%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SYN015-2 : 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 : n004.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 1.29s 1.73s
% Output : CNFRefutation 1.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of clauses : 57 ( 14 unt; 25 nHn; 53 RR)
% Number of literals : 141 ( 0 equ; 53 neg)
% Maximal clause size : 6 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-1 aty)
% Number of variables : 57 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(c_16,negated_conjecture,
( element(X1,k)
| equalish(X1,k)
| ~ equalish(X1,n) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_16) ).
cnf(reflexivityish,axiom,
equalish(X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivityish) ).
cnf(c_20,negated_conjecture,
~ equalish(n,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_20) ).
cnf(transitivityish,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivityish) ).
cnf(c_23,negated_conjecture,
equalish(m,k),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_23) ).
cnf(element_substitutionish2,axiom,
( element(X3,X2)
| ~ element(X1,X2)
| ~ equalish(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_substitutionish2) ).
cnf(element_substitutionish1,axiom,
( element(X3,X2)
| ~ equalish(X1,X2)
| ~ element(X3,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',element_substitutionish1) ).
cnf(symmetryish,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',symmetryish) ).
cnf(c_9,negated_conjecture,
( equalish(X1,X2)
| equalish(X1,m)
| element(X2,m)
| equalish(X2,m)
| ~ element(X1,X2)
| ~ element(X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_9) ).
cnf(c_8,negated_conjecture,
( element(f(X1),X1)
| equalish(X1,m)
| ~ element(X1,m) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_8) ).
cnf(c_7,negated_conjecture,
( element(X1,f(X1))
| equalish(X1,m)
| ~ element(X1,m) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_7) ).
cnf(c_17,negated_conjecture,
( equalish(X1,n)
| equalish(X1,m)
| equalish(X1,k)
| ~ element(X1,k) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_17) ).
cnf(c_11,negated_conjecture,
( element(X1,n)
| equalish(X1,n)
| ~ equalish(g(X1),X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_11) ).
cnf(c_13,negated_conjecture,
( element(g(X1),X1)
| element(X1,n)
| equalish(X1,n) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_13) ).
cnf(c_10,negated_conjecture,
( element(X1,n)
| equalish(X1,n)
| ~ equalish(g(X1),n) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_10) ).
cnf(c_6,negated_conjecture,
( equalish(X1,m)
| ~ equalish(f(X1),X1)
| ~ element(X1,m) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_6) ).
cnf(c_5,negated_conjecture,
( equalish(X1,m)
| ~ equalish(f(X1),m)
| ~ element(X1,m) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_5) ).
cnf(c_0_17,negated_conjecture,
( element(X1,k)
| equalish(X1,k)
| ~ equalish(X1,n) ),
c_16 ).
cnf(c_0_18,axiom,
equalish(X1,X1),
reflexivityish ).
cnf(c_0_19,negated_conjecture,
~ equalish(n,k),
c_20 ).
cnf(c_0_20,axiom,
( equalish(X1,X3)
| ~ equalish(X1,X2)
| ~ equalish(X2,X3) ),
transitivityish ).
cnf(c_0_21,negated_conjecture,
equalish(m,k),
c_23 ).
cnf(c_0_22,axiom,
( element(X3,X2)
| ~ element(X1,X2)
| ~ equalish(X1,X3) ),
element_substitutionish2 ).
cnf(c_0_23,negated_conjecture,
element(n,k),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_19]) ).
cnf(c_0_24,axiom,
( element(X3,X2)
| ~ equalish(X1,X2)
| ~ element(X3,X1) ),
element_substitutionish1 ).
cnf(c_0_25,axiom,
( equalish(X2,X1)
| ~ equalish(X1,X2) ),
symmetryish ).
cnf(c_0_26,negated_conjecture,
( equalish(X1,k)
| ~ equalish(X1,m) ),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,negated_conjecture,
( element(X1,k)
| ~ equalish(n,X1) ),
inference(spm,[status(thm)],[c_0_22,c_0_23]) ).
cnf(c_0_28,negated_conjecture,
( equalish(X1,X2)
| equalish(X1,m)
| element(X2,m)
| equalish(X2,m)
| ~ element(X1,X2)
| ~ element(X2,X1) ),
c_9 ).
cnf(c_0_29,negated_conjecture,
( element(f(X1),X1)
| equalish(X1,m)
| ~ element(X1,m) ),
c_8 ).
cnf(c_0_30,negated_conjecture,
( element(n,X1)
| ~ equalish(k,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_23]) ).
