%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP190-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 14.14s 2.41s
% Output : CNFRefutation 14.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 13
% Syntax : Number of clauses : 68 ( 68 unt; 0 nHn; 35 RR)
% Number of literals : 68 ( 67 equ; 5 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 6 con; 0-2 aty)
% Number of variables : 56 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t5,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t66,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t11,axiom,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t24,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t11]) ).
cnf(t4,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t39,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t4]) ).
cnf(t48,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t24,t39]) ).
cnf(t3,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t19,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t928,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t48,t19]) ).
cnf(t405,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t928]) ).
cnf(t12,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)],[t12]) ).
cnf(t17,axiom,
sFlat1 = inverse(b),
introduced(definition) ).
cnf(t86,plain,
inverse(b) = sFlat1,
inference(orient,[status(thm)],[t17]) ).
cnf(t87,plain,
identity = multiply(sFlat1,b),
inference(cp,[status(thm)],[t39,t86]) ).
cnf(t100,plain,
multiply(sFlat1,b) = identity,
inference(orient,[status(thm)],[t87]) ).
cnf(t105,plain,
multiply(sFlat1,greatest_lower_bound(b,X1)) = greatest_lower_bound(identity,multiply(sFlat1,X1)),
inference(cp,[status(thm)],[t27,t100]) ).
cnf(t871,plain,
greatest_lower_bound(identity,multiply(sFlat1,X1)) = multiply(sFlat1,greatest_lower_bound(b,X1)),
inference(orient,[status(thm)],[t105]) ).
cnf(t13,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(t34,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(greatest_lower_bound(X1,X3),X2),
inference(orient,[status(thm)],[t13]) ).
cnf(t16,axiom,
sFlat0 = inverse(a),
introduced(definition) ).
cnf(t83,plain,
inverse(a) = sFlat0,
inference(orient,[status(thm)],[t16]) ).
cnf(t84,plain,
identity = multiply(sFlat0,a),
inference(cp,[status(thm)],[t39,t83]) ).
cnf(t90,plain,
multiply(sFlat0,a) = identity,
inference(orient,[status(thm)],[t84]) ).
cnf(t91,plain,
multiply(greatest_lower_bound(sFlat0,X1),a) = greatest_lower_bound(identity,multiply(X1,a)),
inference(cp,[status(thm)],[t34,t90]) ).
cnf(t723,plain,
greatest_lower_bound(identity,multiply(X1,a)) = multiply(greatest_lower_bound(sFlat0,X1),a),
inference(orient,[status(thm)],[t91]) ).
cnf(t872,plain,
multiply(sFlat1,greatest_lower_bound(b,a)) = multiply(greatest_lower_bound(sFlat0,sFlat1),a),
inference(cp,[status(thm)],[t871,t723]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t2,axiom,
least_upper_bound(a,b) = a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t7,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t49,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t900,plain,
least_upper_bound(b,a) = a,
inference(step,[status(thm)],[t2,t49]) ).
cnf(t63,plain,
least_upper_bound(b,a) = a,
inference(orient,[status(thm)],[t900]) ).
cnf(t65,plain,
b = greatest_lower_bound(b,a),
inference(cp,[status(thm)],[t23,t63]) ).
cnf(t88,plain,
greatest_lower_bound(b,a) = b,
inference(orient,[status(thm)],[t65]) ).
cnf(t947,plain,
multiply(sFlat1,b) = multiply(greatest_lower_bound(sFlat0,sFlat1),a),
inference(step,[status(thm)],[t872,t88]) ).
cnf(t948,plain,
identity = multiply(greatest_lower_bound(sFlat0,sFlat1),a),
inference(step,[status(thm)],[t947,t100]) ).
cnf(t18,axiom,
sFlat2 = greatest_lower_bound(inverse(a),inverse(b)),
introduced(definition) ).
cnf(t901,plain,
sFlat2 = greatest_lower_bound(inverse(b),inverse(a)),
inference(step,[status(thm)],[t18,t66]) ).
cnf(t80,plain,
greatest_lower_bound(inverse(b),inverse(a)) = sFlat2,
inference(orient,[status(thm)],[t901]) ).
cnf(t902,plain,
greatest_lower_bound(inverse(b),sFlat0) = sFlat2,
inference(step,[status(thm)],[t80,t83]) ).
cnf(t85,plain,
greatest_lower_bound(inverse(b),sFlat0) = sFlat2,
inference(rw,[status(thm)],[t902]) ).
cnf(t903,plain,
greatest_lower_bound(sFlat0,inverse(b)) = sFlat2,
inference(step,[status(thm)],[t85,t66]) ).
cnf(t904,plain,
greatest_lower_bound(sFlat0,sFlat1) = sFlat2,
inference(step,[status(thm)],[t903,t86]) ).
cnf(t110,plain,
greatest_lower_bound(sFlat0,sFlat1) = sFlat2,
inference(orient,[status(thm)],[t904]) ).
cnf(t949,plain,
identity = multiply(sFlat2,a),
inference(step,[status(thm)],[t948,t110]) ).
cnf(t880,plain,
multiply(sFlat2,a) = identity,
inference(orient,[status(thm)],[t949]) ).
cnf(t882,plain,
a = multiply(inverse(sFlat2),identity),
inference(cp,[status(thm)],[t405,t880]) ).
cnf(t412,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t405,t39]) ).
cnf(t542,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t412]) ).
cnf(t415,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t405,t405]) ).
cnf(t583,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t415]) ).
cnf(t933,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t542,t583]) ).
cnf(t591,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t933]) ).
cnf(t592,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t591]) ).
cnf(t950,plain,
a = inverse(sFlat2),
inference(step,[status(thm)],[t882,t592]) ).
cnf(t895,plain,
inverse(sFlat2) = a,
inference(orient,[status(thm)],[t950]) ).
cnf(t593,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t592,t583]) ).
cnf(t936,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t593,t592]) ).
cnf(t602,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t936]) ).
cnf(goal_0,negated_conjecture,
greatest_lower_bound(inverse(a),inverse(b)) != inverse(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
greatest_lower_bound(inverse(b),inverse(a)) != inverse(a),
inference(rw,[status(thm)],[goal_0,t66]) ).
cnf(g0_1,plain,
sFlat2 != inverse(a),
inference(rw,[status(thm)],[g0_0]) ).
cnf(g0_2,plain,
sFlat2 != inverse(inverse(sFlat2)),
inference(rw,[status(thm)],[g0_1,t895]) ).
cnf(g0_3,plain,
sFlat2 != sFlat2,
inference(rw,[status(thm)],[g0_2,t602]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP190-2 : 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 : n019.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 14:05:34 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.14/2.41 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.14/2.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------