%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : GRP176-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n016.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 04:24:40 PM UTC 2026
% Result : Unsatisfiable 0.35s 1.61s
% Output : CNFRefutation 0.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 34
% Syntax : Number of clauses : 156 ( 140 unt; 0 nHn; 9 RR)
% Number of literals : 174 ( 173 equ; 22 neg)
% Maximal clause size : 3 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 220 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(prove_p07,negated_conjecture,
multiply(c,multiply(least_upper_bound(a,b),d)) != least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_p07) ).
cnf(monotony_lub2,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub2) ).
cnf(monotony_glb2,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb2) ).
cnf(monotony_lub1,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_lub1) ).
cnf(monotony_glb1,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',monotony_glb1) ).
cnf(associativity,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',associativity) ).
cnf(associativity_of_lub,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_lub) ).
cnf(associativity_of_glb,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',associativity_of_glb) ).
cnf(lub_absorbtion,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',lub_absorbtion) ).
cnf(glb_absorbtion,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',glb_absorbtion) ).
cnf(symmetry_of_lub,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_lub) ).
cnf(symmetry_of_glb,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',symmetry_of_glb) ).
cnf(left_inverse,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_inverse) ).
cnf(idempotence_of_lub,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_lub) ).
cnf(idempotence_of_gld,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-2.ax',idempotence_of_gld) ).
cnf(left_identity,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/Axioms/GRP004-0.ax',left_identity) ).
cnf(i_0_16,negated_conjecture,
multiply(c,multiply(least_upper_bound(a,b),d)) != least_upper_bound(multiply(c,multiply(a,d)),multiply(c,multiply(b,d))),
prove_p07,
[final] ).
cnf(i_0_17,axiom,
multiply(least_upper_bound(X1,X2),X3) = least_upper_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_lub2,
[final] ).
cnf(i_0_18,axiom,
multiply(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(multiply(X1,X3),multiply(X2,X3)),
monotony_glb2,
[final] ).
cnf(i_0_19,axiom,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_lub1,
[final] ).
cnf(i_0_20,axiom,
multiply(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)),
monotony_glb1,
[final] ).
cnf(i_0_21,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
associativity,
[final] ).
cnf(i_0_22,axiom,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X1,X2),X3),
associativity_of_lub,
[final] ).
cnf(i_0_23,axiom,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(greatest_lower_bound(X1,X2),X3),
associativity_of_glb,
[final] ).
cnf(i_0_24,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
lub_absorbtion,
[final] ).
cnf(i_0_25,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
glb_absorbtion,
[final] ).
cnf(i_0_26,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
symmetry_of_lub,
[final] ).
cnf(i_0_27,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
symmetry_of_glb,
[final] ).
cnf(i_0_28,axiom,
multiply(inverse(X1),X1) = identity,
left_inverse,
[final] ).
cnf(i_0_29,axiom,
least_upper_bound(X1,X1) = X1,
idempotence_of_lub,
[final] ).
cnf(i_0_30,axiom,
greatest_lower_bound(X1,X1) = X1,
idempotence_of_gld,
[final] ).
cnf(i_0_31,axiom,
multiply(identity,X1) = X1,
left_identity,
[final] ).
cnf(i_0_32,axiom,
X1 = X1 ).
cnf(i_0_33,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_34,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_35,axiom,
( X1 != X2
| multiply(X1,X3) = multiply(X2,X3) ) ).
cnf(i_0_36,axiom,
( X1 != X2
| multiply(X3,X1) = multiply(X3,X2) ) ).
cnf(i_0_37,axiom,
( X1 != X2
| least_upper_bound(X1,X3) = least_upper_bound(X2,X3) ) ).
cnf(i_0_38,axiom,
( X1 != X2
| least_upper_bound(X3,X1) = least_upper_bound(X3,X2) ) ).
cnf(i_0_39,axiom,
( X1 != X2
| greatest_lower_bound(X1,X3) = greatest_lower_bound(X2,X3) ) ).
cnf(i_0_40,axiom,
( X1 != X2
| greatest_lower_bound(X3,X1) = greatest_lower_bound(X3,X2) ) ).
cnf(i_0_32_001,axiom,
X1 = X1 ).
cnf(i_0_33_002,axiom,
( X1 = X2
| X2 != X1 ) ).
cnf(i_0_34_003,axiom,
( X1 = X2
| X1 != X3
| X3 != X2 ) ).
