%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : ALG440-1 : TPTP v9.2.1. Released v5.4.0.
% 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 : n019.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 04:08:44 PM UTC 2026
% Result : Unsatisfiable 1.58s 1.80s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 14
% Syntax : Number of clauses : 46 ( 31 unt; 0 nHn; 29 RR)
% Number of literals : 75 ( 17 equ; 31 neg)
% Maximal clause size : 4 ( 1 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-3 aty)
% Number of variables : 119 ( 0 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(sos_010,axiom,
( r(v(X1,X4),v(X2,X5),v(X3,X6))
| ~ r(X1,X2,X3)
| ~ r(X4,X5,X6) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_010) ).
cnf(sos_007,axiom,
u(X1,X1,X2) = v(X1,X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_007) ).
cnf(sos_006,axiom,
v(X1,X2) = v(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_006) ).
cnf(sos_013,axiom,
r(b,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_013) ).
cnf(sos_009,axiom,
( r(u(X1,X4,X7),u(X2,X5,X8),u(X3,X6,X9))
| ~ r(X1,X2,X3)
| ~ r(X4,X5,X6)
| ~ r(X7,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_009) ).
cnf(sos_005,axiom,
u(X1,X1,X2) = u(X2,X1,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_005) ).
cnf(sos_012,axiom,
r(a,b,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_012) ).
cnf(sos_002,axiom,
u(X1,X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_002) ).
cnf(sos_011,axiom,
r(a,a,b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_011) ).
cnf(sos_008,axiom,
( r(m(X1,X4,X7),m(X2,X5,X8),m(X3,X6,X9))
| ~ r(X1,X2,X3)
| ~ r(X4,X5,X6)
| ~ r(X7,X8,X9) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_008) ).
cnf(sos_004,axiom,
u(X1,X1,X2) = u(X1,X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_004) ).
cnf(sos_001,axiom,
m(X1,X2,X2) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos_001) ).
cnf(sos,axiom,
m(X1,X1,X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sos) ).
cnf(goals,negated_conjecture,
~ r(a,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
cnf(c_0_14,axiom,
( r(v(X1,X4),v(X2,X5),v(X3,X6))
| ~ r(X1,X2,X3)
| ~ r(X4,X5,X6) ),
sos_010 ).
cnf(c_0_15,axiom,
u(X1,X1,X2) = v(X1,X2),
sos_007 ).
cnf(c_0_16,axiom,
v(X1,X2) = v(X2,X1),
sos_006 ).
cnf(c_0_17,plain,
( r(u(X1,X1,X4),u(X2,X2,X5),u(X3,X3,X6))
| ~ r(X4,X5,X6)
| ~ r(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]),c_0_15]) ).
cnf(c_0_18,axiom,
r(b,a,a),
sos_013 ).
cnf(c_0_19,axiom,
( r(u(X1,X4,X7),u(X2,X5,X8),u(X3,X6,X9))
| ~ r(X1,X2,X3)
| ~ r(X4,X5,X6)
| ~ r(X7,X8,X9) ),
sos_009 ).
cnf(c_0_20,plain,
u(X1,X1,X2) = u(X2,X2,X1),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_16,c_0_15]),c_0_15]) ).
cnf(c_0_21,axiom,
u(X1,X1,X2) = u(X2,X1,X1),
sos_005 ).
cnf(c_0_22,plain,
( r(u(X1,X1,b),u(X2,X2,a),u(X3,X3,a))
| ~ r(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_23,axiom,
r(a,b,a),
sos_012 ).
cnf(c_0_24,axiom,
u(X1,X1,X1) = X1,
sos_002 ).
cnf(c_0_25,plain,
( r(u(X1,X2,b),u(X3,X4,a),u(X5,X6,a))
| ~ r(X2,X4,X6)
| ~ r(X1,X3,X5) ),
inference(spm,[status(thm)],[c_0_19,c_0_18]) ).
cnf(c_0_26,plain,
u(X1,X2,X2) = u(X1,X1,X2),
inference(spm,[status(thm)],[c_0_20,c_0_21]) ).
