%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP181-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:25:34 PM UTC 2026
% Result : Unsatisfiable 34.02s 4.95s
% Output : CNFRefutation 34.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 54
% Number of leaves : 20
% Syntax : Number of clauses : 212 ( 212 unt; 0 nHn; 45 RR)
% Number of literals : 212 ( 211 equ; 2 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 : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 322 ( 59 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t15,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t26,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t15]) ).
cnf(t5,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t41,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t2,axiom,
inverse(inverse(X1)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t25,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t42,plain,
identity = multiply(X1,inverse(X1)),
inference(cp,[status(thm)],[t41,t25]) ).
cnf(t100,plain,
multiply(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t42]) ).
cnf(t110,plain,
multiply(X1,multiply(inverse(X1),X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t26,t100]) ).
cnf(t4,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t20,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t103099,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(step,[status(thm)],[t110,t20]) ).
cnf(t182,plain,
multiply(X1,multiply(inverse(X1),X2)) = X2,
inference(orient,[status(thm)],[t103099]) ).
cnf(t12,axiom,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t52,plain,
multiply(inverse(X1),inverse(X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t12]) ).
cnf(t184,plain,
inverse(X1) = multiply(X2,inverse(multiply(X1,X2))),
inference(cp,[status(thm)],[t182,t52]) ).
cnf(t206,plain,
multiply(X1,inverse(multiply(X2,X1))) = inverse(X2),
inference(orient,[status(thm)],[t184]) ).
cnf(t19,axiom,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t36,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t19]) ).
cnf(t56,plain,
multiply(least_upper_bound(inverse(X1),X2),inverse(X3)) = least_upper_bound(inverse(multiply(X3,X1)),multiply(X2,inverse(X3))),
inference(cp,[status(thm)],[t36,t52]) ).
cnf(t20366,plain,
least_upper_bound(inverse(multiply(X1,X2)),multiply(X3,inverse(X1))) = multiply(least_upper_bound(inverse(X2),X3),inverse(X1)),
inference(orient,[status(thm)],[t56]) ).
cnf(t20444,plain,
multiply(least_upper_bound(inverse(X1),X2),inverse(X2)) = least_upper_bound(inverse(multiply(X2,X1)),identity),
inference(cp,[status(thm)],[t20366,t100]) ).
cnf(t9,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t81,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t9]) ).
cnf(t103346,plain,
multiply(least_upper_bound(inverse(X1),X2),inverse(X2)) = least_upper_bound(identity,inverse(multiply(X2,X1))),
inference(step,[status(thm)],[t20444,t81]) ).
cnf(t20530,plain,
multiply(least_upper_bound(inverse(X1),X2),inverse(X2)) = least_upper_bound(identity,inverse(multiply(X2,X1))),
inference(orient,[status(thm)],[t103346]) ).
cnf(t20581,plain,
least_upper_bound(identity,inverse(multiply(X1,X2))) = multiply(least_upper_bound(X1,inverse(X2)),inverse(X1)),
inference(cp,[status(thm)],[t20530,t81]) ).
cnf(t20633,plain,
multiply(least_upper_bound(X1,inverse(X2)),inverse(X1)) = least_upper_bound(identity,inverse(multiply(X1,X2))),
inference(orient,[status(thm)],[t20581]) ).
cnf(t18,axiom,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t29,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t18]) ).
cnf(t0,axiom,
inverse(identity) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t97,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t98,plain,
inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)),
inference(cp,[status(thm)],[t52,t97]) ).
cnf(t103088,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(step,[status(thm)],[t98,t20]) ).
cnf(t111,plain,
inverse(multiply(X1,identity)) = inverse(X1),
inference(orient,[status(thm)],[t103088]) ).
cnf(t115,plain,
multiply(X1,identity) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t25,t111]) ).
cnf(t103089,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t115,t25]) ).
cnf(t116,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t103089]) ).
cnf(t117,plain,
multiply(X1,least_upper_bound(identity,X2)) = least_upper_bound(X1,multiply(X1,X2)),
inference(cp,[status(thm)],[t29,t116]) ).
