%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KRS009-1 : TPTP v9.2.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n027.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 04:36:09 PM UTC 2026
% Result : Satisfiable 1.27s 1.72s
% Output : Saturation 1.27s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_33,axiom,
( t3least(X1)
| equalish(X2,X3)
| equalish(X2,X4)
| equalish(X3,X4)
| ~ t(X1,X2)
| ~ t(X1,X3)
| ~ t(X1,X4) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_33) ).
cnf(clause_20,axiom,
( t(X1,X2)
| ~ s(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
cnf(clause_18,axiom,
( t(X1,X2)
| ~ r(X1,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_18) ).
cnf(clause_41,axiom,
( s1most(X1)
| s(X1,u10r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_41) ).
cnf(clause_40,axiom,
( s1most(X1)
| s(X1,u10r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_40) ).
cnf(clause_36,axiom,
( r1most(X1)
| r(X1,u9r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_36) ).
cnf(clause_34,axiom,
( equalish(X1,X2)
| ~ r1most(X3)
| ~ r(X3,X1)
| ~ r(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_34) ).
cnf(clause_25,axiom,
( e(X1)
| ~ a(u7r1(X1))
| ~ t3least(X1)
| ~ r1most(X1)
| ~ s1most(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_25) ).
cnf(clause_16,axiom,
( a(X1)
| ~ c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_16) ).
cnf(clause_7,axiom,
( p2least(X1)
| equalish(X2,X3)
| ~ p(X1,X2)
| ~ p(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
cnf(clause_12,axiom,
( p1most(X1)
| p(X1,u3r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_12) ).
cnf(clause_15,axiom,
( a(X1)
| ~ d(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_15) ).
cnf(clause_24,axiom,
( a(X1)
| ~ e(X2)
| ~ t(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
cnf(clause_32,axiom,
( t(X1,u8r3(X1))
| ~ t3least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_32) ).
cnf(clause_23,axiom,
( t3least(X1)
| ~ e(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
cnf(clause_30,axiom,
( t(X1,u8r1(X1))
| ~ t3least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_30) ).
cnf(clause_31,axiom,
( t(X1,u8r2(X1))
| ~ t3least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
cnf(clause_10,axiom,
( equalish(X1,X2)
| ~ p1most(X3)
| ~ p(X3,X1)
| ~ p(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_10) ).
cnf(clause_5,axiom,
( p(X1,u1r1(X1))
| ~ p2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_5) ).
cnf(clause_17,axiom,
( c(X1)
| ~ r(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_17) ).
cnf(clause_37,axiom,
( r1most(X1)
| r(X1,u9r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_37) ).
cnf(clause_39,axiom,
( s1most(X1)
| ~ equalish(u10r2(X1),u10r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_39) ).
cnf(clause_35,axiom,
( r1most(X1)
| ~ equalish(u9r2(X1),u9r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_35) ).
cnf(clause_3,axiom,
( c(X1)
| ~ p2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
cnf(clause_11,axiom,
( p1most(X1)
| ~ equalish(u3r2(X1),u3r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_11) ).
cnf(clause_13,axiom,
( p1most(X1)
| p(X1,u3r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_13) ).
cnf(clause_9,axiom,
( d(X1)
| ~ p1most(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_9) ).
cnf(clause_14,axiom,
( c(X1)
| d(X1)
| ~ a(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_14) ).
cnf(clause_4,axiom,
( ~ p2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_4) ).
cnf(clause_6,axiom,
( p(X1,u1r2(X1))
| ~ p2least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
cnf(clause_2,axiom,
( p2least(X1)
| ~ c(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
cnf(clause_19,axiom,
( d(X1)
| ~ s(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
cnf(clause_8,axiom,
( p1most(X1)
| ~ d(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
cnf(clause_38,axiom,
( equalish(X1,X2)
| ~ s1most(X3)
| ~ s(X3,X1)
| ~ s(X3,X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_38) ).
cnf(clause_28,axiom,
( ~ t3least(X1)
| ~ equalish(u8r3(X1),u8r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_28) ).
cnf(clause_29,axiom,
( ~ t3least(X1)
| ~ equalish(u8r3(X1),u8r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_29) ).
cnf(clause_27,axiom,
( ~ t3least(X1)
| ~ equalish(u8r2(X1),u8r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_27) ).
