%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : KRS010-1 : 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 : n002.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 : Unsatisfiable 1.25s 1.72s
% Output : CNFRefutation 1.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 13
% Syntax : Number of clauses : 49 ( 5 unt; 12 nHn; 49 RR)
% Number of literals : 159 ( 0 equ; 106 neg)
% Maximal clause size : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-1 aty)
% Number of variables : 58 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(clause_31,axiom,
( f(X1)
| equalish(X2,X3)
| ~ r(X1,X2)
| ~ r(X1,X3)
| ~ d(X2)
| ~ d(X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_31) ).
cnf(clause_22,axiom,
( r(X1,u2r1(X1))
| ~ r3least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_22) ).
cnf(clause_23,axiom,
( r(X1,u2r2(X1))
| ~ r3least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_23) ).
cnf(clause_20,axiom,
( ~ r3least(X1)
| ~ equalish(u2r3(X1),u2r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).
cnf(clause_24,axiom,
( r(X1,u2r3(X1))
| ~ r3least(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_24) ).
cnf(clause_21,axiom,
( ~ r3least(X1)
| ~ equalish(u2r3(X1),u2r2(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_21) ).
cnf(clause_6,axiom,
( equalish(X1,X2)
| ~ e(X3)
| ~ r(X3,X1)
| ~ r(X3,X2)
| ~ c(X1)
| ~ c(X2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).
cnf(clause_7,axiom,
( r3least(X1)
| ~ e(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_7) ).
cnf(clause_3,axiom,
( c(X1)
| d(X1)
| ~ a(X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_3) ).
cnf(clause_8,axiom,
( a(X1)
| ~ e(X2)
| ~ r(X2,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_8) ).
cnf(clause_19,axiom,
( ~ r3least(X1)
| ~ equalish(u2r2(X1),u2r1(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_19) ).
cnf(clause_2,negated_conjecture,
~ f(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_2) ).
cnf(clause_1,negated_conjecture,
e(exist),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_1) ).
cnf(c_0_13,axiom,
( f(X1)
| equalish(X2,X3)
| ~ r(X1,X2)
| ~ r(X1,X3)
| ~ d(X2)
| ~ d(X3) ),
clause_31 ).
cnf(c_0_14,axiom,
( r(X1,u2r1(X1))
| ~ r3least(X1) ),
clause_22 ).
cnf(c_0_15,axiom,
( r(X1,u2r2(X1))
| ~ r3least(X1) ),
clause_23 ).
cnf(c_0_16,axiom,
( ~ r3least(X1)
| ~ equalish(u2r3(X1),u2r1(X1)) ),
clause_20 ).
cnf(c_0_17,plain,
( equalish(X1,u2r1(X2))
| f(X2)
| ~ r3least(X2)
| ~ r(X2,X1)
| ~ d(u2r1(X2))
| ~ d(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_18,axiom,
( r(X1,u2r3(X1))
| ~ r3least(X1) ),
clause_24 ).
cnf(c_0_19,axiom,
( ~ r3least(X1)
| ~ equalish(u2r3(X1),u2r2(X1)) ),
clause_21 ).
cnf(c_0_20,plain,
( equalish(X1,u2r2(X2))
| f(X2)
| ~ r3least(X2)
| ~ r(X2,X1)
| ~ d(u2r2(X2))
| ~ d(X1) ),
inference(spm,[status(thm)],[c_0_13,c_0_15]) ).
cnf(c_0_21,axiom,
( equalish(X1,X2)
| ~ e(X3)
| ~ r(X3,X1)
| ~ r(X3,X2)
| ~ c(X1)
| ~ c(X2) ),
clause_6 ).
cnf(c_0_22,axiom,
( r3least(X1)
| ~ e(X1) ),
clause_7 ).
cnf(c_0_23,plain,
( f(X1)
| ~ r3least(X1)
| ~ d(u2r1(X1))
| ~ d(u2r3(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).
cnf(c_0_24,axiom,
( c(X1)
| d(X1)
| ~ a(X1) ),
clause_3 ).
cnf(c_0_25,plain,
( f(X1)
| ~ r3least(X1)
| ~ d(u2r2(X1))
| ~ d(u2r3(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_18]) ).
cnf(c_0_26,plain,
( equalish(X1,u2r2(X2))
| ~ r(X2,X1)
| ~ c(u2r2(X2))
| ~ c(X1)
| ~ e(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_15]),c_0_22]) ).
