%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN015-1 : TPTP v9.2.1. Released v1.0.0.
% 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 : n024.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 05:35:20 PM UTC 2026
% Result : Unsatisfiable 1.13s 1.61s
% Output : CNFRefutation 1.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 16
% Syntax : Number of clauses : 73 ( 6 unt; 62 nHn; 67 RR)
% Number of literals : 216 ( 129 equ; 48 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 41 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_16,negated_conjecture,
( X1 = k
| X1 = m
| X1 = n
| ~ element(X1,k) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
cnf(c_12,negated_conjecture,
( X1 = n
| element(X1,n)
| element(g(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_12) ).
cnf(c_10,negated_conjecture,
( X1 = n
| element(X1,n)
| g(X1) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_10) ).
cnf(c_9,negated_conjecture,
( X1 = n
| element(X1,n)
| g(X1) != n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_9) ).
cnf(c_11,negated_conjecture,
( X1 = n
| element(X1,n)
| element(X1,g(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_11) ).
cnf(c_7,negated_conjecture,
( X1 = m
| element(f(X1),X1)
| ~ element(X1,m) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).
cnf(c_5,negated_conjecture,
( X1 = m
| ~ element(X1,m)
| f(X1) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).
cnf(c_6,negated_conjecture,
( X1 = m
| element(X1,f(X1))
| ~ element(X1,m) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_6) ).
cnf(c_4,negated_conjecture,
( X1 = m
| ~ element(X1,m)
| f(X1) != m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_4) ).
cnf(c_15,negated_conjecture,
( X1 = k
| element(X1,k)
| X1 != n ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_15) ).
cnf(c_8,negated_conjecture,
( X1 = m
| element(X1,m)
| X2 = m
| X2 = X1
| ~ element(X1,X2)
| ~ element(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_8) ).
cnf(c_1,negated_conjecture,
m != n,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_1) ).
cnf(c_13,negated_conjecture,
( X1 = n
| X2 = n
| X2 = X1
| ~ element(X1,n)
| ~ element(X1,X2)
| ~ element(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_13) ).
cnf(c_14,negated_conjecture,
( X1 = k
| element(X1,k)
| X1 != m ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_14) ).
cnf(c_3,negated_conjecture,
( X1 = j
| X1 = k
| ~ element(X1,j) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_3) ).
cnf(c_2,negated_conjecture,
( X1 = j
| element(X1,j)
| X1 != k ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_2) ).
cnf(c_0_16,negated_conjecture,
( X1 = k
| X1 = m
| X1 = n
| ~ element(X1,k) ),
c_16 ).
cnf(c_0_17,negated_conjecture,
( X1 = n
| element(X1,n)
| element(g(X1),X1) ),
c_12 ).
cnf(c_0_18,negated_conjecture,
( X1 = n
| element(X1,n)
| g(X1) != X1 ),
c_10 ).
cnf(c_0_19,negated_conjecture,
( X1 = n
| element(X1,n)
| g(X1) != n ),
c_9 ).
cnf(c_0_20,negated_conjecture,
( X1 = n
| element(X1,n)
| element(X1,g(X1)) ),
c_11 ).
cnf(c_0_21,negated_conjecture,
( g(k) = m
| k = n
| element(k,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]),c_0_19]) ).
cnf(c_0_22,negated_conjecture,
( X1 = m
| element(f(X1),X1)
| ~ element(X1,m) ),
c_7 ).
cnf(c_0_23,negated_conjecture,
( k = n
| element(k,n)
| element(k,m) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_24,negated_conjecture,
( k = n
| element(k,n)
| k != m ),
inference(spm,[status(thm)],[c_0_18,c_0_21]) ).
cnf(c_0_25,negated_conjecture,
( k = n
| element(f(k),k)
| element(k,n) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]) ).
cnf(c_0_26,negated_conjecture,
( X1 = m
| ~ element(X1,m)
| f(X1) != X1 ),
c_5 ).
cnf(c_0_27,negated_conjecture,
( f(k) = k
| f(k) = n
| f(k) = m
| k = n
| element(k,n) ),
inference(spm,[status(thm)],[c_0_16,c_0_25]) ).
cnf(c_0_28,negated_conjecture,
( X1 = m
| element(X1,f(X1))
| ~ element(X1,m) ),
c_6 ).
cnf(c_0_29,negated_conjecture,
( X1 = m
| ~ element(X1,m)
| f(X1) != m ),
c_4 ).
cnf(c_0_30,negated_conjecture,
( f(k) = m
| f(k) = n
| k = n
| element(k,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_23]),c_0_24]) ).
cnf(c_0_31,negated_conjecture,
( X1 = k
| element(X1,k)
| X1 != n ),
c_15 ).
cnf(c_0_32,negated_conjecture,
( k = n
| element(k,f(k))
| element(k,n) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_23]),c_0_24]) ).
cnf(c_0_33,negated_conjecture,
( f(k) = n
| k = n
| element(k,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_23]),c_0_24]) ).
cnf(c_0_34,negated_conjecture,
( X1 = m
| element(X1,m)
| X2 = m
| X2 = X1
| ~ element(X1,X2)
| ~ element(X2,X1) ),
c_8 ).
cnf(c_0_35,negated_conjecture,
( k = n
| element(n,k) ),
inference(er,[status(thm)],[c_0_31]) ).
cnf(c_0_36,negated_conjecture,
m != n,
c_1 ).
cnf(c_0_37,negated_conjecture,
( X1 = n
| X2 = n
| X2 = X1
| ~ element(X1,n)
| ~ element(X1,X2)
| ~ element(X2,X1) ),
c_13 ).
cnf(c_0_38,negated_conjecture,
( k = n
| element(k,n) ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_39,negated_conjecture,
( X1 = k
| element(X1,k)
| X1 != m ),
c_14 ).