cnf(clause_22,axiom,
( r1most(X1)
| ~ e(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
cnf(clause_21,axiom,
( s1most(X1)
| ~ e(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21) ).
cnf(clause_1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
cnf(c_0_40,axiom,
( t3least(X1)
| equalish(X2,X3)
| equalish(X2,X4)
| equalish(X3,X4)
| ~ t(X1,X2)
| ~ t(X1,X3)
| ~ t(X1,X4) ),
clause_33,
[final] ).
cnf(c_0_41,axiom,
( t(X1,X2)
| ~ s(X1,X2) ),
clause_20,
[final] ).
cnf(c_0_42,axiom,
( t(X1,X2)
| ~ r(X1,X2) ),
clause_18,
[final] ).
cnf(c_0_43,plain,
( t3least(X1)
| equalish(X2,X3)
| equalish(X2,X4)
| equalish(X3,X4)
| ~ s(X1,X4)
| ~ t(X1,X3)
| ~ t(X1,X2) ),
inference(spm,[status(thm)],[c_0_40,c_0_41]),
[final] ).
cnf(c_0_44,axiom,
( s1most(X1)
| s(X1,u10r2(X1)) ),
clause_41,
[final] ).
cnf(c_0_45,axiom,
( s1most(X1)
| s(X1,u10r1(X1)) ),
clause_40,
[final] ).
cnf(c_0_46,plain,
( t3least(X1)
| equalish(X2,X3)
| equalish(X2,X4)
| equalish(X3,X4)
| ~ t(X1,X3)
| ~ t(X1,X2)
| ~ r(X1,X4) ),
inference(spm,[status(thm)],[c_0_40,c_0_42]),
[final] ).
cnf(c_0_47,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r2(X1))
| equalish(X3,u10r2(X1))
| equalish(X3,X2)
| ~ t(X1,X2)
| ~ t(X1,X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_44]),
[final] ).
cnf(c_0_48,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r1(X1))
| equalish(X3,u10r1(X1))
| equalish(X3,X2)
| ~ t(X1,X2)
| ~ t(X1,X3) ),
inference(spm,[status(thm)],[c_0_43,c_0_45]),
[final] ).
cnf(c_0_49,plain,
( t3least(X1)
| equalish(X2,X3)
| equalish(X4,X3)
| equalish(X4,X2)
| ~ s(X1,X2)
| ~ t(X1,X4)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_46,c_0_41]),
[final] ).
cnf(c_0_50,plain,
( t3least(X1)
| equalish(X2,X3)
| equalish(X4,X3)
| equalish(X4,X2)
| ~ t(X1,X4)
| ~ r(X1,X3)
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_46,c_0_42]),
[final] ).
cnf(c_0_51,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r2(X1))
| equalish(X3,u10r2(X1))
| equalish(X2,X3)
| ~ t(X1,X2)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_47,c_0_42]),
[final] ).
cnf(c_0_52,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r1(X1))
| equalish(X3,u10r1(X1))
| equalish(X2,X3)
| ~ t(X1,X2)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_48,c_0_42]),
[final] ).
cnf(c_0_53,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r2(X1))
| equalish(u10r2(X1),X3)
| equalish(X2,X3)
| ~ t(X1,X2)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_44]),
[final] ).
cnf(c_0_54,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r1(X1))
| equalish(u10r1(X1),X3)
| equalish(X2,X3)
| ~ t(X1,X2)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_49,c_0_45]),
[final] ).
cnf(c_0_55,plain,
( t3least(X1)
| equalish(X2,X3)
| equalish(X2,X4)
| equalish(X3,X4)
| ~ s(X1,X2)
| ~ r(X1,X4)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_50,c_0_41]),
[final] ).
cnf(c_0_56,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r2(X1))
| equalish(X3,u10r2(X1))
| equalish(X2,X3)
| ~ s(X1,X3)
| ~ t(X1,X2) ),
inference(spm,[status(thm)],[c_0_47,c_0_41]),
[final] ).
cnf(c_0_57,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r1(X1))
| equalish(X3,u10r1(X1))
| equalish(X2,X3)
| ~ s(X1,X3)
| ~ t(X1,X2) ),
inference(spm,[status(thm)],[c_0_48,c_0_41]),
[final] ).
cnf(c_0_58,plain,
( t3least(X1)
| equalish(X2,X3)
| equalish(X2,X4)
| equalish(X3,X4)
| ~ r(X1,X4)
| ~ r(X1,X3)
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_50,c_0_42]),
[final] ).
