%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : LAT037-1 : TPTP v9.2.1. Released v2.4.0.
% 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 : 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 04:37:24 PM UTC 2026
% Result : Unsatisfiable 2.50s 2.08s
% Output : CNFRefutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of clauses : 64 ( 47 unt; 0 nHn; 28 RR)
% Number of literals : 85 ( 84 equ; 25 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 86 ( 12 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(x_meet_1,axiom,
meet(X1,n1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_1) ).
cnf(commutativity_of_meet,axiom,
meet(X1,X2) = meet(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_meet) ).
cnf(absorption1,axiom,
meet(X1,join(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',absorption1) ).
cnf(associativity_of_join,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_join) ).
cnf(lhs1,axiom,
join(xx,yy) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs1) ).
cnf(modular,axiom,
( meet(X2,join(X1,X3)) = join(X1,meet(X3,X2))
| meet(X1,X2) != X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',modular) ).
cnf(x_join_1,axiom,
join(X1,n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_1) ).
cnf(lhs2,axiom,
join(xx,zz) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs2) ).
cnf(lhs4,axiom,
meet(xx,zz) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs4) ).
cnf(x_join_0,axiom,
join(X1,n0) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_join_0) ).
cnf(commutativity_of_join,axiom,
join(X1,X2) = join(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',commutativity_of_join) ).
cnf(lhs3,axiom,
meet(xx,yy) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lhs3) ).
cnf(associativity_of_meet,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',associativity_of_meet) ).
cnf(idempotence_of_meet,axiom,
meet(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/LAT001-0.ax',idempotence_of_meet) ).
cnf(x_meet_0,axiom,
meet(X1,n0) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_meet_0) ).
cnf(dist_meet,hypothesis,
meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dist_meet) ).
cnf(rhs,negated_conjecture,
yy != zz,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rhs) ).
cnf(c_0_17,axiom,
meet(X1,n1) = X1,
x_meet_1 ).
cnf(c_0_18,axiom,
meet(X1,X2) = meet(X2,X1),
commutativity_of_meet ).
cnf(c_0_19,axiom,
meet(X1,join(X1,X2)) = X1,
absorption1 ).
cnf(c_0_20,plain,
meet(n1,X1) = X1,
inference(spm,[status(thm)],[c_0_17,c_0_18]) ).
cnf(c_0_21,axiom,
join(join(X1,X2),X3) = join(X1,join(X2,X3)),
associativity_of_join ).
cnf(c_0_22,axiom,
join(xx,yy) = n1,
lhs1 ).
cnf(c_0_23,plain,
join(n1,X1) = n1,
inference(spm,[status(thm)],[c_0_19,c_0_20]) ).
cnf(c_0_24,axiom,
( meet(X2,join(X1,X3)) = join(X1,meet(X3,X2))
| meet(X1,X2) != X1 ),
modular ).
cnf(c_0_25,axiom,
join(X1,n1) = n1,
x_join_1 ).
cnf(c_0_26,axiom,
join(xx,zz) = n1,
lhs2 ).
cnf(c_0_27,plain,
join(xx,join(yy,X1)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).
cnf(c_0_28,plain,
( join(X1,X2) = X2
| meet(X1,X2) != X1 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_20]),c_0_25]),c_0_17]) ).
cnf(c_0_29,plain,
join(xx,join(zz,X1)) = n1,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_26]),c_0_23]) ).
cnf(c_0_30,axiom,
meet(xx,zz) = n0,
lhs4 ).
cnf(c_0_31,axiom,
join(X1,n0) = X1,
x_join_0 ).
cnf(c_0_32,axiom,
join(X1,X2) = join(X2,X1),
commutativity_of_join ).
cnf(c_0_33,plain,
( join(xx,X1) = n1
| meet(yy,X1) != yy ),
inference(spm,[status(thm)],[c_0_27,c_0_28]) ).
cnf(c_0_34,axiom,
meet(xx,yy) = n0,
lhs3 ).
cnf(c_0_35,plain,
( join(xx,X1) = n1
| meet(zz,X1) != zz ),
inference(spm,[status(thm)],[c_0_29,c_0_28]) ).
cnf(c_0_36,plain,
( meet(zz,join(X1,xx)) = X1
| meet(X1,zz) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_30]),c_0_31]) ).
cnf(c_0_37,plain,
( join(X1,xx) = n1
| meet(yy,X1) != yy ),
inference(spm,[status(thm)],[c_0_32,c_0_33]) ).
cnf(c_0_38,plain,
( meet(yy,join(X1,xx)) = X1
| meet(X1,yy) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_34]),c_0_31]) ).
