%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP193-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 01:25:39 PM UTC 2026
% Result : Unsatisfiable 7.51s 1.39s
% Output : CNFRefutation 7.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 15
% Syntax : Number of clauses : 96 ( 96 unt; 0 nHn; 66 RR)
% Number of literals : 96 ( 95 equ; 6 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 54 ( 10 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t20,axiom,
sFlat0 = multiply(b,c),
introduced(definition) ).
cnf(t45,plain,
multiply(b,c) = sFlat0,
inference(orient,[status(thm)],[t20]) ).
cnf(t8,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t66,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t21,axiom,
sFlat1 = greatest_lower_bound(a,multiply(b,c)),
introduced(definition) ).
cnf(t3338,plain,
sFlat1 = greatest_lower_bound(a,sFlat0),
inference(step,[status(thm)],[t21,t45]) ).
cnf(t3339,plain,
sFlat1 = greatest_lower_bound(sFlat0,a),
inference(step,[status(thm)],[t3338,t66]) ).
cnf(t80,plain,
greatest_lower_bound(sFlat0,a) = sFlat1,
inference(orient,[status(thm)],[t3339]) ).
cnf(t22,axiom,
sFlat2 = greatest_lower_bound(a,c),
introduced(definition) ).
cnf(t3341,plain,
sFlat2 = greatest_lower_bound(c,a),
inference(step,[status(thm)],[t22,t66]) ).
cnf(t86,plain,
greatest_lower_bound(c,a) = sFlat2,
inference(orient,[status(thm)],[t3341]) ).
cnf(t19,axiom,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t38,plain,
least_upper_bound(greatest_lower_bound(a,multiply(b,c)),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(orient,[status(thm)],[t19]) ).
cnf(t3337,plain,
least_upper_bound(greatest_lower_bound(a,sFlat0),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(step,[status(thm)],[t38,t45]) ).
cnf(t55,plain,
least_upper_bound(greatest_lower_bound(a,sFlat0),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(rw,[status(thm)],[t3337]) ).
cnf(t3522,plain,
least_upper_bound(greatest_lower_bound(sFlat0,a),multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(step,[status(thm)],[t55,t66]) ).
cnf(t3523,plain,
least_upper_bound(sFlat1,multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(step,[status(thm)],[t3522,t80]) ).
cnf(t3524,plain,
least_upper_bound(sFlat1,multiply(greatest_lower_bound(b,a),greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(step,[status(thm)],[t3523,t66]) ).
cnf(t1,axiom,
greatest_lower_bound(a,b) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t3340,plain,
greatest_lower_bound(b,a) = identity,
inference(step,[status(thm)],[t1,t66]) ).
cnf(t83,plain,
greatest_lower_bound(b,a) = identity,
inference(orient,[status(thm)],[t3340]) ).
cnf(t3525,plain,
least_upper_bound(sFlat1,multiply(identity,greatest_lower_bound(a,c))) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(step,[status(thm)],[t3524,t83]) ).
cnf(t6,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t23,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t3526,plain,
least_upper_bound(sFlat1,greatest_lower_bound(a,c)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(step,[status(thm)],[t3525,t23]) ).
cnf(t3527,plain,
least_upper_bound(sFlat1,greatest_lower_bound(c,a)) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(step,[status(thm)],[t3526,t66]) ).
cnf(t3528,plain,
least_upper_bound(sFlat1,sFlat2) = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(step,[status(thm)],[t3527,t86]) ).
cnf(t11,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t27,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t11]) ).
cnf(t12,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(t70,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t81,plain,
greatest_lower_bound(sFlat0,greatest_lower_bound(a,X1)) = greatest_lower_bound(sFlat1,X1),
inference(cp,[status(thm)],[t70,t80]) ).
cnf(t172,plain,
greatest_lower_bound(sFlat0,greatest_lower_bound(a,X1)) = greatest_lower_bound(sFlat1,X1),
inference(orient,[status(thm)],[t81]) ).
cnf(t176,plain,
greatest_lower_bound(sFlat1,X1) = greatest_lower_bound(sFlat0,greatest_lower_bound(X1,a)),
inference(cp,[status(thm)],[t172,t66]) ).