cnf(c_0_59,axiom,
( r1most(X1)
| r(X1,u9r1(X1)) ),
clause_36,
[final] ).
cnf(c_0_60,axiom,
( equalish(X1,X2)
| ~ r1most(X3)
| ~ r(X3,X1)
| ~ r(X3,X2) ),
clause_34,
[final] ).
cnf(c_0_61,axiom,
( e(X1)
| ~ a(u7r1(X1))
| ~ t3least(X1)
| ~ r1most(X1)
| ~ s1most(X1) ),
clause_25 ).
cnf(c_0_62,axiom,
( a(X1)
| ~ c(X1) ),
clause_16,
[final] ).
cnf(c_0_63,axiom,
( p2least(X1)
| equalish(X2,X3)
| ~ p(X1,X2)
| ~ p(X1,X3) ),
clause_7,
[final] ).
cnf(c_0_64,axiom,
( p1most(X1)
| p(X1,u3r1(X1)) ),
clause_12,
[final] ).
cnf(c_0_65,axiom,
( a(X1)
| ~ d(X1) ),
clause_15,
[final] ).
cnf(c_0_66,axiom,
( a(X1)
| ~ e(X2)
| ~ t(X2,X1) ),
clause_24,
[final] ).
cnf(c_0_67,axiom,
( t(X1,u8r3(X1))
| ~ t3least(X1) ),
clause_32,
[final] ).
cnf(c_0_68,axiom,
( t3least(X1)
| ~ e(X1) ),
clause_23,
[final] ).
cnf(c_0_69,axiom,
( t(X1,u8r1(X1))
| ~ t3least(X1) ),
clause_30,
[final] ).
cnf(c_0_70,axiom,
( t(X1,u8r2(X1))
| ~ t3least(X1) ),
clause_31,
[final] ).
cnf(c_0_71,axiom,
( equalish(X1,X2)
| ~ p1most(X3)
| ~ p(X3,X1)
| ~ p(X3,X2) ),
clause_10,
[final] ).
cnf(c_0_72,axiom,
( p(X1,u1r1(X1))
| ~ p2least(X1) ),
clause_5,
[final] ).
cnf(c_0_73,axiom,
( c(X1)
| ~ r(X2,X1) ),
clause_17,
[final] ).
cnf(c_0_74,axiom,
( r1most(X1)
| r(X1,u9r2(X1)) ),
clause_37,
[final] ).
cnf(c_0_75,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r2(X1))
| equalish(X3,u10r2(X1))
| equalish(X3,X2)
| ~ r(X1,X2)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_51,c_0_42]),
[final] ).
cnf(c_0_76,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r1(X1))
| equalish(X3,u10r1(X1))
| equalish(X3,X2)
| ~ r(X1,X2)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_52,c_0_42]),
[final] ).
cnf(c_0_77,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r2(X1),X2)
| equalish(X3,u10r2(X1))
| equalish(X3,X2)
| ~ r(X1,X2)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_53,c_0_42]),
[final] ).
cnf(c_0_78,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r1(X1),X2)
| equalish(X3,u10r1(X1))
| equalish(X3,X2)
| ~ r(X1,X2)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_54,c_0_42]),
[final] ).
cnf(c_0_79,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r2(X1),X2)
| equalish(u10r2(X1),X3)
| equalish(X3,X2)
| ~ r(X1,X2)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_44]),
[final] ).
cnf(c_0_80,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r2(X1))
| equalish(X3,u10r2(X1))
| equalish(X3,X2)
| ~ s(X1,X3)
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_51,c_0_41]),
[final] ).
cnf(c_0_81,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r1(X1),X2)
| equalish(u10r1(X1),X3)
| equalish(X3,X2)
| ~ r(X1,X2)
| ~ r(X1,X3) ),
inference(spm,[status(thm)],[c_0_55,c_0_45]),
[final] ).
cnf(c_0_82,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r1(X1))
| equalish(X3,u10r1(X1))
| equalish(X3,X2)
| ~ s(X1,X3)
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_52,c_0_41]),
[final] ).
cnf(c_0_83,axiom,
( s1most(X1)
| ~ equalish(u10r2(X1),u10r1(X1)) ),
clause_39,
[final] ).
