%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP170-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 19.62s 3.03s
% Output : CNFRefutation 19.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 13
% Syntax : Number of clauses : 68 ( 68 unt; 0 nHn; 42 RR)
% Number of literals : 68 ( 67 equ; 5 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 : 46 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t17,axiom,
sF0 = multiply(a,c),
introduced(definition) ).
cnf(t25,plain,
multiply(a,c) = sF0,
inference(orient,[status(thm)],[t17]) ).
cnf(t18,axiom,
sF1 = multiply(b,d),
introduced(definition) ).
cnf(t26,plain,
multiply(b,d) = sF1,
inference(orient,[status(thm)],[t18]) ).
cnf(t19,axiom,
sF2 = greatest_lower_bound(multiply(a,c),multiply(b,d)),
introduced(definition) ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t32,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t14125,plain,
sF2 = greatest_lower_bound(multiply(b,d),multiply(a,c)),
inference(step,[status(thm)],[t19,t32]) ).
cnf(t14126,plain,
sF2 = greatest_lower_bound(sF1,multiply(a,c)),
inference(step,[status(thm)],[t14125,t26]) ).
cnf(t14127,plain,
sF2 = greatest_lower_bound(sF1,sF0),
inference(step,[status(thm)],[t14126,t25]) ).
cnf(t14128,plain,
sF2 = greatest_lower_bound(sF0,sF1),
inference(step,[status(thm)],[t14127,t32]) ).
cnf(t335,plain,
greatest_lower_bound(sF0,sF1) = sF2,
inference(orient,[status(thm)],[t14128]) ).
cnf(t9,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t39,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
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(t45,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(t338,plain,
greatest_lower_bound(sF0,greatest_lower_bound(sF1,X1)) = greatest_lower_bound(sF2,X1),
inference(cp,[status(thm)],[t45,t335]) ).
cnf(t714,plain,
greatest_lower_bound(sF0,greatest_lower_bound(sF1,X1)) = greatest_lower_bound(sF2,X1),
inference(orient,[status(thm)],[t338]) ).
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(t97,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t13]) ).
cnf(t100,plain,
multiply(b,greatest_lower_bound(d,X1)) = greatest_lower_bound(sF1,multiply(b,X1)),
inference(cp,[status(thm)],[t97,t26]) ).
cnf(t222,plain,
greatest_lower_bound(sF1,multiply(b,X1)) = multiply(b,greatest_lower_bound(d,X1)),
inference(orient,[status(thm)],[t100]) ).
cnf(t723,plain,
greatest_lower_bound(sF2,multiply(b,X1)) = greatest_lower_bound(sF0,multiply(b,greatest_lower_bound(d,X1))),
inference(cp,[status(thm)],[t714,t222]) ).
cnf(t13937,plain,
greatest_lower_bound(sF0,multiply(b,greatest_lower_bound(d,X1))) = greatest_lower_bound(sF2,multiply(b,X1)),
inference(orient,[status(thm)],[t723]) ).
cnf(t7,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t28,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t7]) ).
cnf(t3,axiom,
least_upper_bound(c,d) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t23,plain,
least_upper_bound(c,d) = d,
inference(orient,[status(thm)],[t3]) ).
cnf(t30,plain,
c = greatest_lower_bound(c,d),
inference(cp,[status(thm)],[t28,t23]) ).
cnf(t14108,plain,
c = greatest_lower_bound(d,c),
inference(step,[status(thm)],[t30,t32]) ).
cnf(t35,plain,
greatest_lower_bound(d,c) = c,
inference(orient,[status(thm)],[t14108]) ).
cnf(t13941,plain,
greatest_lower_bound(sF2,multiply(b,c)) = greatest_lower_bound(sF0,multiply(b,c)),
inference(cp,[status(thm)],[t13937,t35]) ).
cnf(t14,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(t137,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t14]) ).
cnf(t140,plain,
multiply(greatest_lower_bound(a,X1),c) = greatest_lower_bound(sF0,multiply(X1,c)),
inference(cp,[status(thm)],[t137,t25]) ).
cnf(t317,plain,
greatest_lower_bound(sF0,multiply(X1,c)) = multiply(greatest_lower_bound(a,X1),c),
inference(orient,[status(thm)],[t140]) ).