cnf(t439,plain,
greatest_lower_bound(sFlat0,greatest_lower_bound(X1,a)) = greatest_lower_bound(sFlat1,X1),
inference(orient,[status(thm)],[t176]) ).
cnf(t9,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t25,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t69,plain,
X1 = least_upper_bound(X1,greatest_lower_bound(X2,X1)),
inference(cp,[status(thm)],[t27,t66]) ).
cnf(t125,plain,
least_upper_bound(X1,greatest_lower_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t69]) ).
cnf(t132,plain,
a = least_upper_bound(a,sFlat2),
inference(cp,[status(thm)],[t125,t86]) ).
cnf(t10,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t89,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t10]) ).
cnf(t3343,plain,
a = least_upper_bound(sFlat2,a),
inference(step,[status(thm)],[t132,t89]) ).
cnf(t137,plain,
least_upper_bound(sFlat2,a) = a,
inference(orient,[status(thm)],[t3343]) ).
cnf(t138,plain,
sFlat2 = greatest_lower_bound(sFlat2,a),
inference(cp,[status(thm)],[t25,t137]) ).
cnf(t143,plain,
greatest_lower_bound(sFlat2,a) = sFlat2,
inference(orient,[status(thm)],[t138]) ).
cnf(t441,plain,
greatest_lower_bound(sFlat1,sFlat2) = greatest_lower_bound(sFlat0,sFlat2),
inference(cp,[status(thm)],[t439,t143]) ).
cnf(t13,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(t93,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t88,plain,
c = least_upper_bound(c,sFlat2),
inference(cp,[status(thm)],[t27,t86]) ).
cnf(t3342,plain,
c = least_upper_bound(sFlat2,c),
inference(step,[status(thm)],[t88,t89]) ).
cnf(t114,plain,
least_upper_bound(sFlat2,c) = c,
inference(orient,[status(thm)],[t3342]) ).
cnf(t116,plain,
least_upper_bound(sFlat2,least_upper_bound(c,X1)) = least_upper_bound(c,X1),
inference(cp,[status(thm)],[t93,t114]) ).
cnf(t323,plain,
least_upper_bound(sFlat2,least_upper_bound(c,X1)) = least_upper_bound(c,X1),
inference(orient,[status(thm)],[t116]) ).
cnf(t325,plain,
sFlat2 = greatest_lower_bound(sFlat2,least_upper_bound(c,X1)),
inference(cp,[status(thm)],[t25,t323]) ).
cnf(t326,plain,
greatest_lower_bound(sFlat2,least_upper_bound(c,X1)) = sFlat2,
inference(orient,[status(thm)],[t325]) ).
cnf(t327,plain,
sFlat2 = greatest_lower_bound(sFlat2,least_upper_bound(X1,c)),
inference(cp,[status(thm)],[t326,t89]) ).
cnf(t331,plain,
greatest_lower_bound(sFlat2,least_upper_bound(X1,c)) = sFlat2,
inference(orient,[status(thm)],[t327]) ).
cnf(t16,axiom,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t32,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t16]) ).
cnf(t33,plain,
multiply(greatest_lower_bound(identity,X1),X2) = greatest_lower_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t32,t23]) ).
cnf(t244,plain,
greatest_lower_bound(X1,multiply(X2,X1)) = multiply(greatest_lower_bound(identity,X2),X1),
inference(orient,[status(thm)],[t33]) ).
cnf(t248,plain,
multiply(greatest_lower_bound(identity,b),c) = greatest_lower_bound(c,sFlat0),
inference(cp,[status(thm)],[t244,t45]) ).
cnf(t4,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t106,plain,
least_upper_bound(identity,b) = b,
inference(orient,[status(thm)],[t4]) ).
cnf(t107,plain,
identity = greatest_lower_bound(identity,b),
inference(cp,[status(thm)],[t25,t106]) ).
cnf(t119,plain,
greatest_lower_bound(identity,b) = identity,
inference(orient,[status(thm)],[t107]) ).
cnf(t3352,plain,
multiply(identity,c) = greatest_lower_bound(c,sFlat0),
inference(step,[status(thm)],[t248,t119]) ).
cnf(t3353,plain,
c = greatest_lower_bound(c,sFlat0),
inference(step,[status(thm)],[t3352,t23]) ).
cnf(t3354,plain,
c = greatest_lower_bound(sFlat0,c),
inference(step,[status(thm)],[t3353,t66]) ).