cnf(c_0_84,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r2(X1),u10r2(X1))
| equalish(X2,u10r2(X1))
| ~ t(X1,X2) ),
inference(spm,[status(thm)],[c_0_56,c_0_44]) ).
cnf(c_0_85,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r1(X1),u10r1(X1))
| equalish(X2,u10r1(X1))
| ~ t(X1,X2) ),
inference(spm,[status(thm)],[c_0_57,c_0_45]) ).
cnf(c_0_86,plain,
( t3least(X1)
| equalish(X2,u9r1(X1))
| equalish(X3,u9r1(X1))
| equalish(X3,X2)
| ~ r(X1,X2)
| ~ r(X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_60]),
[final] ).
cnf(c_0_87,axiom,
( r1most(X1)
| ~ equalish(u9r2(X1),u9r1(X1)) ),
clause_35,
[final] ).
cnf(c_0_88,plain,
( e(X1)
| ~ t3least(X1)
| ~ r1most(X1)
| ~ s1most(X1)
| ~ c(u7r1(X1)) ),
inference(spm,[status(thm)],[c_0_61,c_0_62]) ).
cnf(c_0_89,axiom,
( c(X1)
| ~ p2least(X1) ),
clause_3,
[final] ).
cnf(c_0_90,axiom,
( p1most(X1)
| ~ equalish(u3r2(X1),u3r1(X1)) ),
clause_11,
[final] ).
cnf(c_0_91,plain,
( p1most(X1)
| equalish(X2,u3r1(X1))
| p2least(X1)
| ~ p(X1,X2) ),
inference(spm,[status(thm)],[c_0_63,c_0_64]) ).
cnf(c_0_92,axiom,
( p1most(X1)
| p(X1,u3r2(X1)) ),
clause_13,
[final] ).
cnf(c_0_93,plain,
( e(X1)
| ~ t3least(X1)
| ~ r1most(X1)
| ~ s1most(X1)
| ~ d(u7r1(X1)) ),
inference(spm,[status(thm)],[c_0_61,c_0_65]) ).
cnf(c_0_94,axiom,
( d(X1)
| ~ p1most(X1) ),
clause_9,
[final] ).
cnf(c_0_95,axiom,
( c(X1)
| d(X1)
| ~ a(X1) ),
clause_14,
[final] ).
cnf(c_0_96,plain,
( a(u8r3(X1))
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_68]),
[final] ).
cnf(c_0_97,plain,
( a(u8r1(X1))
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_69]),c_0_68]),
[final] ).
cnf(c_0_98,plain,
( a(u8r2(X1))
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_70]),c_0_68]),
[final] ).
cnf(c_0_99,axiom,
( ~ p2least(X1)
| ~ equalish(u1r2(X1),u1r1(X1)) ),
clause_4,
[final] ).
cnf(c_0_100,plain,
( equalish(X1,u1r1(X2))
| ~ p1most(X2)
| ~ p(X2,X1)
| ~ p2least(X2) ),
inference(spm,[status(thm)],[c_0_71,c_0_72]) ).
cnf(c_0_101,axiom,
( p(X1,u1r2(X1))
| ~ p2least(X1) ),
clause_6,
[final] ).
cnf(c_0_102,axiom,
( p2least(X1)
| ~ c(X1) ),
clause_2,
[final] ).
cnf(c_0_103,plain,
( r1most(X1)
| c(u9r2(X1)) ),
inference(spm,[status(thm)],[c_0_73,c_0_74]),
[final] ).
cnf(c_0_104,plain,
( r1most(X1)
| c(u9r1(X1)) ),
inference(spm,[status(thm)],[c_0_73,c_0_59]),
[final] ).
cnf(c_0_105,axiom,
( d(X1)
| ~ s(X2,X1) ),
clause_19,
[final] ).
cnf(c_0_106,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r1(X1),u10r2(X1))
| equalish(X2,u9r1(X1))
| equalish(X2,u10r2(X1))
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_59]),
[final] ).
cnf(c_0_107,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r1(X1),u10r1(X1))
| equalish(X2,u9r1(X1))
| equalish(X2,u10r1(X1))
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_59]),
[final] ).
cnf(c_0_108,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u10r2(X1),u9r2(X1))
| equalish(X2,u9r2(X1))
| equalish(X2,u10r2(X1))
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_74]),
[final] ).