cnf(c_0_27,axiom,
r(a,a,b),
sos_011 ).
cnf(c_0_28,axiom,
( r(m(X1,X4,X7),m(X2,X5,X8),m(X3,X6,X9))
| ~ r(X1,X2,X3)
| ~ r(X4,X5,X6)
| ~ r(X7,X8,X9) ),
sos_008 ).
cnf(c_0_29,plain,
r(u(a,a,b),u(a,a,b),a),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_24]),c_0_20]) ).
cnf(c_0_30,plain,
( r(u(X1,a,b),u(X2,b,a),u(X3,a,a))
| ~ r(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_25,c_0_23]) ).
cnf(c_0_31,axiom,
u(X1,X1,X2) = u(X1,X2,X1),
sos_004 ).
cnf(c_0_32,plain,
u(X1,X2,X2) = u(X2,X1,X1),
inference(spm,[status(thm)],[c_0_21,c_0_26]) ).
cnf(c_0_33,plain,
r(u(a,a,b),a,u(a,a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_27]),c_0_24]),c_0_20]) ).
cnf(c_0_34,plain,
( r(m(X1,X2,u(a,a,b)),m(X3,X4,u(a,a,b)),m(X5,X6,a))
| ~ r(X2,X4,X6)
| ~ r(X1,X3,X5) ),
inference(spm,[status(thm)],[c_0_28,c_0_29]) ).
cnf(c_0_35,plain,
r(u(a,a,b),u(a,a,b),u(a,a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_27]),c_0_31]),c_0_32]),c_0_26]) ).
cnf(c_0_36,axiom,
m(X1,X2,X2) = X1,
sos_001 ).
cnf(c_0_37,plain,
( r(u(X1,X1,a),u(X2,X2,b),u(X3,X3,a))
| ~ r(X1,X2,X3) ),
inference(spm,[status(thm)],[c_0_17,c_0_23]) ).
cnf(c_0_38,plain,
( r(m(X1,X2,u(a,a,b)),m(X3,X4,a),m(X5,X6,u(a,a,b)))
| ~ r(X2,X4,X6)
| ~ r(X1,X3,X5) ),
inference(spm,[status(thm)],[c_0_28,c_0_33]) ).
cnf(c_0_39,plain,
( r(X1,X2,m(X3,u(a,a,b),a))
| ~ r(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_36]),c_0_36]) ).
cnf(c_0_40,plain,
r(a,u(a,a,b),u(a,a,b)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_27]),c_0_24]),c_0_20]) ).
cnf(c_0_41,axiom,
m(X1,X1,X2) = X2,
sos ).
cnf(c_0_42,plain,
( r(X1,m(X2,u(a,a,b),a),X3)
| ~ r(X1,X2,X3) ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_35]),c_0_36]),c_0_36]) ).
cnf(c_0_43,plain,
r(a,u(a,a,b),a),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_41]) ).
cnf(c_0_44,negated_conjecture,
~ r(a,a,a),
goals ).
cnf(c_0_45,plain,
$false,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_41]),c_0_44]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : ALG440-1 : TPTP v9.2.1. Released v5.4.0.
% 0.00/0.11 % 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
% 0.15/0.32 % Computer : n019.cluster.edu
% 0.15/0.32 % Model : x86_64 x86_64
% 0.15/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.32 % Memory : 8042.1875MB
% 0.15/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.32 % CPULimit : 300
% 0.15/0.32 % WCLimit : 300
% 0.15/0.32 % DateTime : Tue May 5 10:34:59 EDT 2026
% 0.15/0.32 % CPUTime :
% 0.15/0.34 % start to proof: theBenchmark
% 1.58/1.80 % Version : CSE_E---1.7
% 1.58/1.80 % Problem : theBenchmark.p
% 1.58/1.80 % SZS status Unsatisfiable for theBenchmark.p
% 1.58/1.80 % SZS output start CNFRefutation
% See solution above
% 1.58/1.80 % Total time : 1.372s
%------------------------------------------------------------------------------