84,negated_conjecture,
( d1(f(X1,a3))
| d1(X2)
| c(f(a3,a1))
| c(f(X1,a3))
| c(X2)
| ~ d1(f(X2,X1)) ),
inference(spm,[status(thm)],[c_0_80,c_0_37]) ).
cnf(c_0_85,negated_conjecture,
( d1(f(a3,f(a1,a3)))
| d1(f(a1,a1))
| c(f(a3,f(a1,a3)))
| c(f(a3,a1)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_81,c_0_22]),c_0_82]) ).
cnf(c_0_86,hypothesis,
( d2(f(a3,f(a1,f(a1,a1))))
| d1(f(a3,f(a1,f(a1,a1))))
| c(f(a3,a1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_83]),c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_87,negated_conjecture,
( d1(f(a1,f(a3,a3)))
| d1(f(a1,a1))
| c(f(a3,f(a1,a3)))
| c(f(a3,a1)) ),
inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_84,c_0_85]),c_0_17]),c_0_17]),c_0_50]),c_0_64]),c_0_51]) ).
cnf(c_0_88,hypothesis,
( c(f(a3,a1))
| ~ c(f(a3,f(a1,f(a1,a1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_86]),c_0_26]) ).
cnf(c_0_89,negated_conjecture,
( d1(f(X1,a1))
| c(f(a3,f(a1,a3)))
| c(f(a3,a1))
| c(f(X1,a1))
| ~ d1(f(a3,X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_73,c_0_87]),c_0_48]) ).
cnf(c_0_90,negated_conjecture,
( c(f(a3,a1))
| ~ d1(f(a1,a1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_88,c_0_40]),c_0_37]) ).
cnf(c_0_91,negated_conjecture,
( c(f(a3,f(a1,a3)))
| c(f(a3,a1)) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_89,c_0_49]),c_0_82]),c_0_50]),c_0_51]),c_0_90]) ).
cnf(c_0_92,negated_conjecture,
( d2(f(X1,f(X2,X3)))
| d1(f(X1,f(X2,X3)))
| ~ d1(X3)
| ~ d1(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_32]) ).
cnf(c_0_93,hypothesis,
( d2(f(a3,f(a1,f(a3,a1))))
| d1(f(a3,f(a1,f(a3,a1))))
| c(f(a3,a1)) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_91]),c_0_17]),c_0_17]),c_0_17]),c_0_17]) ).
cnf(c_0_94,hypothesis,
( d2(f(X1,f(X2,a2)))
| d1(f(X1,f(X2,a2)))
| ~ d1(X2)
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_92,c_0_46]) ).
cnf(c_0_95,hypothesis,
( c(f(a3,a1))
| ~ c(f(a3,f(a1,f(a3,a1)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_93]),c_0_26]) ).
cnf(c_0_96,hypothesis,
( d2(f(X1,f(a2,a2)))
| d1(f(X1,f(a2,a2)))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_94,c_0_46]) ).
cnf(c_0_97,negated_conjecture,
c(f(a3,a1)),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_95,c_0_40]),c_0_37]) ).
cnf(c_0_98,negated_conjecture,
( d2(f(X1,f(X2,f(a2,a2))))
| d1(f(X1,f(X2,f(a2,a2))))
| ~ d2(X2)
| ~ d2(X1) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_12]),c_0_17]),c_0_17]) ).
cnf(c_0_99,hypothesis,
( d2(f(a3,f(a1,f(a3,a3))))
| d1(f(a3,f(a1,f(a3,a3)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_97]),c_0_17]),c_0_17]) ).
cnf(c_0_100,negated_conjecture,
( d2(f(X1,f(X2,f(a2,a2))))
| d1(f(X1,f(X2,f(a2,a2))))
| d1(X2)
| c(X2)
| ~ d2(X1) ),
inference(spm,[status(thm)],[c_0_98,c_0_22]) ).
cnf(c_0_101,hypothesis,
~ c(f(a3,f(a1,f(a3,a3)))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_99]),c_0_26]) ).
cnf(c_0_102,hypothesis,
( d2(f(a3,f(a1,f(a2,a2))))
| d1(f(a3,f(a1,f(a2,a2)))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_96,c_0_97]),c_0_17]),c_0_17]) ).
cnf(c_0_103,hypothesis,
( d2(f(a3,f(X1,f(a2,a2))))
| d1(f(a3,f(X1,f(a2,a2))))
| d1(X1)
| c(X1) ),
inference(spm,[status(thm)],[c_0_100,c_0_15]) ).