cnf(c_0_40,negated_conjecture,
( k = n
| k = m
| element(k,m)
| ~ element(k,n) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]) ).
cnf(c_0_41,negated_conjecture,
( k = n
| k = X1
| X1 = n
| ~ element(X1,k)
| ~ element(k,X1) ),
inference(spm,[status(thm)],[c_0_37,c_0_38]) ).
cnf(c_0_42,negated_conjecture,
( k = m
| element(m,k) ),
inference(er,[status(thm)],[c_0_39]) ).
cnf(c_0_43,negated_conjecture,
( k = m
| k = n
| element(k,m) ),
inference(spm,[status(thm)],[c_0_40,c_0_38]) ).
cnf(c_0_44,negated_conjecture,
( k = m
| k = n ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_42]),c_0_36]),c_0_43]) ).
cnf(c_0_45,negated_conjecture,
( k = n
| element(n,m) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_44]),c_0_36]) ).
cnf(c_0_46,negated_conjecture,
( g(X1) = m
| X1 = n
| X1 = m
| element(X1,n)
| element(X1,m) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_17]),c_0_20]),c_0_18]) ).
cnf(c_0_47,negated_conjecture,
( k = n
| element(n,f(n)) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_45]),c_0_36]) ).
cnf(c_0_48,negated_conjecture,
( X1 = m
| X1 = n
| element(X1,n)
| element(X1,m) ),
inference(spm,[status(thm)],[c_0_20,c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( k = n
| X1 = n
| X1 = m
| ~ element(X1,m) ),
inference(spm,[status(thm)],[c_0_16,c_0_44]) ).
cnf(c_0_50,negated_conjecture,
( f(n) = n
| f(n) = m
| k = n ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_47]),c_0_36]),c_0_48]),c_0_49]) ).
cnf(c_0_51,negated_conjecture,
( X1 = j
| X1 = k
| ~ element(X1,j) ),
c_3 ).
cnf(c_0_52,negated_conjecture,
( f(n) = n
| k = n ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_50]),c_0_36]),c_0_45]) ).
cnf(c_0_53,negated_conjecture,
( g(j) = k
| j = n
| element(j,n) ),
inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_17]),c_0_18]) ).
cnf(c_0_54,negated_conjecture,
( X1 = j
| element(X1,j)
| X1 != k ),
c_2 ).
cnf(c_0_55,negated_conjecture,
k = n,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_52]),c_0_36]),c_0_45]) ).
cnf(c_0_56,negated_conjecture,
( j = n
| element(j,n)
| element(j,k) ),
inference(spm,[status(thm)],[c_0_20,c_0_53]) ).
cnf(c_0_57,negated_conjecture,
( j = k
| element(k,j) ),
inference(er,[status(thm)],[c_0_54]) ).
cnf(c_0_58,negated_conjecture,
( j = n
| element(j,n)
| j != k ),
inference(spm,[status(thm)],[c_0_18,c_0_53]) ).
cnf(c_0_59,negated_conjecture,
( j = n
| element(j,n)
| k != n ),
inference(spm,[status(thm)],[c_0_19,c_0_53]) ).
cnf(c_0_60,negated_conjecture,
( X1 = n
| X1 = m
| ~ element(X1,n) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_55]),c_0_55])]) ).
cnf(c_0_61,negated_conjecture,
( j = n
| element(j,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_56]),c_0_57]),c_0_58]),c_0_59]) ).
cnf(c_0_62,negated_conjecture,
( j = n
| element(n,j) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_57,c_0_55]),c_0_55]) ).
cnf(c_0_63,negated_conjecture,
( j = m
| j = n ),
inference(spm,[status(thm)],[c_0_60,c_0_61]) ).
cnf(c_0_64,negated_conjecture,
( j = n
| element(n,m) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_36]) ).
cnf(c_0_65,negated_conjecture,
( j = n
| element(f(n),n) ),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_64]),c_0_36]) ).
cnf(c_0_66,negated_conjecture,
( f(n) = m
| f(n) = n
| j = n ),
inference(spm,[status(thm)],[c_0_60,c_0_65]) ).
cnf(c_0_67,negated_conjecture,
( f(n) = n
| j = n ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_66]),c_0_36]),c_0_64]) ).
cnf(c_0_68,negated_conjecture,
( X1 = n
| X1 = j
| ~ element(X1,j) ),
inference(rw,[status(thm)],[c_0_51,c_0_55]) ).
cnf(c_0_69,negated_conjecture,
j = n,
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_67]),c_0_36]),c_0_64]) ).
cnf(c_0_70,negated_conjecture,
( X1 = n
| ~ element(X1,n) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_68,c_0_69]),c_0_69])]) ).
cnf(c_0_71,negated_conjecture,
element(m,n),
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_55]),c_0_55]),c_0_36]) ).
cnf(c_0_72,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_71]),c_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SYN015-1 : TPTP v9.2.1. Released v1.0.0.
% 0.00/0.06 % 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
% 0.06/0.24 % Computer : n024.cluster.edu
% 0.06/0.24 % Model : x86_64 x86_64
% 0.06/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.24 % Memory : 8042.1875MB
% 0.06/0.24 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.24 % CPULimit : 300
% 0.06/0.24 % WCLimit : 300
% 0.06/0.24 % DateTime : Tue May 5 03:04:41 EDT 2026
% 0.06/0.24 % CPUTime :
% 0.06/0.25 % start to proof: theBenchmark
% 1.13/1.61 % Version : CSE_E---1.7
% 1.13/1.61 % Problem : theBenchmark.p
% 1.13/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 1.13/1.61 % SZS output start CNFRefutation
% See solution above
% 1.13/1.61 % Total time : 1.361s
%------------------------------------------------------------------------------