cnf(t275,plain,
least_upper_bound(X1,multiply(X1,X2)) = multiply(X1,least_upper_bound(identity,X2)),
inference(orient,[status(thm)],[t117]) ).
cnf(t279,plain,
multiply(X1,least_upper_bound(identity,multiply(inverse(X1),X2))) = least_upper_bound(X1,X2),
inference(cp,[status(thm)],[t275,t182]) ).
cnf(t3320,plain,
multiply(X1,least_upper_bound(identity,multiply(inverse(X1),X2))) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t279]) ).
cnf(t47,plain,
multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(cp,[status(thm)],[t29,t41]) ).
cnf(t6634,plain,
multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(orient,[status(thm)],[t47]) ).
cnf(t10,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t24,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t10]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t65,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t68,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t24,t65]) ).
cnf(t121,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t68]) ).
cnf(t6658,plain,
least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = multiply(inverse(X1),X1),
inference(cp,[status(thm)],[t6634,t121]) ).
cnf(t103237,plain,
least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = identity,
inference(step,[status(thm)],[t6658,t41]) ).
cnf(t6788,plain,
least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = identity,
inference(orient,[status(thm)],[t103237]) ).
cnf(t17,axiom,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t30,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t17]) ).
cnf(t31,plain,
multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t30,t20]) ).
cnf(t230,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(identity,X2),X1),
inference(orient,[status(thm)],[t31]) ).
cnf(t55,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(cp,[status(thm)],[t52,t25]) ).
cnf(t198,plain,
inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
inference(orient,[status(thm)],[t55]) ).
cnf(t51,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t26,t41]) ).
cnf(t103098,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t51,t20]) ).
cnf(t171,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t103098]) ).
cnf(t199,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(cp,[status(thm)],[t198,t171]) ).
cnf(t219,plain,
multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
inference(orient,[status(thm)],[t199]) ).
cnf(t236,plain,
multiply(greatest_lower_bound(identity,inverse(multiply(X1,X2))),X1) = greatest_lower_bound(X1,inverse(X2)),
inference(cp,[status(thm)],[t230,t219]) ).
cnf(t10652,plain,
multiply(greatest_lower_bound(identity,inverse(multiply(X1,X2))),X1) = greatest_lower_bound(X1,inverse(X2)),
inference(orient,[status(thm)],[t236]) ).
cnf(t16,axiom,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t27,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t16]) ).
cnf(t109,plain,
multiply(X1,greatest_lower_bound(X2,inverse(X1))) = greatest_lower_bound(multiply(X1,X2),identity),
inference(cp,[status(thm)],[t27,t100]) ).
cnf(t103126,plain,
multiply(X1,greatest_lower_bound(X2,inverse(X1))) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(step,[status(thm)],[t109,t65]) ).
cnf(t1066,plain,
multiply(X1,greatest_lower_bound(X2,inverse(X1))) = greatest_lower_bound(identity,multiply(X1,X2)),
inference(orient,[status(thm)],[t103126]) ).
cnf(t10661,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = multiply(greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,multiply(X1,X2)))),X1),
inference(cp,[status(thm)],[t10652,t1066]) ).
cnf(t234,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(inverse(X1),identity),
inference(cp,[status(thm)],[t230,t100]) ).
cnf(t103104,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(step,[status(thm)],[t234,t65]) ).
cnf(t602,plain,
multiply(greatest_lower_bound(identity,X1),inverse(X1)) = greatest_lower_bound(identity,inverse(X1)),
inference(orient,[status(thm)],[t103104]) ).
cnf(t13,axiom,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t69,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t1,axiom,
greatest_lower_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t21,plain,
greatest_lower_bound(X1,X1) = X1,
inference(orient,[status(thm)],[t1]) ).
cnf(t73,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(cp,[status(thm)],[t69,t21]) ).
cnf(t139,plain,
greatest_lower_bound(X1,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X1,X2),
inference(orient,[status(thm)],[t73]) ).
cnf(t603,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) = multiply(greatest_lower_bound(identity,X1),inverse(greatest_lower_bound(identity,X1))),
inference(cp,[status(thm)],[t602,t139]) ).
cnf(t103105,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) = identity,
inference(step,[status(thm)],[t603,t100]) ).