cnf(i_0_35_004,axiom,
( X1 != X2
| multiply(X1,X3) = multiply(X2,X3) ) ).
cnf(i_0_36_005,axiom,
( X1 != X2
| multiply(X3,X1) = multiply(X3,X2) ) ).
cnf(i_0_37_006,axiom,
( X1 != X2
| least_upper_bound(X1,X3) = least_upper_bound(X2,X3) ) ).
cnf(i_0_38_007,axiom,
( X1 != X2
| least_upper_bound(X3,X1) = least_upper_bound(X3,X2) ) ).
cnf(i_0_39_008,axiom,
( X1 != X2
| greatest_lower_bound(X1,X3) = greatest_lower_bound(X2,X3) ) ).
cnf(i_0_40_009,axiom,
( X1 != X2
| greatest_lower_bound(X3,X1) = greatest_lower_bound(X3,X2) ) ).
cnf(i_0_41,plain,
X1 = least_upper_bound(X1,X1),
inference(scs_inference,[],[i_0_29,i_0_33]) ).
cnf(i_0_42,plain,
multiply(c,multiply(least_upper_bound(a,b),d)) != least_upper_bound(multiply(c,multiply(b,d)),multiply(c,multiply(a,d))),
inference(scs_inference,[],[i_0_16,i_0_29,i_0_26,i_0_33,i_0_34]) ).
cnf(i_0_43,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(rename_variables,[],[i_0_26]) ).
cnf(i_0_44,plain,
X1 = greatest_lower_bound(X1,X1),
inference(scs_inference,[],[i_0_30,i_0_33]) ).
cnf(i_0_45,plain,
greatest_lower_bound(X1,X1) = least_upper_bound(X1,X1),
inference(scs_inference,[],[i_0_41,i_0_30,i_0_33,i_0_34]) ).
cnf(i_0_46,plain,
X1 = least_upper_bound(X1,X1),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_47,plain,
least_upper_bound(X1,X1) = greatest_lower_bound(X1,X1),
inference(scs_inference,[],[i_0_45,i_0_33]) ).
cnf(i_0_48,plain,
X1 = greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),
inference(scs_inference,[],[i_0_44,i_0_41,i_0_45,i_0_33,i_0_34]) ).
cnf(i_0_49,plain,
X1 = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_50,plain,
greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)) = X1,
inference(scs_inference,[],[i_0_48,i_0_33]) ).
cnf(i_0_51,plain,
least_upper_bound(X1,X1) = greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(scs_inference,[],[i_0_47,i_0_44,i_0_48,i_0_33,i_0_34]) ).
cnf(i_0_52,plain,
X1 = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_53,plain,
greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = least_upper_bound(X1,X1),
inference(scs_inference,[],[i_0_51,i_0_33]) ).
cnf(i_0_54,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(X1,X1),
inference(scs_inference,[],[i_0_50,i_0_47,i_0_51,i_0_33,i_0_34]) ).
cnf(i_0_55,plain,
greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)) = X1,
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_56,plain,
greatest_lower_bound(X1,X1) = greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_54,i_0_33]) ).
cnf(i_0_57,plain,
greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),
inference(scs_inference,[],[i_0_53,i_0_41,i_0_54,i_0_33,i_0_34]) ).
cnf(i_0_58,plain,
X1 = least_upper_bound(X1,X1),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_59,plain,
least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)) = greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(scs_inference,[],[i_0_57,i_0_33]) ).
cnf(i_0_60,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_56,i_0_50,i_0_57,i_0_33,i_0_34]) ).
cnf(i_0_61,plain,
greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)) = X1,
inference(rename_variables,[],[i_0_50]) ).
cnf(i_0_62,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_60,i_0_33]) ).
cnf(i_0_63,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(scs_inference,[],[i_0_59,i_0_53,i_0_60,i_0_33,i_0_34]) ).
cnf(i_0_64,plain,
greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = least_upper_bound(X1,X1),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_65,plain,
greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_63,i_0_33]) ).
cnf(i_0_66,plain,
least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(scs_inference,[],[i_0_59,i_0_63,i_0_33,i_0_34]) ).
cnf(i_0_67,plain,
least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)) = greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_68,plain,
greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_66,i_0_33]) ).
cnf(i_0_69,plain,
least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_65,i_0_47,i_0_66,i_0_33,i_0_34]) ).