cnf(c_0_104,negated_conjecture,
~ d2(f(a1,f(a3,a3))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_101,c_0_12]),c_0_15])]) ).
cnf(c_0_105,hypothesis,
~ c(f(a3,f(a1,f(a2,a2)))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_102]),c_0_26]) ).
cnf(c_0_106,hypothesis,
( d1(X1)
| c(X1)
| ~ c(f(a3,f(X1,f(a2,a2)))) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_103]),c_0_26]) ).
cnf(c_0_107,hypothesis,
d1(f(a1,f(a3,a3))),
inference(sr,[status(thm)],[c_0_53,c_0_104]) ).
cnf(c_0_108,hypothesis,
( d2(f(a1,f(a2,a2)))
| d1(f(a1,f(a2,a2))) ),
inference(spm,[status(thm)],[c_0_96,c_0_13]) ).
cnf(c_0_109,negated_conjecture,
~ d2(f(a1,f(a2,a2))),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_105,c_0_12]),c_0_15])]) ).
cnf(c_0_110,negated_conjecture,
( d1(X1)
| c(X1)
| ~ d1(f(a3,f(X1,a2))) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_61]),c_0_46])]) ).
cnf(c_0_111,negated_conjecture,
( d1(f(a3,X1))
| c(f(a3,X1))
| ~ d1(X1) ),
inference(spm,[status(thm)],[c_0_68,c_0_107]) ).
cnf(c_0_112,hypothesis,
d1(f(a1,f(a2,a2))),
inference(sr,[status(thm)],[c_0_108,c_0_109]) ).
cnf(c_0_113,hypothesis,
~ c(f(a1,f(a2,a2))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_108]),c_0_26]) ).
cnf(c_0_114,negated_conjecture,
( d1(f(X1,X2))
| c(f(X1,X2))
| ~ d1(f(a3,f(X1,f(X2,a2)))) ),
inference(spm,[status(thm)],[c_0_110,c_0_17]) ).
cnf(c_0_115,hypothesis,
d1(f(a3,f(a1,f(a2,a2)))),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_112]),c_0_105]) ).
cnf(c_0_116,negated_conjecture,
~ d1(f(a1,a2)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_113,c_0_40]),c_0_46])]) ).
cnf(c_0_117,negated_conjecture,
c(f(a1,a2)),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_115]),c_0_116]) ).
cnf(c_0_118,hypothesis,
( d2(f(a3,f(a1,a1)))
| d1(f(a3,f(a1,a1))) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_97]),c_0_17]),c_0_17]) ).
cnf(c_0_119,negated_conjecture,
( d2(f(X1,f(a1,a2)))
| d1(f(X1,f(a1,a2)))
| ~ c(X1) ),
inference(spm,[status(thm)],[c_0_11,c_0_117]) ).
cnf(c_0_120,hypothesis,
~ c(f(a3,f(a1,a1))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_118]),c_0_26]) ).
cnf(c_0_121,hypothesis,
( d2(f(a1,f(a1,a2)))
| d1(f(a1,f(a1,a2))) ),
inference(spm,[status(thm)],[c_0_119,c_0_13]) ).
cnf(c_0_122,negated_conjecture,
~ d2(f(a1,a1)),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_120,c_0_12]),c_0_15])]) ).
cnf(c_0_123,hypothesis,
~ c(f(a1,f(a1,a2))),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_121]),c_0_26]) ).
cnf(c_0_124,hypothesis,
d1(f(a1,a1)),
inference(sr,[status(thm)],[c_0_77,c_0_122]) ).
cnf(c_0_125,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_123,c_0_40]),c_0_124]),c_0_46])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ALG012-1 : TPTP v9.2.1. Released v2.7.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox/solver/bin/cse --final-prover /export/starexec/sandbox/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.14/0.31 % Computer : n023.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.32 % CPULimit : 300
% 0.14/0.32 % WCLimit : 300
% 0.14/0.32 % DateTime : Tue May 5 10:15:23 EDT 2026
% 0.14/0.32 % CPUTime :
% 0.14/0.33 % start to proof: theBenchmark
% 6.14/4.44 % Version : CSE_E---1.7
% 6.14/4.44 % Problem : theBenchmark.p
% 6.14/4.44 % SZS status Unsatisfiable for theBenchmark.p
% 6.14/4.44 % SZS output start CNFRefutation
% See solution above
% 6.14/4.46 % Total time : 3.375s
%------------------------------------------------------------------------------