%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP170-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 17.50s 3.03s
% Output : CNFRefutation 17.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 18
% Syntax : Number of clauses : 109 ( 109 unt; 0 nHn; 42 RR)
% Number of literals : 109 ( 108 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 : 109 ( 27 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t70,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t18,axiom,
sFlat1 = multiply(b,d),
introduced(definition) ).
cnf(t50,plain,
multiply(b,d) = sFlat1,
inference(orient,[status(thm)],[t18]) ).
cnf(t17,axiom,
sFlat0 = multiply(a,c),
introduced(definition) ).
cnf(t40,plain,
multiply(a,c) = sFlat0,
inference(orient,[status(thm)],[t17]) ).
cnf(t19,axiom,
sFlat2 = greatest_lower_bound(multiply(a,c),multiply(b,d)),
introduced(definition) ).
cnf(t22872,plain,
sFlat2 = greatest_lower_bound(multiply(b,d),multiply(a,c)),
inference(step,[status(thm)],[t19,t70]) ).
cnf(t22873,plain,
sFlat2 = greatest_lower_bound(sFlat1,multiply(a,c)),
inference(step,[status(thm)],[t22872,t50]) ).
cnf(t22874,plain,
sFlat2 = greatest_lower_bound(sFlat1,sFlat0),
inference(step,[status(thm)],[t22873,t40]) ).
cnf(t22875,plain,
sFlat2 = greatest_lower_bound(sFlat0,sFlat1),
inference(step,[status(thm)],[t22874,t70]) ).
cnf(t84,plain,
greatest_lower_bound(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t22875]) ).
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(t12,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
cnf(t20,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t22900,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t69,t20]) ).
cnf(t465,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t22900]) ).
cnf(t11,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(t97,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/sandbox2/benchmark/theBenchmark.p') ).
cnf(t24,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t2,axiom,
greatest_lower_bound(c,d) = c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t22877,plain,
greatest_lower_bound(d,c) = c,
inference(step,[status(thm)],[t2,t70]) ).
cnf(t90,plain,
greatest_lower_bound(d,c) = c,
inference(orient,[status(thm)],[t22877]) ).
cnf(t92,plain,
d = least_upper_bound(d,c),
inference(cp,[status(thm)],[t24,t90]) ).
cnf(t111,plain,
least_upper_bound(d,c) = d,
inference(orient,[status(thm)],[t92]) ).
cnf(t112,plain,
least_upper_bound(d,least_upper_bound(c,X1)) = least_upper_bound(d,X1),
inference(cp,[status(thm)],[t97,t111]) ).
cnf(t217,plain,
least_upper_bound(d,least_upper_bound(c,X1)) = least_upper_bound(d,X1),
inference(orient,[status(thm)],[t112]) ).
cnf(t16,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(t35,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t16]) ).
cnf(t36,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t35,t20]) ).
cnf(t652,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t36]) ).
cnf(t675,plain,
least_upper_bound(d,multiply(X1,c)) = least_upper_bound(d,multiply(least_upper_bound(identity,X1),c)),
inference(cp,[status(thm)],[t217,t652]) ).
cnf(t22605,plain,
least_upper_bound(d,multiply(least_upper_bound(identity,X1),c)) = least_upper_bound(d,multiply(X1,c)),
inference(orient,[status(thm)],[t675]) ).
cnf(t15,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(t28,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t15]) ).
cnf(t65,plain,
multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(cp,[status(thm)],[t28,t60]) ).
cnf(t4443,plain,
multiply(inverse(X1),least_upper_bound(X1,X2)) = least_upper_bound(identity,multiply(inverse(X1),X2)),
inference(orient,[status(thm)],[t65]) ).
cnf(t73,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t24,t70]) ).
cnf(t113,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t73]) ).
cnf(t4448,plain,
least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = multiply(inverse(X1),X1),
inference(cp,[status(thm)],[t4443,t113]) ).
cnf(t23106,plain,
least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = identity,
inference(step,[status(thm)],[t4448,t60]) ).
cnf(t11968,plain,
least_upper_bound(identity,multiply(inverse(X1),greatest_lower_bound(X2,X1))) = identity,
inference(orient,[status(thm)],[t23106]) ).