cnf(c_0_39,plain,
( join(X1,xx) = n1
| meet(zz,X1) != zz ),
inference(spm,[status(thm)],[c_0_32,c_0_35]) ).
cnf(c_0_40,axiom,
meet(meet(X1,X2),X3) = meet(X1,meet(X2,X3)),
associativity_of_meet ).
cnf(c_0_41,axiom,
meet(X1,X1) = X1,
idempotence_of_meet ).
cnf(c_0_42,axiom,
meet(X1,n0) = n0,
x_meet_0 ).
cnf(c_0_43,plain,
( zz = X1
| meet(yy,X1) != yy
| meet(X1,zz) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_17]) ).
cnf(c_0_44,plain,
( yy = X1
| meet(zz,X1) != zz
| meet(X1,yy) != X1 ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_39]),c_0_17]) ).
cnf(c_0_45,hypothesis,
meet(X1,join(X2,X3)) = join(meet(X1,X2),meet(X1,X3)),
dist_meet ).
cnf(c_0_46,plain,
meet(X1,meet(X1,X2)) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_40,c_0_41]) ).
cnf(c_0_47,plain,
meet(X1,meet(X2,X3)) = meet(X3,meet(X1,X2)),
inference(spm,[status(thm)],[c_0_18,c_0_40]) ).
cnf(c_0_48,plain,
meet(n0,X1) = n0,
inference(spm,[status(thm)],[c_0_42,c_0_18]) ).
cnf(c_0_49,plain,
( zz = X1
| meet(yy,X1) != yy
| meet(zz,X1) != X1 ),
inference(spm,[status(thm)],[c_0_43,c_0_18]) ).
cnf(c_0_50,plain,
( yy = X1
| meet(zz,X1) != zz
| meet(yy,X1) != X1 ),
inference(spm,[status(thm)],[c_0_44,c_0_18]) ).
cnf(c_0_51,negated_conjecture,
yy != zz,
rhs ).
cnf(c_0_52,hypothesis,
( meet(X1,join(X2,X3)) = meet(X1,X3)
| meet(X1,meet(X2,meet(X1,X3))) != meet(X1,X2) ),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_28]),c_0_40]) ).
cnf(c_0_53,plain,
meet(X1,meet(X2,meet(X1,X3))) = meet(X2,meet(X1,X3)),
inference(spm,[status(thm)],[c_0_46,c_0_47]) ).
cnf(c_0_54,plain,
meet(xx,meet(zz,X1)) = n0,
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_30]),c_0_48]) ).
cnf(c_0_55,plain,
( meet(zz,X1) = zz
| meet(yy,meet(zz,X1)) != yy ),
inference(spm,[status(thm)],[c_0_49,c_0_46]) ).
cnf(c_0_56,plain,
meet(X1,meet(X2,meet(X1,X2))) = meet(X1,X2),
inference(spm,[status(thm)],[c_0_41,c_0_40]) ).
cnf(c_0_57,plain,
meet(X1,meet(X2,X3)) = meet(X2,meet(X1,X3)),
inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_18]),c_0_40]) ).
cnf(c_0_58,plain,
meet(yy,zz) != zz,
inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_41]),c_0_51]) ).
cnf(c_0_59,hypothesis,
( meet(X1,join(X2,X3)) = meet(X1,X3)
| meet(X2,meet(X1,X3)) != meet(X1,X2) ),
inference(rw,[status(thm)],[c_0_52,c_0_53]) ).
cnf(c_0_60,plain,
meet(xx,meet(X1,zz)) = n0,
inference(spm,[status(thm)],[c_0_54,c_0_18]) ).
cnf(c_0_61,plain,
meet(yy,zz) != yy,
inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_56]),c_0_57]),c_0_41]),c_0_58]) ).
cnf(c_0_62,hypothesis,
( meet(X1,zz) = X1
| meet(X1,xx) != n0 ),
inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_59,c_0_26]),c_0_17]),c_0_60]) ).
cnf(c_0_63,hypothesis,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_62]),c_0_18]),c_0_34])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.13 % Problem : LAT037-1 : TPTP v9.2.1. Released v2.4.0.
% 0.13/0.13 % 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
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Mon May 4 20:48:18 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.22/0.36 % start to proof: theBenchmark
% 2.50/2.08 % Version : CSE_E---1.7
% 2.50/2.08 % Problem : theBenchmark.p
% 2.50/2.08 % SZS status Unsatisfiable for theBenchmark.p
% 2.50/2.08 % SZS output start CNFRefutation
% See solution above
% 2.50/2.08 % Total time : 1.375s
%------------------------------------------------------------------------------