cnf(t631,plain,
greatest_lower_bound(identity,inverse(greatest_lower_bound(identity,X1))) = identity,
inference(orient,[status(thm)],[t103105]) ).
cnf(t103263,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = multiply(identity,X1),
inference(step,[status(thm)],[t10661,t631]) ).
cnf(t103264,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = X1,
inference(step,[status(thm)],[t103263,t20]) ).
cnf(t10782,plain,
greatest_lower_bound(X1,inverse(greatest_lower_bound(X2,inverse(X1)))) = X1,
inference(orient,[status(thm)],[t103264]) ).
cnf(t10795,plain,
inverse(X1) = greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))),
inference(cp,[status(thm)],[t10782,t25]) ).
cnf(t10871,plain,
greatest_lower_bound(inverse(X1),inverse(greatest_lower_bound(X2,X1))) = inverse(X1),
inference(orient,[status(thm)],[t10795]) ).
cnf(t10984,plain,
identity = least_upper_bound(identity,multiply(inverse(inverse(greatest_lower_bound(X1,X2))),inverse(X2))),
inference(cp,[status(thm)],[t6788,t10871]) ).
cnf(t103271,plain,
identity = least_upper_bound(identity,inverse(multiply(X2,inverse(greatest_lower_bound(X1,X2))))),
inference(step,[status(thm)],[t10984,t52]) ).
cnf(t54,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(cp,[status(thm)],[t52,t25]) ).
cnf(t193,plain,
inverse(multiply(X1,inverse(X2))) = multiply(X2,inverse(X1)),
inference(orient,[status(thm)],[t54]) ).
cnf(t103272,plain,
identity = least_upper_bound(identity,multiply(greatest_lower_bound(X1,X2),inverse(X2))),
inference(step,[status(thm)],[t103271,t193]) ).
cnf(t11220,plain,
least_upper_bound(identity,multiply(greatest_lower_bound(X1,X2),inverse(X2))) = identity,
inference(orient,[status(thm)],[t103272]) ).
cnf(t7,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t22,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t11249,plain,
identity = least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))),
inference(cp,[status(thm)],[t11220,t22]) ).
cnf(t11586,plain,
least_upper_bound(identity,multiply(X1,inverse(least_upper_bound(X1,X2)))) = identity,
inference(orient,[status(thm)],[t11249]) ).
cnf(t11627,plain,
least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = multiply(X1,identity),
inference(cp,[status(thm)],[t3320,t11586]) ).
cnf(t103277,plain,
least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = X1,
inference(step,[status(thm)],[t11627,t116]) ).
cnf(t11630,plain,
least_upper_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = X1,
inference(orient,[status(thm)],[t103277]) ).
cnf(t11632,plain,
X1 = least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))),
inference(cp,[status(thm)],[t11630,t81]) ).
cnf(t11665,plain,
least_upper_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = X1,
inference(orient,[status(thm)],[t11632]) ).
cnf(t11678,plain,
inverse(X1) = least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))),
inference(cp,[status(thm)],[t11665,t25]) ).
cnf(t11750,plain,
least_upper_bound(inverse(X1),inverse(least_upper_bound(X2,X1))) = inverse(X1),
inference(orient,[status(thm)],[t11678]) ).
cnf(t125,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))),
inference(cp,[status(thm)],[t121,t69]) ).
cnf(t502,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = X1,
inference(orient,[status(thm)],[t125]) ).
cnf(t505,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(greatest_lower_bound(X2,X1),X3)),
inference(cp,[status(thm)],[t502,t65]) ).
cnf(t103102,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))),
inference(step,[status(thm)],[t505,t69]) ).
cnf(t539,plain,
least_upper_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X1,X3))) = X1,
inference(orient,[status(thm)],[t103102]) ).
cnf(t8,axiom,
greatest_lower_bound(b,c) = greatest_lower_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t103084,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(a,c),
inference(step,[status(thm)],[t8,t65]) ).
cnf(t103085,plain,
greatest_lower_bound(c,b) = greatest_lower_bound(c,a),
inference(step,[status(thm)],[t103084,t65]) ).