cnf(c_0_27,plain,
( c(u2r3(X1))
| f(X1)
| ~ r3least(X1)
| ~ a(u2r3(X1))
| ~ d(u2r1(X1)) ),
inference(spm,[status(thm)],[c_0_23,c_0_24]) ).
cnf(c_0_28,axiom,
( a(X1)
| ~ e(X2)
| ~ r(X2,X1) ),
clause_8 ).
cnf(c_0_29,axiom,
( ~ r3least(X1)
| ~ equalish(u2r2(X1),u2r1(X1)) ),
clause_19 ).
cnf(c_0_30,plain,
( equalish(X1,u2r1(X2))
| ~ r(X2,X1)
| ~ c(u2r1(X2))
| ~ c(X1)
| ~ e(X2) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_14]),c_0_22]) ).
cnf(c_0_31,plain,
( c(u2r3(X1))
| f(X1)
| ~ r3least(X1)
| ~ a(u2r3(X1))
| ~ d(u2r2(X1)) ),
inference(spm,[status(thm)],[c_0_25,c_0_24]) ).
cnf(c_0_32,plain,
( ~ c(u2r2(X1))
| ~ c(u2r3(X1))
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_26]),c_0_18]),c_0_22]) ).
cnf(c_0_33,plain,
( c(u2r1(X1))
| c(u2r3(X1))
| f(X1)
| ~ r3least(X1)
| ~ a(u2r3(X1))
| ~ a(u2r1(X1)) ),
inference(spm,[status(thm)],[c_0_27,c_0_24]) ).
cnf(c_0_34,plain,
( a(u2r1(X1))
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_14]),c_0_22]) ).
cnf(c_0_35,plain,
( a(u2r3(X1))
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_18]),c_0_22]) ).
cnf(c_0_36,plain,
( ~ c(u2r1(X1))
| ~ c(u2r2(X1))
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_15]),c_0_22]) ).
cnf(c_0_37,plain,
( f(X1)
| ~ r3least(X1)
| ~ d(u2r1(X1))
| ~ d(u2r2(X1)) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_17]),c_0_15]) ).
cnf(c_0_38,plain,
( ~ c(u2r1(X1))
| ~ c(u2r3(X1))
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_30]),c_0_18]),c_0_22]) ).
cnf(c_0_39,plain,
( c(u2r2(X1))
| c(u2r3(X1))
| f(X1)
| ~ r3least(X1)
| ~ a(u2r3(X1))
| ~ a(u2r2(X1)) ),
inference(spm,[status(thm)],[c_0_31,c_0_24]) ).
cnf(c_0_40,plain,
( a(u2r2(X1))
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_15]),c_0_22]) ).
cnf(c_0_41,plain,
( f(X1)
| ~ c(u2r2(X1))
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_33]),c_0_34]),c_0_35]),c_0_22]),c_0_36]) ).
cnf(c_0_42,plain,
( c(u2r1(X1))
| f(X1)
| ~ r3least(X1)
| ~ a(u2r1(X1))
| ~ d(u2r2(X1)) ),
inference(spm,[status(thm)],[c_0_37,c_0_24]) ).
cnf(c_0_43,plain,
( f(X1)
| ~ c(u2r1(X1))
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_40]),c_0_35]),c_0_22]),c_0_41]) ).
cnf(c_0_44,plain,
( c(u2r2(X1))
| c(u2r1(X1))
| f(X1)
| ~ r3least(X1)
| ~ a(u2r1(X1))
| ~ a(u2r2(X1)) ),
inference(spm,[status(thm)],[c_0_42,c_0_24]) ).
cnf(c_0_45,negated_conjecture,
~ f(exist),
clause_2 ).
cnf(c_0_46,plain,
( f(X1)
| ~ e(X1) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_40]),c_0_34]),c_0_22]),c_0_41]) ).
cnf(c_0_47,negated_conjecture,
e(exist),
clause_1 ).
cnf(c_0_48,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_47])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KRS010-1 : 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 : n002.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 20:34:01 EDT 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.25/1.72 % Version : CSE_E---1.7
% 1.25/1.72 % Problem : theBenchmark.p
% 1.25/1.72 % SZS status Unsatisfiable for theBenchmark.p
% 1.25/1.72 % SZS output start CNFRefutation
% See solution above
% 1.25/1.72 % Total time : 1.373s
%------------------------------------------------------------------------------