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t93,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t96,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t22,t93]) ).
cnf(t121,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t96]) ).
cnf(t10,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(t74,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(t1,axiom,
greatest_lower_bound(a,b) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t22876,plain,
greatest_lower_bound(b,a) = a,
inference(step,[status(thm)],[t1,t70]) ).
cnf(t87,plain,
greatest_lower_bound(b,a) = a,
inference(orient,[status(thm)],[t22876]) ).
cnf(t88,plain,
greatest_lower_bound(b,greatest_lower_bound(a,X1)) = greatest_lower_bound(a,X1),
inference(cp,[status(thm)],[t74,t87]) ).
cnf(t185,plain,
greatest_lower_bound(b,greatest_lower_bound(a,X1)) = greatest_lower_bound(a,X1),
inference(orient,[status(thm)],[t88]) ).
cnf(t187,plain,
b = least_upper_bound(b,greatest_lower_bound(a,X1)),
inference(cp,[status(thm)],[t24,t185]) ).
cnf(t188,plain,
least_upper_bound(b,greatest_lower_bound(a,X1)) = b,
inference(orient,[status(thm)],[t187]) ).
cnf(t190,plain,
greatest_lower_bound(a,X1) = greatest_lower_bound(greatest_lower_bound(a,X1),b),
inference(cp,[status(thm)],[t121,t188]) ).
cnf(t22889,plain,
greatest_lower_bound(a,X1) = greatest_lower_bound(a,greatest_lower_bound(X1,b)),
inference(step,[status(thm)],[t190,t74]) ).
cnf(t327,plain,
greatest_lower_bound(a,greatest_lower_bound(X1,b)) = greatest_lower_bound(a,X1),
inference(orient,[status(thm)],[t22889]) ).
cnf(t330,plain,
greatest_lower_bound(a,X1) = greatest_lower_bound(a,greatest_lower_bound(b,X1)),
inference(cp,[status(thm)],[t327,t70]) ).
cnf(t414,plain,
greatest_lower_bound(a,greatest_lower_bound(b,X1)) = greatest_lower_bound(a,X1),
inference(orient,[status(thm)],[t330]) ).
cnf(t417,plain,
greatest_lower_bound(a,least_upper_bound(b,X1)) = greatest_lower_bound(a,b),
inference(cp,[status(thm)],[t414,t22]) ).
cnf(t22896,plain,
greatest_lower_bound(a,least_upper_bound(b,X1)) = greatest_lower_bound(b,a),
inference(step,[status(thm)],[t417,t70]) ).
cnf(t22897,plain,
greatest_lower_bound(a,least_upper_bound(b,X1)) = a,
inference(step,[status(thm)],[t22896,t87]) ).
cnf(t439,plain,
greatest_lower_bound(a,least_upper_bound(b,X1)) = a,
inference(orient,[status(thm)],[t22897]) ).
cnf(t446,plain,
a = greatest_lower_bound(a,least_upper_bound(X1,b)),
inference(cp,[status(thm)],[t439,t93]) ).
cnf(t448,plain,
greatest_lower_bound(a,least_upper_bound(X1,b)) = a,
inference(orient,[status(thm)],[t446]) ).
cnf(t12033,plain,
identity = least_upper_bound(identity,multiply(inverse(least_upper_bound(X1,b)),a)),
inference(cp,[status(thm)],[t11968,t448]) ).
cnf(t14634,plain,
least_upper_bound(identity,multiply(inverse(least_upper_bound(X1,b)),a)) = identity,
inference(orient,[status(thm)],[t12033]) ).
cnf(t22620,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)],[t22605,t14634]) ).
cnf(t23319,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)],[t22620,t25]) ).
cnf(t23320,plain,
least_upper_bound(d,multiply(inverse(least_upper_bound(X1,b)),sFlat0)) = least_upper_bound(d,multiply(identity,c)),
inference(step,[status(thm)],[t23319,t40]) ).
cnf(t23321,plain,
least_upper_bound(d,multiply(inverse(least_upper_bound(X1,b)),sFlat0)) = least_upper_bound(d,c),
inference(step,[status(thm)],[t23320,t20]) ).
cnf(t23322,plain,
least_upper_bound(d,multiply(inverse(least_upper_bound(X1,b)),sFlat0)) = d,
inference(step,[status(thm)],[t23321,t111]) ).
cnf(t22670,plain,
least_upper_bound(d,multiply(inverse(least_upper_bound(X1,b)),sFlat0)) = d,
inference(orient,[status(thm)],[t23322]) ).