cnf(t258,plain,
greatest_lower_bound(sFlat0,c) = c,
inference(orient,[status(thm)],[t3354]) ).
cnf(t260,plain,
sFlat0 = least_upper_bound(sFlat0,c),
inference(cp,[status(thm)],[t27,t258]) ).
cnf(t261,plain,
least_upper_bound(sFlat0,c) = sFlat0,
inference(orient,[status(thm)],[t260]) ).
cnf(t332,plain,
sFlat2 = greatest_lower_bound(sFlat2,sFlat0),
inference(cp,[status(thm)],[t331,t261]) ).
cnf(t3356,plain,
sFlat2 = greatest_lower_bound(sFlat0,sFlat2),
inference(step,[status(thm)],[t332,t66]) ).
cnf(t337,plain,
greatest_lower_bound(sFlat0,sFlat2) = sFlat2,
inference(orient,[status(thm)],[t3356]) ).
cnf(t3361,plain,
greatest_lower_bound(sFlat1,sFlat2) = sFlat2,
inference(step,[status(thm)],[t441,t337]) ).
cnf(t450,plain,
greatest_lower_bound(sFlat1,sFlat2) = sFlat2,
inference(orient,[status(thm)],[t3361]) ).
cnf(t454,plain,
sFlat1 = least_upper_bound(sFlat1,sFlat2),
inference(cp,[status(thm)],[t27,t450]) ).
cnf(t470,plain,
least_upper_bound(sFlat1,sFlat2) = sFlat1,
inference(orient,[status(thm)],[t454]) ).
cnf(t3529,plain,
sFlat1 = multiply(greatest_lower_bound(a,b),greatest_lower_bound(a,c)),
inference(step,[status(thm)],[t3528,t470]) ).
cnf(t3530,plain,
sFlat1 = multiply(greatest_lower_bound(b,a),greatest_lower_bound(a,c)),
inference(step,[status(thm)],[t3529,t66]) ).
cnf(t3531,plain,
sFlat1 = multiply(identity,greatest_lower_bound(a,c)),
inference(step,[status(thm)],[t3530,t83]) ).
cnf(t3532,plain,
sFlat1 = greatest_lower_bound(a,c),
inference(step,[status(thm)],[t3531,t23]) ).
cnf(t3533,plain,
sFlat1 = greatest_lower_bound(c,a),
inference(step,[status(thm)],[t3532,t66]) ).
cnf(t3534,plain,
sFlat1 = sFlat2,
inference(step,[status(thm)],[t3533,t86]) ).
cnf(t3309,plain,
sFlat2 = sFlat1,
inference(orient,[status(thm)],[t3534]) ).
cnf(t3535,plain,
greatest_lower_bound(c,a) = sFlat1,
inference(step,[status(thm)],[t86,t3309]) ).
cnf(t3310,plain,
greatest_lower_bound(c,a) = sFlat1,
inference(orient,[status(thm)],[t3535]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(a,multiply(b,c)) != greatest_lower_bound(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
greatest_lower_bound(a,sFlat0) != greatest_lower_bound(a,c),
inference(rw,[status(thm)],[goal_0,t45]) ).
cnf(g0_1,plain,
greatest_lower_bound(sFlat0,a) != greatest_lower_bound(a,c),
inference(rw,[status(thm)],[g0_0,t66]) ).
cnf(g0_2,plain,
sFlat1 != greatest_lower_bound(a,c),
inference(rw,[status(thm)],[g0_1,t80]) ).
cnf(g0_3,plain,
sFlat1 != greatest_lower_bound(c,a),
inference(rw,[status(thm)],[g0_2,t66]) ).
cnf(g0_4,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_3,t3310]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GRP193-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.02/0.30 % Computer : n012.cluster.edu
% 0.02/0.30 % Model : x86_64 x86_64
% 0.02/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.30 % Memory : 8046.5625MB
% 0.02/0.30 % OS : Linux 6.8.0-71-generic
% 0.02/0.30 % CPULimit : 300
% 0.02/0.30 % WCLimit : 300
% 0.02/0.30 % DateTime : Wed Sep 23 14:06:18 UTC 2026
% 0.02/0.30 % CPUTime :
% 0.02/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.51/1.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.51/1.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------