cnf(c_0_109,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u10r2(X1),u9r1(X1))
| equalish(X2,u9r1(X1))
| equalish(X2,u10r2(X1))
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_77,c_0_59]),
[final] ).
cnf(c_0_110,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u10r1(X1),u9r2(X1))
| equalish(X2,u9r2(X1))
| equalish(X2,u10r1(X1))
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_78,c_0_74]),
[final] ).
cnf(c_0_111,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u10r1(X1),u9r1(X1))
| equalish(X2,u9r1(X1))
| equalish(X2,u10r1(X1))
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_78,c_0_59]),
[final] ).
cnf(c_0_112,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u10r2(X1),u9r1(X1))
| equalish(X2,u9r1(X1))
| equalish(u10r2(X1),X2)
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_59]),
[final] ).
cnf(c_0_113,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r1(X1),u10r2(X1))
| equalish(u10r1(X1),X2)
| equalish(X2,u10r2(X1))
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_80,c_0_45]),
[final] ).
cnf(c_0_114,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u10r1(X1),u9r1(X1))
| equalish(X2,u9r1(X1))
| equalish(u10r1(X1),X2)
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_59]),
[final] ).
cnf(c_0_115,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r2(X1),X2)
| equalish(X2,u10r1(X1))
| ~ r(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_82,c_0_44]),c_0_83]),
[final] ).
cnf(c_0_116,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r1(X1),X2)
| equalish(X3,u10r1(X1))
| equalish(X3,X2)
| ~ s(X1,X3)
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_54,c_0_41]),
[final] ).
cnf(c_0_117,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r2(X1),u10r2(X1))
| equalish(X2,u10r2(X1))
| ~ s(X1,X2) ),
inference(spm,[status(thm)],[c_0_84,c_0_41]) ).
cnf(c_0_118,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r1(X1),u10r1(X1))
| equalish(X2,u10r1(X1))
| ~ s(X1,X2) ),
inference(spm,[status(thm)],[c_0_85,c_0_41]) ).
cnf(c_0_119,plain,
( t3least(X1)
| r1most(X1)
| equalish(X2,u9r2(X1))
| equalish(X2,u9r1(X1))
| ~ r(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_86,c_0_74]),c_0_87]),
[final] ).
cnf(c_0_120,plain,
( t3least(X1)
| r1most(X1)
| equalish(u9r1(X1),u9r1(X1))
| equalish(X2,u9r1(X1))
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_86,c_0_59]) ).
cnf(c_0_121,plain,
( e(X1)
| ~ t3least(X1)
| ~ r1most(X1)
| ~ s1most(X1)
| ~ p2least(u7r1(X1)) ),
inference(spm,[status(thm)],[c_0_88,c_0_89]) ).
cnf(c_0_122,plain,
( p1most(X1)
| p2least(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_90,c_0_91]),c_0_92]),
[final] ).
cnf(c_0_123,plain,
( e(X1)
| ~ t3least(X1)
| ~ r1most(X1)
| ~ s1most(X1)
| ~ p1most(u7r1(X1)) ),
inference(spm,[status(thm)],[c_0_93,c_0_94]) ).
cnf(c_0_124,axiom,
( p1most(X1)
| ~ d(X1) ),
clause_8,
[final] ).
cnf(c_0_125,plain,
( d(u8r3(X1))
| c(u8r3(X1))
| ~ e(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_96]),
[final] ).
cnf(c_0_126,plain,
( d(u8r1(X1))
| c(u8r1(X1))
| ~ e(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_97]),
[final] ).
cnf(c_0_127,plain,
( d(u8r2(X1))
| c(u8r2(X1))
| ~ e(X1) ),
inference(spm,[status(thm)],[c_0_95,c_0_98]),
[final] ).
cnf(c_0_128,plain,
( ~ p1most(X1)
| ~ p2least(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_99,c_0_100]),c_0_101]),
[final] ).
cnf(c_0_129,plain,
( r1most(X1)
| p2least(u9r2(X1)) ),
inference(spm,[status(thm)],[c_0_102,c_0_103]),
[final] ).
cnf(c_0_130,plain,
( r1most(X1)
| p2least(u9r1(X1)) ),
inference(spm,[status(thm)],[c_0_102,c_0_104]),
[final] ).
cnf(c_0_131,plain,
( s1most(X1)
| d(u10r1(X1)) ),
inference(spm,[status(thm)],[c_0_105,c_0_45]),
[final] ).