cnf(t79,plain,
greatest_lower_bound(c,a) = greatest_lower_bound(c,b),
inference(orient,[status(thm)],[t103085]) ).
cnf(t80,plain,
greatest_lower_bound(c,greatest_lower_bound(a,X1)) = greatest_lower_bound(greatest_lower_bound(c,b),X1),
inference(cp,[status(thm)],[t69,t79]) ).
cnf(t103100,plain,
greatest_lower_bound(c,greatest_lower_bound(a,X1)) = greatest_lower_bound(c,greatest_lower_bound(b,X1)),
inference(step,[status(thm)],[t80,t69]) ).
cnf(t257,plain,
greatest_lower_bound(c,greatest_lower_bound(a,X1)) = greatest_lower_bound(c,greatest_lower_bound(b,X1)),
inference(orient,[status(thm)],[t103100]) ).
cnf(t258,plain,
greatest_lower_bound(c,greatest_lower_bound(b,multiply(X1,a))) = greatest_lower_bound(c,multiply(greatest_lower_bound(identity,X1),a)),
inference(cp,[status(thm)],[t257,t230]) ).
cnf(t20228,plain,
greatest_lower_bound(c,greatest_lower_bound(b,multiply(X1,a))) = greatest_lower_bound(c,multiply(greatest_lower_bound(identity,X1),a)),
inference(orient,[status(thm)],[t258]) ).
cnf(t20267,plain,
b = least_upper_bound(b,greatest_lower_bound(c,multiply(greatest_lower_bound(identity,X1),a))),
inference(cp,[status(thm)],[t539,t20228]) ).
cnf(t20279,plain,
least_upper_bound(b,greatest_lower_bound(c,multiply(greatest_lower_bound(identity,X1),a))) = b,
inference(orient,[status(thm)],[t20267]) ).
cnf(t605,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = multiply(identity,inverse(least_upper_bound(identity,X1))),
inference(cp,[status(thm)],[t602,t22]) ).
cnf(t103110,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)),
inference(step,[status(thm)],[t605,t20]) ).
cnf(t784,plain,
greatest_lower_bound(identity,inverse(least_upper_bound(identity,X1))) = inverse(least_upper_bound(identity,X1)),
inference(orient,[status(thm)],[t103110]) ).
cnf(t20281,plain,
b = least_upper_bound(b,greatest_lower_bound(c,multiply(inverse(least_upper_bound(identity,X1)),a))),
inference(cp,[status(thm)],[t20279,t784]) ).
cnf(t101627,plain,
least_upper_bound(b,greatest_lower_bound(c,multiply(inverse(least_upper_bound(identity,X1)),a))) = b,
inference(orient,[status(thm)],[t20281]) ).
cnf(t106,plain,
multiply(X1,least_upper_bound(inverse(X1),X2)) = least_upper_bound(identity,multiply(X1,X2)),
inference(cp,[status(thm)],[t29,t100]) ).
cnf(t976,plain,
multiply(X1,least_upper_bound(inverse(X1),X2)) = least_upper_bound(identity,multiply(X1,X2)),
inference(orient,[status(thm)],[t106]) ).
cnf(t1004,plain,
inverse(least_upper_bound(inverse(X1),X2)) = multiply(inverse(least_upper_bound(identity,multiply(X1,X2))),X1),
inference(cp,[status(thm)],[t219,t976]) ).
cnf(t32954,plain,
multiply(inverse(least_upper_bound(identity,multiply(X1,X2))),X1) = inverse(least_upper_bound(inverse(X1),X2)),
inference(orient,[status(thm)],[t1004]) ).
cnf(t101629,plain,
b = least_upper_bound(b,greatest_lower_bound(c,inverse(least_upper_bound(inverse(a),X1)))),
inference(cp,[status(thm)],[t101627,t32954]) ).
cnf(t101771,plain,
least_upper_bound(b,greatest_lower_bound(c,inverse(least_upper_bound(inverse(a),X1)))) = b,
inference(orient,[status(thm)],[t101629]) ).
cnf(t84,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t22,t81]) ).
cnf(t127,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t84]) ).
