%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 01:25:31 PM UTC 2026
% Result : Unsatisfiable 18.06s 2.79s
% Output : CNFRefutation 18.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 19
% Syntax : Number of clauses : 111 ( 111 unt; 0 nHn; 43 RR)
% Number of literals : 111 ( 110 equ; 7 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 : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 112 ( 25 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t70,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t18,axiom,
sFlat1 = multiply(b,d),
introduced(definition) ).
cnf(t40,plain,
multiply(b,d) = sFlat1,
inference(orient,[status(thm)],[t18]) ).
cnf(t17,axiom,
sFlat0 = multiply(a,c),
introduced(definition) ).
cnf(t50,plain,
multiply(a,c) = sFlat0,
inference(orient,[status(thm)],[t17]) ).
cnf(t19,axiom,
sFlat2 = least_upper_bound(multiply(a,c),multiply(b,d)),
introduced(definition) ).
cnf(t21453,plain,
sFlat2 = least_upper_bound(multiply(b,d),multiply(a,c)),
inference(step,[status(thm)],[t19,t70]) ).
cnf(t21454,plain,
sFlat2 = least_upper_bound(sFlat1,multiply(a,c)),
inference(step,[status(thm)],[t21453,t40]) ).
cnf(t21455,plain,
sFlat2 = least_upper_bound(sFlat1,sFlat0),
inference(step,[status(thm)],[t21454,t50]) ).
cnf(t21456,plain,
sFlat2 = least_upper_bound(sFlat0,sFlat1),
inference(step,[status(thm)],[t21455,t70]) ).
cnf(t84,plain,
least_upper_bound(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t21456]) ).
cnf(t12,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t25,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t5,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t60,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t69,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t25,t60]) ).
cnf(t4,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t20,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t21484,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t69,t20]) ).
cnf(t463,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t21484]) ).
cnf(t11,axiom,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t74,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t9,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t22,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t1,axiom,
greatest_lower_bound(c,d) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t89,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t21458,plain,
greatest_lower_bound(d,c) = c,
inference(step,[status(thm)],[t1,t89]) ).
cnf(t103,plain,
greatest_lower_bound(d,c) = c,
inference(orient,[status(thm)],[t21458]) ).
cnf(t104,plain,
d = least_upper_bound(d,c),
inference(cp,[status(thm)],[t22,t103]) ).
cnf(t108,plain,
least_upper_bound(d,c) = d,
inference(orient,[status(thm)],[t104]) ).
cnf(t109,plain,
least_upper_bound(d,least_upper_bound(c,X1)) = least_upper_bound(d,X1),
inference(cp,[status(thm)],[t74,t108]) ).
cnf(t215,plain,
least_upper_bound(d,least_upper_bound(c,X1)) = least_upper_bound(d,X1),
inference(orient,[status(thm)],[t109]) ).
cnf(t16,axiom,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t29,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t16]) ).
cnf(t30,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t29,t20]) ).
cnf(t261,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t30]) ).
cnf(t272,plain,
least_upper_bound(d,multiply(X1,c)) = least_upper_bound(d,multiply(least_upper_bound(identity,X1),c)),
inference(cp,[status(thm)],[t215,t261]) ).
cnf(t21094,plain,
least_upper_bound(d,multiply(least_upper_bound(identity,X1),c)) = least_upper_bound(d,multiply(X1,c)),
inference(orient,[status(thm)],[t272]) ).
cnf(t13,axiom,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t28,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t66,plain,
multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(multiply(inverse(X1),X2),identity),
inference(cp,[status(thm)],[t28,t60]) ).
cnf(t21611,plain,
multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)),
inference(step,[status(thm)],[t66,t89]) ).
cnf(t6145,plain,
multiply(inverse(X1),greatest_lower_bound(X2,X1)) = greatest_lower_bound(identity,multiply(inverse(X1),X2)),
inference(orient,[status(thm)],[t21611]) ).
cnf(t6288,plain,
identity = least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))),
inference(cp,[status(thm)],[t22,t6145]) ).
cnf(t12480,plain,
least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = identity,
inference(orient,[status(thm)],[t6288]) ).
cnf(t7,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t24,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t73,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t24,t70]) ).
cnf(t110,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t73]) ).
cnf(t3,axiom,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t21457,plain,
least_upper_bound(b,a) = b,
inference(step,[status(thm)],[t3,t70]) ).