cnf(t14435,plain,
greatest_lower_bound(sF2,multiply(b,c)) = multiply(greatest_lower_bound(a,b),c),
inference(step,[status(thm)],[t13941,t317]) ).
cnf(t141,plain,
multiply(greatest_lower_bound(X1,a),c) = greatest_lower_bound(multiply(X1,c),sF0),
inference(cp,[status(thm)],[t137,t25]) ).
cnf(t14123,plain,
multiply(greatest_lower_bound(X1,a),c) = greatest_lower_bound(sF0,multiply(X1,c)),
inference(step,[status(thm)],[t141,t32]) ).
cnf(t14124,plain,
multiply(greatest_lower_bound(X1,a),c) = multiply(greatest_lower_bound(a,X1),c),
inference(step,[status(thm)],[t14123,t317]) ).
cnf(t324,plain,
multiply(greatest_lower_bound(X1,a),c) = multiply(greatest_lower_bound(a,X1),c),
inference(orient,[status(thm)],[t14124]) ).
cnf(t14436,plain,
greatest_lower_bound(sF2,multiply(b,c)) = multiply(greatest_lower_bound(b,a),c),
inference(step,[status(thm)],[t14435,t324]) ).
cnf(t2,axiom,
least_upper_bound(a,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t22,plain,
least_upper_bound(a,b) = b,
inference(orient,[status(thm)],[t2]) ).
cnf(t29,plain,
a = greatest_lower_bound(a,b),
inference(cp,[status(thm)],[t28,t22]) ).
cnf(t31,plain,
greatest_lower_bound(a,b) = a,
inference(orient,[status(thm)],[t29]) ).
cnf(t14107,plain,
greatest_lower_bound(b,a) = a,
inference(step,[status(thm)],[t31,t32]) ).
cnf(t33,plain,
greatest_lower_bound(b,a) = a,
inference(rw,[status(thm)],[t14107]) ).
cnf(t37,plain,
greatest_lower_bound(b,a) = a,
inference(orient,[status(thm)],[t33]) ).
cnf(t14437,plain,
greatest_lower_bound(sF2,multiply(b,c)) = multiply(a,c),
inference(step,[status(thm)],[t14436,t37]) ).
cnf(t14438,plain,
greatest_lower_bound(sF2,multiply(b,c)) = sF0,
inference(step,[status(thm)],[t14437,t25]) ).
cnf(t14042,plain,
greatest_lower_bound(sF2,multiply(b,c)) = sF0,
inference(orient,[status(thm)],[t14438]) ).
cnf(t14044,plain,
sF2 = least_upper_bound(sF2,sF0),
inference(cp,[status(thm)],[t39,t14042]) ).
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t69,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t14439,plain,
sF2 = least_upper_bound(sF0,sF2),
inference(step,[status(thm)],[t14044,t69]) ).
cnf(t337,plain,
sF0 = least_upper_bound(sF0,sF2),
inference(cp,[status(thm)],[t39,t335]) ).
cnf(t342,plain,
least_upper_bound(sF0,sF2) = sF0,
inference(orient,[status(thm)],[t337]) ).
cnf(t14440,plain,
sF2 = sF0,
inference(step,[status(thm)],[t14439,t342]) ).
cnf(t14073,plain,
sF2 = sF0,
inference(orient,[status(thm)],[t14440]) ).
cnf(t14441,plain,
greatest_lower_bound(sF0,sF1) = sF0,
inference(step,[status(thm)],[t335,t14073]) ).
cnf(t14074,plain,
greatest_lower_bound(sF0,sF1) = sF0,
inference(orient,[status(thm)],[t14441]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(multiply(a,c),multiply(b,d)) != multiply(a,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
greatest_lower_bound(sF0,multiply(b,d)) != multiply(a,c),
inference(rw,[status(thm)],[goal_0,t25]) ).
cnf(g0_1,plain,
greatest_lower_bound(sF0,sF1) != multiply(a,c),
inference(rw,[status(thm)],[g0_0,t26]) ).
cnf(g0_2,plain,
sF0 != multiply(a,c),
inference(rw,[status(thm)],[g0_1,t14074]) ).
cnf(g0_3,plain,
sF0 != sF0,
inference(rw,[status(thm)],[g0_2,t25]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP170-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n013.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 13:57:05 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 19.62/3.03 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.62/3.03 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------