cnf(t11684,plain,
inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(inverse(least_upper_bound(X1,inverse(X2))),X2),
inference(cp,[status(thm)],[t127,t11665]) ).
cnf(t103294,plain,
inverse(least_upper_bound(X1,inverse(X2))) = greatest_lower_bound(X2,inverse(least_upper_bound(X1,inverse(X2)))),
inference(step,[status(thm)],[t11684,t65]) ).
cnf(t13168,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(X2,inverse(X1)))) = inverse(least_upper_bound(X2,inverse(X1))),
inference(orient,[status(thm)],[t103294]) ).
cnf(t101772,plain,
b = least_upper_bound(b,inverse(least_upper_bound(inverse(a),inverse(c)))),
inference(cp,[status(thm)],[t101771,t13168]) ).
cnf(t103760,plain,
b = least_upper_bound(b,inverse(least_upper_bound(inverse(c),inverse(a)))),
inference(step,[status(thm)],[t101772,t81]) ).
cnf(t102405,plain,
least_upper_bound(b,inverse(least_upper_bound(inverse(c),inverse(a)))) = b,
inference(orient,[status(thm)],[t103760]) ).
cnf(t102419,plain,
inverse(inverse(least_upper_bound(inverse(c),inverse(a)))) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(c),inverse(a)))),inverse(b)),
inference(cp,[status(thm)],[t11750,t102405]) ).
cnf(t103768,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(c),inverse(a)))),inverse(b)),
inference(step,[status(thm)],[t102419,t25]) ).
cnf(t103769,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(b),inverse(inverse(least_upper_bound(inverse(c),inverse(a))))),
inference(step,[status(thm)],[t103768,t81]) ).
cnf(t103770,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(b),least_upper_bound(inverse(c),inverse(a))),
inference(step,[status(thm)],[t103769,t25]) ).
cnf(t14,axiom,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t85,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t93,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(least_upper_bound(X2,X1),X3),
inference(cp,[status(thm)],[t85,t81]) ).
cnf(t103431,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(step,[status(thm)],[t93,t85]) ).
cnf(t30331,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X2,least_upper_bound(X1,X3)),
inference(orient,[status(thm)],[t103431]) ).
cnf(t103771,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(c),least_upper_bound(inverse(b),inverse(a))),
inference(step,[status(thm)],[t103770,t30331]) ).
cnf(t512,plain,
a = least_upper_bound(a,greatest_lower_bound(X1,greatest_lower_bound(c,b))),
inference(cp,[status(thm)],[t502,t79]) ).
cnf(t553,plain,
least_upper_bound(a,greatest_lower_bound(X1,greatest_lower_bound(c,b))) = a,
inference(orient,[status(thm)],[t512]) ).
cnf(t555,plain,
a = least_upper_bound(a,greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(c,b)))),
inference(cp,[status(thm)],[t553,t69]) ).
cnf(t3972,plain,
least_upper_bound(a,greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(c,b)))) = a,
inference(orient,[status(thm)],[t555]) ).
cnf(t129,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(greatest_lower_bound(X1,X2),X1),
inference(cp,[status(thm)],[t127,t24]) ).
cnf(t103091,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X1,greatest_lower_bound(X2,X1)),
inference(step,[status(thm)],[t129,t69]) ).
cnf(t153,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X1)) = greatest_lower_bound(X1,X2),
inference(orient,[status(thm)],[t103091]) ).
cnf(t156,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,X3)) = greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))),
inference(cp,[status(thm)],[t153,t69]) ).
cnf(t2818,plain,
greatest_lower_bound(X1,greatest_lower_bound(X2,greatest_lower_bound(X3,X1))) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t156]) ).
cnf(t3973,plain,
a = least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(X1,c))),
inference(cp,[status(thm)],[t3972,t2818]) ).
cnf(t3984,plain,
least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(X1,c))) = a,
inference(orient,[status(thm)],[t3973]) ).
cnf(t3990,plain,
a = least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X1))),
inference(cp,[status(thm)],[t3984,t65]) ).
cnf(t3999,plain,
least_upper_bound(a,greatest_lower_bound(b,greatest_lower_bound(c,X1))) = a,
inference(orient,[status(thm)],[t3990]) ).