cnf(i_0_70,plain,
least_upper_bound(X1,X1) = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_71,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(scs_inference,[],[i_0_69,i_0_33]) ).
cnf(i_0_72,plain,
greatest_lower_bound(X1,X1) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_65,i_0_44,i_0_69,i_0_33,i_0_34]) ).
cnf(i_0_73,plain,
X1 = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_44]) ).
cnf(i_0_74,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(X1,X1),
inference(scs_inference,[],[i_0_72,i_0_33]) ).
cnf(i_0_75,plain,
least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(scs_inference,[],[i_0_71,i_0_59,i_0_72,i_0_33,i_0_34]) ).
cnf(i_0_76,plain,
least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)) = greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_77,plain,
least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_75,i_0_33]) ).
cnf(i_0_78,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_74,i_0_56,i_0_75,i_0_33,i_0_34]) ).
cnf(i_0_79,plain,
greatest_lower_bound(X1,X1) = greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_80,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_78,i_0_33]) ).
cnf(i_0_81,plain,
greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_68,i_0_47,i_0_78,i_0_33,i_0_34]) ).
cnf(i_0_82,plain,
least_upper_bound(X1,X1) = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_83,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(scs_inference,[],[i_0_81,i_0_33]) ).
cnf(i_0_84,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(scs_inference,[],[i_0_80,i_0_71,i_0_81,i_0_33,i_0_34]) ).
cnf(i_0_85,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(rename_variables,[],[i_0_71]) ).
cnf(i_0_86,plain,
least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_84,i_0_33]) ).
cnf(i_0_87,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_77,i_0_53,i_0_84,i_0_33,i_0_34]) ).
cnf(i_0_88,plain,
greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = least_upper_bound(X1,X1),
inference(rename_variables,[],[i_0_53]) ).
cnf(i_0_89,plain,
least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_87,i_0_33]) ).
cnf(i_0_90,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_83,i_0_41,i_0_87,i_0_33,i_0_34]) ).
cnf(i_0_91,plain,
X1 = least_upper_bound(X1,X1),
inference(rename_variables,[],[i_0_41]) ).
cnf(i_0_92,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_90,i_0_33]) ).
cnf(i_0_93,plain,
least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_86,i_0_90,i_0_33,i_0_34]) ).
cnf(i_0_94,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(rename_variables,[],[i_0_90]) ).
cnf(i_0_95,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(scs_inference,[],[i_0_93,i_0_33]) ).
cnf(i_0_96,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_62,i_0_92,i_0_93,i_0_33,i_0_34]) ).
cnf(i_0_97,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(rename_variables,[],[i_0_62]) ).
cnf(i_0_98,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_96,i_0_33]) ).
cnf(i_0_99,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_95,i_0_77,i_0_96,i_0_33,i_0_34]) ).
cnf(i_0_100,plain,
least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(rename_variables,[],[i_0_77]) ).
cnf(i_0_101,plain,
least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_99,i_0_33]) ).
cnf(i_0_102,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_98,i_0_47,i_0_99,i_0_33,i_0_34]) ).
cnf(i_0_103,plain,
least_upper_bound(X1,X1) = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_47]) ).
cnf(i_0_104,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_102,i_0_33]) ).
cnf(i_0_105,plain,
least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_89,i_0_102,i_0_57,i_0_33,i_0_34]) ).
cnf(i_0_106,plain,
greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),
inference(rename_variables,[],[i_0_57]) ).
cnf(i_0_107,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_105,i_0_33]) ).
cnf(i_0_108,plain,
greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_68,i_0_105,i_0_33,i_0_34]) ).
cnf(i_0_109,plain,
least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(rename_variables,[],[i_0_105]) ).
cnf(i_0_110,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(scs_inference,[],[i_0_108,i_0_33]) ).
cnf(i_0_111,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_101,i_0_107,i_0_108,i_0_33,i_0_34]) ).
cnf(i_0_112,plain,
least_upper_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(rename_variables,[],[i_0_101]) ).
cnf(i_0_113,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_111,i_0_33]) ).
cnf(i_0_114,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_110,i_0_65,i_0_111,i_0_33,i_0_34]) ).
cnf(i_0_115,plain,
greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(rename_variables,[],[i_0_65]) ).
cnf(i_0_116,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_114,i_0_33]) ).
cnf(i_0_117,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_113,i_0_114,i_0_33,i_0_34]) ).