cnf(t87,plain,
least_upper_bound(b,a) = b,
inference(orient,[status(thm)],[t21457]) ).
cnf(t88,plain,
least_upper_bound(b,least_upper_bound(a,X1)) = least_upper_bound(b,X1),
inference(cp,[status(thm)],[t74,t87]) ).
cnf(t184,plain,
least_upper_bound(b,least_upper_bound(a,X1)) = least_upper_bound(b,X1),
inference(orient,[status(thm)],[t88]) ).
cnf(t185,plain,
least_upper_bound(b,greatest_lower_bound(a,X1)) = least_upper_bound(b,a),
inference(cp,[status(thm)],[t184,t22]) ).
cnf(t21464,plain,
least_upper_bound(b,greatest_lower_bound(a,X1)) = b,
inference(step,[status(thm)],[t185,t87]) ).
cnf(t189,plain,
least_upper_bound(b,greatest_lower_bound(a,X1)) = b,
inference(orient,[status(thm)],[t21464]) ).
cnf(t191,plain,
greatest_lower_bound(a,X1) = greatest_lower_bound(greatest_lower_bound(a,X1),b),
inference(cp,[status(thm)],[t110,t189]) ).
cnf(t10,axiom,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t93,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t21473,plain,
greatest_lower_bound(a,X1) = greatest_lower_bound(a,greatest_lower_bound(X1,b)),
inference(step,[status(thm)],[t191,t93]) ).
cnf(t323,plain,
greatest_lower_bound(a,greatest_lower_bound(X1,b)) = greatest_lower_bound(a,X1),
inference(orient,[status(thm)],[t21473]) ).
cnf(t326,plain,
greatest_lower_bound(a,X1) = greatest_lower_bound(a,greatest_lower_bound(b,X1)),
inference(cp,[status(thm)],[t323,t89]) ).
cnf(t412,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X1)) = greatest_lower_bound(a,X1),
inference(orient,[status(thm)],[t326]) ).
cnf(t414,plain,
greatest_lower_bound(a,least_upper_bound(b,X1)) = greatest_lower_bound(a,b),
inference(cp,[status(thm)],[t412,t24]) ).
cnf(t21480,plain,
greatest_lower_bound(a,least_upper_bound(b,X1)) = greatest_lower_bound(b,a),
inference(step,[status(thm)],[t414,t89]) ).
cnf(t114,plain,
a = greatest_lower_bound(a,b),
inference(cp,[status(thm)],[t110,t87]) ).
cnf(t21459,plain,
a = greatest_lower_bound(b,a),
inference(step,[status(thm)],[t114,t89]) ).
cnf(t118,plain,
greatest_lower_bound(b,a) = a,
inference(orient,[status(thm)],[t21459]) ).
cnf(t21481,plain,
greatest_lower_bound(a,least_upper_bound(b,X1)) = a,
inference(step,[status(thm)],[t21480,t118]) ).
cnf(t435,plain,
greatest_lower_bound(a,least_upper_bound(b,X1)) = a,
inference(orient,[status(thm)],[t21481]) ).
cnf(t443,plain,
a = greatest_lower_bound(a,least_upper_bound(X1,b)),
inference(cp,[status(thm)],[t435,t70]) ).
cnf(t445,plain,
greatest_lower_bound(a,least_upper_bound(X1,b)) = a,
inference(orient,[status(thm)],[t443]) ).
cnf(t12560,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X1,b)),a)),
inference(cp,[status(thm)],[t12480,t445]) ).
cnf(t14888,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X1,b)),a)) = identity,
inference(orient,[status(thm)],[t12560]) ).
cnf(t21110,plain,
least_upper_bound(d,multiply(multiply(inverse(least_upper_bound(X1,b)),a),c)) = least_upper_bound(d,multiply(identity,c)),
inference(cp,[status(thm)],[t21094,t14888]) ).
cnf(t21875,plain,
least_upper_bound(d,multiply(inverse(least_upper_bound(X1,b)),multiply(a,c))) = least_upper_bound(d,multiply(identity,c)),
inference(step,[status(thm)],[t21110,t25]) ).
cnf(t21876,plain,
least_upper_bound(d,multiply(inverse(least_upper_bound(X1,b)),sFlat0)) = least_upper_bound(d,multiply(identity,c)),
inference(step,[status(thm)],[t21875,t50]) ).