cnf(t11640,plain,
inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(inverse(least_upper_bound(inverse(X1),X2)),X1),
inference(cp,[status(thm)],[t127,t11630]) ).
cnf(t103293,plain,
inverse(least_upper_bound(inverse(X1),X2)) = greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))),
inference(step,[status(thm)],[t11640,t65]) ).
cnf(t13115,plain,
greatest_lower_bound(X1,inverse(least_upper_bound(inverse(X1),X2))) = inverse(least_upper_bound(inverse(X1),X2)),
inference(orient,[status(thm)],[t103293]) ).
cnf(t13138,plain,
a = least_upper_bound(a,greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1)))),
inference(cp,[status(thm)],[t3999,t13115]) ).
cnf(t15180,plain,
least_upper_bound(a,greatest_lower_bound(b,inverse(least_upper_bound(inverse(c),X1)))) = a,
inference(orient,[status(thm)],[t13138]) ).
cnf(t15181,plain,
a = least_upper_bound(a,inverse(least_upper_bound(inverse(c),inverse(b)))),
inference(cp,[status(thm)],[t15180,t13168]) ).
cnf(t15246,plain,
least_upper_bound(a,inverse(least_upper_bound(inverse(c),inverse(b)))) = a,
inference(orient,[status(thm)],[t15181]) ).
cnf(t15253,plain,
inverse(inverse(least_upper_bound(inverse(c),inverse(b)))) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(c),inverse(b)))),inverse(a)),
inference(cp,[status(thm)],[t11750,t15246]) ).
cnf(t103454,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(inverse(least_upper_bound(inverse(c),inverse(b)))),inverse(a)),
inference(step,[status(thm)],[t15253,t25]) ).
cnf(t103455,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(a),inverse(inverse(least_upper_bound(inverse(c),inverse(b))))),
inference(step,[status(thm)],[t103454,t81]) ).
cnf(t103456,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(a),least_upper_bound(inverse(c),inverse(b))),
inference(step,[status(thm)],[t103455,t25]) ).
cnf(t88,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)),
inference(cp,[status(thm)],[t85,t81]) ).
cnf(t29643,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X1,X2)),
inference(orient,[status(thm)],[t88]) ).
cnf(t123,plain,
least_upper_bound(X1,X2) = least_upper_bound(least_upper_bound(X1,X2),X1),
inference(cp,[status(thm)],[t121,t22]) ).
cnf(t103090,plain,
least_upper_bound(X1,X2) = least_upper_bound(X1,least_upper_bound(X2,X1)),
inference(step,[status(thm)],[t123,t85]) ).
cnf(t147,plain,
least_upper_bound(X1,least_upper_bound(X2,X1)) = least_upper_bound(X1,X2),
inference(orient,[status(thm)],[t103090]) ).
cnf(t29697,plain,
least_upper_bound(least_upper_bound(X1,X2),least_upper_bound(X3,X2)) = least_upper_bound(X3,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t29643,t147]) ).
cnf(t103435,plain,
least_upper_bound(X1,least_upper_bound(X2,least_upper_bound(X3,X2))) = least_upper_bound(X3,least_upper_bound(X2,X1)),
inference(step,[status(thm)],[t29697,t85]) ).
cnf(t103436,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X2,X1)),
inference(step,[status(thm)],[t103435,t147]) ).
cnf(t31431,plain,
least_upper_bound(X1,least_upper_bound(X2,X3)) = least_upper_bound(X3,least_upper_bound(X2,X1)),
inference(orient,[status(thm)],[t103436]) ).
cnf(t103457,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(b),least_upper_bound(inverse(c),inverse(a))),
inference(step,[status(thm)],[t103456,t31431]) ).
cnf(t103458,plain,
least_upper_bound(inverse(c),inverse(b)) = least_upper_bound(inverse(c),least_upper_bound(inverse(b),inverse(a))),
inference(step,[status(thm)],[t103457,t30331]) ).
cnf(t34342,plain,
least_upper_bound(inverse(c),least_upper_bound(inverse(b),inverse(a))) = least_upper_bound(inverse(c),inverse(b)),
inference(orient,[status(thm)],[t103458]) ).