cnf(i_0_118,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(rename_variables,[],[i_0_114]) ).
cnf(i_0_119,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_117,i_0_33]) ).
cnf(i_0_120,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_116,i_0_59,i_0_117,i_0_33,i_0_34]) ).
cnf(i_0_121,plain,
least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)) = greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(rename_variables,[],[i_0_59]) ).
cnf(i_0_122,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_120,i_0_33]) ).
cnf(i_0_123,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_104,i_0_120,i_0_60,i_0_33,i_0_34]) ).
cnf(i_0_124,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(rename_variables,[],[i_0_60]) ).
cnf(i_0_125,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_123,i_0_33]) ).
cnf(i_0_126,plain,
greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(X1,X1),
inference(scs_inference,[],[i_0_122,i_0_74,i_0_123,i_0_33,i_0_34]) ).
cnf(i_0_127,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_74]) ).
cnf(i_0_128,plain,
greatest_lower_bound(X1,X1) = greatest_lower_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_126,i_0_33]) ).
cnf(i_0_129,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(X1,X1),
inference(scs_inference,[],[i_0_92,i_0_126,i_0_54,i_0_33,i_0_34]) ).
cnf(i_0_130,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(X1,X1),
inference(rename_variables,[],[i_0_54]) ).
cnf(i_0_131,plain,
greatest_lower_bound(X1,X1) = least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_129,i_0_33]) ).
cnf(i_0_132,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_119,i_0_129,i_0_96,i_0_33,i_0_34]) ).
cnf(i_0_133,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(rename_variables,[],[i_0_96]) ).
cnf(i_0_134,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_132,i_0_33]) ).
cnf(i_0_135,plain,
greatest_lower_bound(X1,X1) = least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_131,i_0_113,i_0_132,i_0_33,i_0_34]) ).
cnf(i_0_136,plain,
least_upper_bound(greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(rename_variables,[],[i_0_113]) ).
cnf(i_0_137,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(X1,X1),
inference(scs_inference,[],[i_0_135,i_0_33]) ).
cnf(i_0_138,plain,
greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(scs_inference,[],[i_0_134,i_0_135,i_0_63,i_0_33,i_0_34]) ).
cnf(i_0_139,plain,
greatest_lower_bound(greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),greatest_lower_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),
inference(rename_variables,[],[i_0_63]) ).
cnf(i_0_140,plain,
greatest_lower_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)) = greatest_lower_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_138,i_0_33]) ).
cnf(i_0_141,plain,
least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))) = greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(scs_inference,[],[i_0_137,i_0_56,i_0_138,i_0_33,i_0_34]) ).
cnf(i_0_142,plain,
greatest_lower_bound(X1,X1) = greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))),
inference(rename_variables,[],[i_0_56]) ).
cnf(i_0_143,plain,
greatest_lower_bound(least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1)),least_upper_bound(least_upper_bound(X1,X1),least_upper_bound(X1,X1))) = least_upper_bound(least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1)),least_upper_bound(greatest_lower_bound(X1,X1),greatest_lower_bound(X1,X1))),
inference(scs_inference,[],[i_0_141,i_0_33]) ).
cnf(i_0_144,plain,
multiply(c,multiply(least_upper_bound(a,b),d)) != multiply(c,least_upper_bound(multiply(a,d),multiply(b,d))),
inference(scs_inference,[],[i_0_16,i_0_141,i_0_19,i_0_33,i_0_34]) ).
cnf(i_0_145,plain,
multiply(X1,least_upper_bound(X2,X3)) = least_upper_bound(multiply(X1,X2),multiply(X1,X3)),
inference(rename_variables,[],[i_0_19]) ).
cnf(i_0_146,plain,
$false,
inference(scs_inference,[],[i_0_16,i_0_141,i_0_17,i_0_19,i_0_33,i_0_34,i_0_36]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GRP176-1 : TPTP v9.2.1. Bugfixed v1.2.1.
% 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 : n016.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 18:28:21 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 0.35/1.61 % Version : CSE_E---1.7
% 0.35/1.61 % Problem : theBenchmark.p
% 0.35/1.61 % SZS status Unsatisfiable for theBenchmark.p
% 0.35/1.61 % SZS output start CNFRefutation
% See solution above
% 0.46/1.77 % Total time : 1.269s
%------------------------------------------------------------------------------