cnf(t3,axiom,
least_upper_bound(X1,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
least_upper_bound(X1,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t22671,plain,
d = least_upper_bound(d,multiply(inverse(b),sFlat0)),
inference(cp,[status(thm)],[t22670,t23]) ).
cnf(t469,plain,
d = multiply(inverse(b),sFlat1),
inference(cp,[status(thm)],[t465,t50]) ).
cnf(t485,plain,
multiply(inverse(b),sFlat1) = d,
inference(orient,[status(thm)],[t469]) ).
cnf(t492,plain,
multiply(inverse(b),least_upper_bound(sFlat1,X1)) = least_upper_bound(d,multiply(inverse(b),X1)),
inference(cp,[status(thm)],[t28,t485]) ).
cnf(t15595,plain,
least_upper_bound(d,multiply(inverse(b),X1)) = multiply(inverse(b),least_upper_bound(sFlat1,X1)),
inference(orient,[status(thm)],[t492]) ).
cnf(t23323,plain,
d = multiply(inverse(b),least_upper_bound(sFlat1,sFlat0)),
inference(step,[status(thm)],[t22671,t15595]) ).
cnf(t23324,plain,
d = multiply(inverse(b),least_upper_bound(sFlat0,sFlat1)),
inference(step,[status(thm)],[t23323,t93]) ).
cnf(t22693,plain,
multiply(inverse(b),least_upper_bound(sFlat0,sFlat1)) = d,
inference(orient,[status(thm)],[t23324]) ).
cnf(t22697,plain,
least_upper_bound(sFlat0,sFlat1) = multiply(inverse(inverse(b)),d),
inference(cp,[status(thm)],[t465,t22693]) ).
cnf(t486,plain,
sFlat1 = multiply(inverse(inverse(b)),d),
inference(cp,[status(thm)],[t465,t485]) ).
cnf(t528,plain,
multiply(inverse(inverse(b)),d) = sFlat1,
inference(orient,[status(thm)],[t486]) ).
cnf(t23325,plain,
least_upper_bound(sFlat0,sFlat1) = sFlat1,
inference(step,[status(thm)],[t22697,t528]) ).
cnf(t22731,plain,
least_upper_bound(sFlat0,sFlat1) = sFlat1,
inference(orient,[status(thm)],[t23325]) ).
cnf(t22732,plain,
sFlat0 = greatest_lower_bound(sFlat0,sFlat1),
inference(cp,[status(thm)],[t22,t22731]) ).
cnf(t23326,plain,
sFlat0 = sFlat2,
inference(step,[status(thm)],[t22732,t84]) ).
cnf(t22759,plain,
sFlat2 = sFlat0,
inference(orient,[status(thm)],[t23326]) ).
cnf(t23327,plain,
greatest_lower_bound(sFlat0,sFlat1) = sFlat0,
inference(step,[status(thm)],[t84,t22759]) ).
cnf(t22760,plain,
greatest_lower_bound(sFlat0,sFlat1) = sFlat0,
inference(orient,[status(thm)],[t23327]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
greatest_lower_bound(multiply(b,d),multiply(a,c)) != multiply(a,c),
inference(rw,[status(thm)],[goal_0,t70]) ).
cnf(g0_1,plain,
greatest_lower_bound(sFlat1,multiply(a,c)) != multiply(a,c),
inference(rw,[status(thm)],[g0_0,t50]) ).
cnf(g0_2,plain,
greatest_lower_bound(sFlat1,sFlat0) != multiply(a,c),
inference(rw,[status(thm)],[g0_1,t40]) ).
cnf(g0_3,plain,
greatest_lower_bound(sFlat0,sFlat1) != multiply(a,c),
inference(rw,[status(thm)],[g0_2,t70]) ).
cnf(g0_4,plain,
sFlat0 != multiply(a,c),
inference(rw,[status(thm)],[g0_3,t22760]) ).
cnf(g0_5,plain,
sFlat0 != sFlat0,
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 : GRP170-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.52 % Computer : n017.cluster.edu
% 0.11/0.52 % Model : x86_64 x86_64
% 0.11/0.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.52 % Memory : 8046.5625MB
% 0.11/0.52 % OS : Linux 6.8.0-71-generic
% 0.11/0.52 % CPULimit : 300
% 0.11/0.52 % WCLimit : 300
% 0.11/0.52 % DateTime : Wed Sep 23 13:52:30 UTC 2026
% 0.11/0.52 % CPUTime :
% 0.11/0.52 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 17.50/3.03 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 17.50/3.03 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------