%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT013-1 : TPTP v9.2.1. Released v2.2.0.
% 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 : n001.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 04:37:19 PM UTC 2026
% Result : Unsatisfiable 11.67s 7.47s
% Output : CNFRefutation 11.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 5
% Syntax : Number of clauses : 54 ( 54 unt; 0 nHn; 4 RR)
% Number of literals : 54 ( 53 equ; 3 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 138 ( 32 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(mckenzie2,axiom,
meet(X1,join(X2,join(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie2) ).
cnf(mckenzie1,axiom,
join(X1,meet(X2,meet(X1,X3))) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie1) ).
cnf(mckenzie3,axiom,
join(join(meet(X1,X2),meet(X2,X3)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie3) ).
cnf(mckenzie4,axiom,
meet(meet(join(X1,X2),join(X2,X3)),X2) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mckenzie4) ).
cnf(prove_associativity_of_meet,negated_conjecture,
meet(meet(a,b),c) != meet(a,meet(b,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_associativity_of_meet) ).
cnf(c_0_5,axiom,
meet(X1,join(X2,join(X1,X3))) = X1,
mckenzie2 ).
cnf(c_0_6,axiom,
join(X1,meet(X2,meet(X1,X3))) = X1,
mckenzie1 ).
cnf(c_0_7,plain,
meet(X1,join(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_5,c_0_6]) ).
cnf(c_0_8,axiom,
join(join(meet(X1,X2),meet(X2,X3)),X2) = X2,
mckenzie3 ).
cnf(c_0_9,plain,
meet(meet(X1,meet(X2,X3)),X2) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_7,c_0_6]) ).
cnf(c_0_10,plain,
meet(X1,X1) = X1,
inference(spm,[status(thm)],[c_0_7,c_0_8]) ).
cnf(c_0_11,axiom,
meet(meet(join(X1,X2),join(X2,X3)),X2) = X2,
mckenzie4 ).
cnf(c_0_12,plain,
join(X1,meet(X2,X1)) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_5]) ).
cnf(c_0_13,plain,
join(meet(X1,X2),X2) = X2,
inference(spm,[status(thm)],[c_0_8,c_0_6]) ).
cnf(c_0_14,plain,
meet(meet(X1,X2),X1) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_9,c_0_10]) ).
cnf(c_0_15,plain,
meet(meet(X1,join(meet(X2,X1),X3)),meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_11,c_0_12]) ).
cnf(c_0_16,plain,
join(meet(X1,X2),X1) = X1,
inference(spm,[status(thm)],[c_0_13,c_0_14]) ).
cnf(c_0_17,plain,
meet(meet(X1,X2),X2) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_7,c_0_12]) ).
cnf(c_0_18,plain,
meet(meet(X1,X2),meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_15,c_0_16]) ).
cnf(c_0_19,plain,
meet(meet(X1,X2),join(X3,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_5,c_0_13]) ).
cnf(c_0_20,plain,
meet(join(X1,X2),X2) = X2,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_6]),c_0_17]) ).
cnf(c_0_21,plain,
meet(meet(X1,join(meet(X2,meet(X1,X3)),X4)),meet(X2,meet(X1,X3))) = meet(X2,meet(X1,X3)),
inference(spm,[status(thm)],[c_0_11,c_0_6]) ).
cnf(c_0_22,plain,
meet(X1,X2) = meet(X2,X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_18]),c_0_18]) ).
cnf(c_0_23,plain,
meet(meet(X1,X2),join(X3,X1)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_19,c_0_14]) ).
cnf(c_0_24,plain,
meet(X1,meet(X2,X1)) = meet(X2,X1),
inference(spm,[status(thm)],[c_0_20,c_0_12]) ).
cnf(c_0_25,plain,
meet(meet(X1,meet(X2,X3)),meet(X2,join(meet(X1,meet(X2,X3)),X4))) = meet(X1,meet(X2,X3)),
inference(rw,[status(thm)],[c_0_21,c_0_22]) ).
cnf(c_0_26,plain,
meet(meet(meet(X1,X2),X3),X1) = meet(meet(X1,X2),X3),
inference(spm,[status(thm)],[c_0_9,c_0_14]) ).
cnf(c_0_27,plain,
meet(X1,meet(meet(X2,X1),X3)) = meet(meet(X2,X1),X3),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_12]),c_0_22]) ).
cnf(c_0_28,plain,
meet(meet(X1,meet(X2,X3)),X3) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_9,c_0_24]) ).
cnf(c_0_29,plain,
meet(meet(X1,X2),meet(X2,join(meet(X1,X2),X3))) = meet(X1,X2),
inference(rw,[status(thm)],[c_0_15,c_0_22]) ).