cnf(c_0_132,plain,
( s1most(X1)
| d(u10r2(X1)) ),
inference(spm,[status(thm)],[c_0_105,c_0_44]),
[final] ).
cnf(c_0_133,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r2(X1),u10r2(X1))
| equalish(u9r1(X1),u10r2(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_106,c_0_74]),c_0_87]),
[final] ).
cnf(c_0_134,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r2(X1),u10r1(X1))
| equalish(u9r1(X1),u10r1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_107,c_0_74]),c_0_87]),
[final] ).
cnf(c_0_135,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r1(X1),u10r2(X1))
| equalish(u9r1(X1),u9r2(X1))
| equalish(u10r2(X1),u9r2(X1)) ),
inference(spm,[status(thm)],[c_0_108,c_0_59]),
[final] ).
cnf(c_0_136,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r2(X1),u10r2(X1))
| equalish(u10r2(X1),u9r1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_109,c_0_74]),c_0_87]),
[final] ).
cnf(c_0_137,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r1(X1),u10r1(X1))
| equalish(u9r1(X1),u9r2(X1))
| equalish(u10r1(X1),u9r2(X1)) ),
inference(spm,[status(thm)],[c_0_110,c_0_59]),
[final] ).
cnf(c_0_138,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r2(X1),u10r1(X1))
| equalish(u10r1(X1),u9r1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_111,c_0_74]),c_0_87]),
[final] ).
cnf(c_0_139,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u10r2(X1),u9r2(X1))
| equalish(u10r2(X1),u9r1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_112,c_0_74]),c_0_87]),
[final] ).
cnf(c_0_140,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r2(X1),u10r2(X1))
| equalish(u10r1(X1),u9r2(X1))
| equalish(u10r1(X1),u10r2(X1)) ),
inference(spm,[status(thm)],[c_0_113,c_0_74]),
[final] ).
cnf(c_0_141,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r2(X1),u10r2(X1))
| equalish(X2,u9r2(X1))
| equalish(X2,u10r2(X1))
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_75,c_0_74]),
[final] ).
cnf(c_0_142,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r2(X1),u10r1(X1))
| equalish(X2,u9r2(X1))
| equalish(X2,u10r1(X1))
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_76,c_0_74]),
[final] ).
cnf(c_0_143,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r1(X1),u10r2(X1))
| equalish(u10r1(X1),u9r1(X1))
| equalish(u10r1(X1),u10r2(X1)) ),
inference(spm,[status(thm)],[c_0_113,c_0_59]),
[final] ).
cnf(c_0_144,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u10r2(X1),u9r2(X1))
| equalish(X2,u9r2(X1))
| equalish(u10r2(X1),X2)
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_79,c_0_74]),
[final] ).
cnf(c_0_145,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u10r1(X1),u9r2(X1))
| equalish(X2,u9r2(X1))
| equalish(u10r1(X1),X2)
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_81,c_0_74]),
[final] ).
cnf(c_0_146,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u10r1(X1),u9r2(X1))
| equalish(u10r1(X1),u9r1(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_114,c_0_74]),c_0_87]),
[final] ).
cnf(c_0_147,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r2(X1),u10r1(X1))
| equalish(u10r2(X1),u9r2(X1)) ),
inference(spm,[status(thm)],[c_0_115,c_0_74]),
[final] ).
cnf(c_0_148,plain,
( t3least(X1)
| r1most(X1)
| s1most(X1)
| equalish(u9r1(X1),u10r1(X1))
| equalish(u10r2(X1),u9r1(X1)) ),
inference(spm,[status(thm)],[c_0_115,c_0_59]),
[final] ).
cnf(c_0_149,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r2(X1),X2)
| equalish(X3,u10r2(X1))
| equalish(X3,X2)
| ~ s(X1,X3)
| ~ r(X1,X2) ),
inference(spm,[status(thm)],[c_0_53,c_0_41]),
[final] ).
cnf(c_0_150,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r2(X1),X2)
| equalish(u10r1(X1),X2)
| ~ r(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_116,c_0_44]),c_0_83]),
[final] ).
cnf(c_0_151,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r2(X1),u10r2(X1)) ),
inference(spm,[status(thm)],[c_0_117,c_0_44]),
[final] ).