cnf(t103772,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(c),inverse(b)),
inference(step,[status(thm)],[t103771,t34342]) ).
cnf(t102895,plain,
least_upper_bound(inverse(c),inverse(a)) = least_upper_bound(inverse(c),inverse(b)),
inference(orient,[status(thm)],[t103772]) ).
cnf(t102910,plain,
least_upper_bound(identity,inverse(multiply(inverse(c),a))) = multiply(least_upper_bound(inverse(c),inverse(b)),inverse(inverse(c))),
inference(cp,[status(thm)],[t20633,t102895]) ).
cnf(t103773,plain,
least_upper_bound(identity,multiply(inverse(a),c)) = multiply(least_upper_bound(inverse(c),inverse(b)),inverse(inverse(c))),
inference(step,[status(thm)],[t102910,t198]) ).
cnf(t48,plain,
multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(multiply(inverse(X1),X2),identity),
inference(cp,[status(thm)],[t29,t41]) ).
cnf(t103258,plain,
multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(step,[status(thm)],[t48,t81]) ).
cnf(t9153,plain,
multiply(inverse(X1),least_upper_bound(X2,X1)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(orient,[status(thm)],[t103258]) ).
cnf(t103774,plain,
multiply(inverse(a),least_upper_bound(c,a)) = multiply(least_upper_bound(inverse(c),inverse(b)),inverse(inverse(c))),
inference(step,[status(thm)],[t103773,t9153]) ).
cnf(t11,axiom,
least_upper_bound(b,c) = least_upper_bound(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t103086,plain,
least_upper_bound(c,b) = least_upper_bound(a,c),
inference(step,[status(thm)],[t11,t81]) ).
cnf(t103087,plain,
least_upper_bound(c,b) = least_upper_bound(c,a),
inference(step,[status(thm)],[t103086,t81]) ).
cnf(t95,plain,
least_upper_bound(c,a) = least_upper_bound(c,b),
inference(orient,[status(thm)],[t103087]) ).
cnf(t103775,plain,
multiply(inverse(a),least_upper_bound(c,b)) = multiply(least_upper_bound(inverse(c),inverse(b)),inverse(inverse(c))),
inference(step,[status(thm)],[t103774,t95]) ).
cnf(t103776,plain,
multiply(inverse(a),least_upper_bound(c,b)) = least_upper_bound(identity,inverse(multiply(inverse(c),b))),
inference(step,[status(thm)],[t103775,t20633]) ).
cnf(t103777,plain,
multiply(inverse(a),least_upper_bound(c,b)) = least_upper_bound(identity,multiply(inverse(b),c)),
inference(step,[status(thm)],[t103776,t198]) ).
cnf(t103778,plain,
multiply(inverse(a),least_upper_bound(c,b)) = multiply(inverse(b),least_upper_bound(c,b)),
inference(step,[status(thm)],[t103777,t9153]) ).
cnf(t102981,plain,
multiply(inverse(a),least_upper_bound(c,b)) = multiply(inverse(b),least_upper_bound(c,b)),
inference(orient,[status(thm)],[t103778]) ).
cnf(t103045,plain,
inverse(inverse(a)) = multiply(least_upper_bound(c,b),inverse(multiply(inverse(b),least_upper_bound(c,b)))),
inference(cp,[status(thm)],[t206,t102981]) ).
cnf(t103779,plain,
a = multiply(least_upper_bound(c,b),inverse(multiply(inverse(b),least_upper_bound(c,b)))),
inference(step,[status(thm)],[t103045,t25]) ).
cnf(t103780,plain,
a = inverse(inverse(b)),
inference(step,[status(thm)],[t103779,t206]) ).
cnf(t103781,plain,
a = b,
inference(step,[status(thm)],[t103780,t25]) ).
cnf(t103062,plain,
a = b,
inference(orient,[status(thm)],[t103781]) ).
cnf(goal_0,negated_conjecture,
b != a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
b != b,
inference(rw,[status(thm)],[goal_0,t103062]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP181-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.37 % Computer : n020.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Wed Sep 23 14:01:47 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 34.02/4.95 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 34.02/4.95 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------