cnf(c_0_30,plain,
join(X1,join(X2,X1)) = join(X2,X1),
inference(spm,[status(thm)],[c_0_13,c_0_7]) ).
cnf(c_0_31,plain,
join(X1,meet(X1,X2)) = X1,
inference(spm,[status(thm)],[c_0_6,c_0_11]) ).
cnf(c_0_32,plain,
meet(meet(X1,X2),meet(X2,meet(X1,X3))) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_16]),c_0_22]) ).
cnf(c_0_33,plain,
meet(X1,meet(meet(X1,X2),X3)) = meet(meet(X1,X2),X3),
inference(rw,[status(thm)],[c_0_26,c_0_22]) ).
cnf(c_0_34,plain,
join(meet(meet(X1,X2),X3),X2) = X2,
inference(spm,[status(thm)],[c_0_16,c_0_27]) ).
cnf(c_0_35,plain,
meet(X1,meet(X2,meet(X3,X1))) = meet(X2,meet(X3,X1)),
inference(rw,[status(thm)],[c_0_28,c_0_22]) ).
cnf(c_0_36,plain,
meet(meet(X1,X2),meet(X2,join(X3,meet(X1,X2)))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_29,c_0_30]) ).
cnf(c_0_37,plain,
join(meet(X1,X2),meet(X2,meet(X1,X3))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_31,c_0_32]) ).
cnf(c_0_38,plain,
meet(meet(X1,X2),meet(X2,meet(X3,X1))) = meet(X2,meet(X3,X1)),
inference(spm,[status(thm)],[c_0_32,c_0_24]) ).
cnf(c_0_39,plain,
meet(meet(X1,X2),meet(meet(X2,X1),X3)) = meet(meet(X2,X1),X3),
inference(spm,[status(thm)],[c_0_33,c_0_18]) ).
cnf(c_0_40,plain,
meet(meet(X1,X2),meet(meet(X3,X2),X1)) = meet(meet(X3,X2),X1),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_34]),c_0_22]) ).
cnf(c_0_41,plain,
meet(meet(X1,X2),meet(X1,meet(X3,X2))) = meet(X1,meet(X3,X2)),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_42,plain,
meet(meet(X1,X2),meet(X1,X3)) = meet(X3,meet(X1,X2)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).
cnf(c_0_43,plain,
meet(meet(X1,X2),meet(meet(X3,X1),X2)) = meet(meet(X3,X1),X2),
inference(spm,[status(thm)],[c_0_39,c_0_40]) ).
cnf(c_0_44,plain,
meet(meet(X1,X2),meet(X3,X2)) = meet(X3,meet(X1,X2)),
inference(rw,[status(thm)],[c_0_41,c_0_42]) ).
cnf(c_0_45,plain,
meet(meet(X1,X2),meet(X1,meet(X2,X3))) = meet(X1,meet(X2,X3)),
inference(spm,[status(thm)],[c_0_39,c_0_32]) ).
cnf(c_0_46,plain,
meet(meet(X1,X2),meet(X2,X3)) = meet(meet(X1,X2),X3),
inference(rw,[status(thm)],[c_0_43,c_0_44]) ).
cnf(c_0_47,plain,
meet(meet(X1,X2),meet(X3,X1)) = meet(X3,meet(X1,X2)),
inference(rw,[status(thm)],[c_0_45,c_0_42]) ).
cnf(c_0_48,negated_conjecture,
meet(meet(a,b),c) != meet(a,meet(b,c)),
prove_associativity_of_meet ).
cnf(c_0_49,plain,
meet(meet(X1,X2),meet(meet(X1,X3),X2)) = meet(meet(X1,X3),X2),
inference(spm,[status(thm)],[c_0_32,c_0_22]) ).
cnf(c_0_50,plain,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_46]),c_0_47]) ).
cnf(c_0_51,negated_conjecture,
meet(c,meet(a,b)) != meet(a,meet(b,c)),
inference(rw,[status(thm)],[c_0_48,c_0_22]) ).
cnf(c_0_52,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X3,X1)),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_44]),c_0_42]),c_0_50]) ).
cnf(c_0_53,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_52]),c_0_22]),c_0_52]),c_0_22])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : LAT013-1 : TPTP v9.2.1. Released v2.2.0.
% 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
% 0.16/0.33 % Computer : n001.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Mon May 4 20:47:33 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.35 % start to proof: theBenchmark
% 11.67/7.47 % Version : CSE_E---1.7
% 11.67/7.47 % Problem : theBenchmark.p
% 11.67/7.47 % SZS status Unsatisfiable for theBenchmark.p
% 11.67/7.47 % SZS output start CNFRefutation
% See solution above
% 11.76/7.52 % Total time : 5.375s
%------------------------------------------------------------------------------