cnf(c_0_152,plain,
( t3least(X1)
| s1most(X1)
| equalish(X2,u10r2(X1))
| equalish(X2,u10r1(X1))
| ~ t(X1,X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_57,c_0_44]),c_0_83]),
[final] ).
cnf(c_0_153,plain,
( t3least(X1)
| s1most(X1)
| equalish(u10r1(X1),u10r1(X1)) ),
inference(spm,[status(thm)],[c_0_118,c_0_45]),
[final] ).
cnf(c_0_154,plain,
( t3least(X1)
| equalish(X2,u9r2(X1))
| equalish(X3,u9r2(X1))
| equalish(X3,X2)
| ~ r(X1,X2)
| ~ r(X1,X3) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_74]),c_0_60]),
[final] ).
cnf(c_0_155,plain,
( t3least(X1)
| r1most(X1)
| equalish(u9r2(X1),u9r2(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_87,c_0_119]),c_0_74]),
[final] ).
cnf(c_0_156,plain,
( t3least(X1)
| r1most(X1)
| equalish(u9r1(X1),u9r1(X1)) ),
inference(spm,[status(thm)],[c_0_120,c_0_59]),
[final] ).
cnf(c_0_157,plain,
( e(X1)
| ~ t3least(X1)
| ~ r1most(X1)
| ~ s1most(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_121,c_0_122]),c_0_123]),
[final] ).
cnf(c_0_158,plain,
( p1most(u8r3(X1))
| c(u8r3(X1))
| ~ e(X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_125]),
[final] ).
cnf(c_0_159,plain,
( p1most(u8r1(X1))
| c(u8r1(X1))
| ~ e(X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_126]),
[final] ).
cnf(c_0_160,plain,
( p1most(u8r2(X1))
| c(u8r2(X1))
| ~ e(X1) ),
inference(spm,[status(thm)],[c_0_124,c_0_127]),
[final] ).
cnf(c_0_161,plain,
( r1most(X1)
| ~ p1most(u9r2(X1)) ),
inference(spm,[status(thm)],[c_0_128,c_0_129]),
[final] ).
cnf(c_0_162,plain,
( r1most(X1)
| ~ p1most(u9r1(X1)) ),
inference(spm,[status(thm)],[c_0_128,c_0_130]),
[final] ).
cnf(c_0_163,axiom,
( equalish(X1,X2)
| ~ s1most(X3)
| ~ s(X3,X1)
| ~ s(X3,X2) ),
clause_38,
[final] ).
cnf(c_0_164,plain,
( s1most(X1)
| p1most(u10r1(X1)) ),
inference(spm,[status(thm)],[c_0_124,c_0_131]),
[final] ).
cnf(c_0_165,plain,
( s1most(X1)
| p1most(u10r2(X1)) ),
inference(spm,[status(thm)],[c_0_124,c_0_132]),
[final] ).
cnf(c_0_166,plain,
( a(X1)
| ~ s(X2,X1)
| ~ e(X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_41]),
[final] ).
cnf(c_0_167,plain,
( a(X1)
| ~ r(X2,X1)
| ~ e(X2) ),
inference(spm,[status(thm)],[c_0_66,c_0_42]),
[final] ).
cnf(c_0_168,axiom,
( ~ t3least(X1)
| ~ equalish(u8r3(X1),u8r1(X1)) ),
clause_28,
[final] ).
cnf(c_0_169,axiom,
( ~ t3least(X1)
| ~ equalish(u8r3(X1),u8r2(X1)) ),
clause_29,
[final] ).
cnf(c_0_170,axiom,
( ~ t3least(X1)
| ~ equalish(u8r2(X1),u8r1(X1)) ),
clause_27,
[final] ).
cnf(c_0_171,axiom,
( r1most(X1)
| ~ e(X1) ),
clause_22,
[final] ).
cnf(c_0_172,axiom,
( s1most(X1)
| ~ e(X1) ),
clause_21,
[final] ).
cnf(c_0_173,negated_conjecture,
e(exist),
clause_1,
[final] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS009-1 : TPTP v9.2.1. Released v2.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Mon May 4 20:34:05 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.27/1.72 % Version : CSE_E---1.7
% 1.27/1.72 % Problem : theBenchmark.p
% 1.27/1.72 % SZS status Satisfiable for theBenchmark.p
% 1.27/1.72 % SZS output start Saturation
% See solution above
% 1.27/1.72 % Total time : 1.367s
%------------------------------------------------------------------------------