cnf(t21877,plain,
least_upper_bound(d,multiply(inverse(least_upper_bound(X1,b)),sFlat0)) = least_upper_bound(d,c),
inference(step,[status(thm)],[t21876,t20]) ).
cnf(t21878,plain,
least_upper_bound(d,multiply(inverse(least_upper_bound(X1,b)),sFlat0)) = d,
inference(step,[status(thm)],[t21877,t108]) ).
cnf(t21166,plain,
least_upper_bound(d,multiply(inverse(least_upper_bound(X1,b)),sFlat0)) = d,
inference(orient,[status(thm)],[t21878]) ).
cnf(t2,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t21,plain,
least_upper_bound(X1,X1) = X1,
inference(orient,[status(thm)],[t2]) ).
cnf(t21167,plain,
d = least_upper_bound(d,multiply(inverse(b),sFlat0)),
inference(cp,[status(thm)],[t21166,t21]) ).
cnf(t15,axiom,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t26,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t15]) ).
cnf(t469,plain,
d = multiply(inverse(b),sFlat1),
inference(cp,[status(thm)],[t463,t40]) ).
cnf(t495,plain,
multiply(inverse(b),sFlat1) = d,
inference(orient,[status(thm)],[t469]) ).
cnf(t504,plain,
multiply(inverse(b),least_upper_bound(sFlat1,X1)) = least_upper_bound(d,multiply(inverse(b),X1)),
inference(cp,[status(thm)],[t26,t495]) ).
cnf(t15791,plain,
least_upper_bound(d,multiply(inverse(b),X1)) = multiply(inverse(b),least_upper_bound(sFlat1,X1)),
inference(orient,[status(thm)],[t504]) ).
cnf(t21879,plain,
d = multiply(inverse(b),least_upper_bound(sFlat1,sFlat0)),
inference(step,[status(thm)],[t21167,t15791]) ).
cnf(t21880,plain,
d = multiply(inverse(b),least_upper_bound(sFlat0,sFlat1)),
inference(step,[status(thm)],[t21879,t70]) ).
cnf(t21881,plain,
d = multiply(inverse(b),sFlat2),
inference(step,[status(thm)],[t21880,t84]) ).
cnf(t21188,plain,
multiply(inverse(b),sFlat2) = d,
inference(orient,[status(thm)],[t21881]) ).
cnf(t21192,plain,
sFlat2 = multiply(inverse(inverse(b)),d),
inference(cp,[status(thm)],[t463,t21188]) ).
cnf(t496,plain,
sFlat1 = multiply(inverse(inverse(b)),d),
inference(cp,[status(thm)],[t463,t495]) ).
cnf(t538,plain,
multiply(inverse(inverse(b)),d) = sFlat1,
inference(orient,[status(thm)],[t496]) ).
cnf(t21885,plain,
sFlat2 = sFlat1,
inference(step,[status(thm)],[t21192,t538]) ).
cnf(t21355,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t21885]) ).
cnf(t21886,plain,
least_upper_bound(sFlat0,sFlat1) = sFlat1,
inference(step,[status(thm)],[t84,t21355]) ).
cnf(t21356,plain,
least_upper_bound(sFlat0,sFlat1) = sFlat1,
inference(orient,[status(thm)],[t21886]) ).
cnf(goal_0,negated_conjecture,
least_upper_bound(multiply(a,c),multiply(b,d)) != multiply(b,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
least_upper_bound(multiply(b,d),multiply(a,c)) != multiply(b,d),
inference(rw,[status(thm)],[goal_0,t70]) ).
cnf(g0_1,plain,
least_upper_bound(sFlat1,multiply(a,c)) != multiply(b,d),
inference(rw,[status(thm)],[g0_0,t40]) ).
cnf(g0_2,plain,
least_upper_bound(sFlat1,sFlat0) != multiply(b,d),
inference(rw,[status(thm)],[g0_1,t50]) ).
cnf(g0_3,plain,
least_upper_bound(sFlat0,sFlat1) != multiply(b,d),
inference(rw,[status(thm)],[g0_2,t70]) ).
cnf(g0_4,plain,
sFlat1 != multiply(b,d),
inference(rw,[status(thm)],[g0_3,t21356]) ).
cnf(g0_5,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_4,t40]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP170-4 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n001.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 14:03:19 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 18.06/2.79 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.06/2.79 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------