cnf(c_0_31,negated_conjecture,
equalish(k,m),
inference(spm,[status(thm)],[c_0_25,c_0_21]) ).
cnf(c_0_32,negated_conjecture,
~ equalish(n,m),
inference(spm,[status(thm)],[c_0_19,c_0_26]) ).
cnf(c_0_33,negated_conjecture,
( element(X1,f(X1))
| equalish(X1,m)
| ~ element(X1,m) ),
c_7 ).
cnf(c_0_34,negated_conjecture,
( element(X1,X2)
| ~ equalish(k,X2)
| ~ equalish(n,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_27]) ).
cnf(c_0_35,negated_conjecture,
( element(X1,m)
| equalish(X1,m)
| equalish(X2,X1)
| ~ element(X1,X2)
| ~ element(X2,X1) ),
inference(csr,[status(thm)],[c_0_28,c_0_24]) ).
cnf(c_0_36,negated_conjecture,
element(f(n),n),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_37,negated_conjecture,
element(n,f(n)),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_30]),c_0_31])]),c_0_32]) ).
cnf(c_0_38,negated_conjecture,
( element(X1,m)
| ~ equalish(n,X1) ),
inference(spm,[status(thm)],[c_0_34,c_0_31]) ).
cnf(c_0_39,negated_conjecture,
( equalish(X1,n)
| equalish(X1,m)
| equalish(X1,k)
| ~ element(X1,k) ),
c_17 ).
cnf(c_0_40,negated_conjecture,
( equalish(X1,m)
| ~ equalish(X1,k) ),
inference(spm,[status(thm)],[c_0_20,c_0_31]) ).
cnf(c_0_41,negated_conjecture,
( element(X1,n)
| equalish(X1,n)
| ~ equalish(g(X1),X1) ),
c_11 ).
cnf(c_0_42,negated_conjecture,
( element(f(n),m)
| equalish(f(n),m) ),
inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37])]),c_0_38]) ).
cnf(c_0_43,negated_conjecture,
( equalish(X1,m)
| equalish(X1,n)
| ~ element(X1,k) ),
inference(csr,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,negated_conjecture,
( element(g(X1),X1)
| element(X1,n)
| equalish(X1,n) ),
c_13 ).
cnf(c_0_45,negated_conjecture,
( element(X1,n)
| equalish(X1,n)
| ~ equalish(g(X1),n) ),
c_10 ).
cnf(c_0_46,negated_conjecture,
( element(k,n)
| equalish(k,n)
| ~ equalish(g(k),m) ),
inference(spm,[status(thm)],[c_0_41,c_0_26]) ).
cnf(c_0_47,negated_conjecture,
( element(f(n),X1)
| equalish(f(n),m)
| ~ equalish(m,X1) ),
inference(spm,[status(thm)],[c_0_24,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
( element(k,n)
| equalish(k,n) ),
inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]),c_0_46]) ).
cnf(c_0_49,negated_conjecture,
( element(f(n),k)
| equalish(f(n),m) ),
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_26]),c_0_18])]) ).
cnf(c_0_50,negated_conjecture,
( element(n,m)
| equalish(k,n) ),
inference(csr,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_23]),c_0_32]),c_0_48]) ).
cnf(c_0_51,negated_conjecture,
( equalish(X1,m)
| ~ equalish(f(X1),X1)
| ~ element(X1,m) ),
c_6 ).
cnf(c_0_52,negated_conjecture,
( equalish(f(n),n)
| equalish(f(n),m) ),
inference(spm,[status(thm)],[c_0_43,c_0_49]) ).
cnf(c_0_53,negated_conjecture,
element(n,m),
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_50]),c_0_19]) ).
cnf(c_0_54,negated_conjecture,
( equalish(X1,m)
| ~ equalish(f(X1),m)
| ~ element(X1,m) ),
c_5 ).
cnf(c_0_55,negated_conjecture,
equalish(f(n),m),
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_52]),c_0_53])]),c_0_32]) ).
cnf(c_0_56,negated_conjecture,
$false,
inference(sr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_54,c_0_55]),c_0_53])]),c_0_32]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYN015-2 : TPTP v9.2.1. Released v1.0.0.
% 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
% 0.15/0.33 % Computer : n004.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 : Tue May 5 08:04:47 EDT 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.35 % start to proof: theBenchmark
% 1.29/1.73 % Version : CSE_E---1.7
% 1.29/1.73 % Problem : theBenchmark.p
% 1.29/1.73 % SZS status Unsatisfiable for theBenchmark.p
% 1.29/1.73 % SZS output start CNFRefutation
% See solution above
% 1.29/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------