%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP166-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 01:25:29 PM UTC 2026
% Result : Unsatisfiable 4.63s 1.13s
% Output : CNFRefutation 4.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 12
% Syntax : Number of clauses : 55 ( 55 unt; 0 nHn; 27 RR)
% Number of literals : 55 ( 54 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 : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 49 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t17,axiom,
sFlat0 = multiply(a,b),
introduced(definition) ).
cnf(t39,plain,
multiply(a,b) = sFlat0,
inference(orient,[status(thm)],[t17]) ).
cnf(t8,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t59,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t8]) ).
cnf(t18,axiom,
sFlat1 = least_upper_bound(a,multiply(a,b)),
introduced(definition) ).
cnf(t1087,plain,
sFlat1 = least_upper_bound(a,sFlat0),
inference(step,[status(thm)],[t18,t39]) ).
cnf(t1088,plain,
sFlat1 = least_upper_bound(sFlat0,a),
inference(step,[status(thm)],[t1087,t59]) ).
cnf(t73,plain,
least_upper_bound(sFlat0,a) = sFlat1,
inference(orient,[status(thm)],[t1088]) ).
cnf(t9,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t21,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t9]) ).
cnf(t13,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)],[t13]) ).
cnf(t44,plain,
multiply(a,greatest_lower_bound(b,X1)) = greatest_lower_bound(sFlat0,multiply(a,X1)),
inference(cp,[status(thm)],[t27,t39]) ).
cnf(t1052,plain,
greatest_lower_bound(sFlat0,multiply(a,X1)) = multiply(a,greatest_lower_bound(b,X1)),
inference(orient,[status(thm)],[t44]) ).
cnf(t12,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)],[t12]) ).
cnf(t5,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t49,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t5]) ).
cnf(t58,plain,
multiply(inverse(X1),multiply(X1,X2)) = multiply(identity,X2),
inference(cp,[status(thm)],[t24,t49]) ).
cnf(t4,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t19,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t4]) ).
cnf(t1143,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t58,t19]) ).
cnf(t831,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t1143]) ).
cnf(t832,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t831,t49]) ).
cnf(t869,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t832]) ).
cnf(t837,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t831,t831]) ).
cnf(t905,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t837]) ).
cnf(t1144,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t869,t905]) ).
cnf(t914,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t1144]) ).
cnf(t915,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t914]) ).
cnf(t1056,plain,
multiply(a,greatest_lower_bound(b,identity)) = greatest_lower_bound(sFlat0,a),
inference(cp,[status(thm)],[t1052,t915]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t82,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t6]) ).
cnf(t1152,plain,
multiply(a,greatest_lower_bound(identity,b)) = greatest_lower_bound(sFlat0,a),
inference(step,[status(thm)],[t1056,t82]) ).
cnf(t7,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)],[t7]) ).
cnf(t3,axiom,
least_upper_bound(b,identity) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t1090,plain,
least_upper_bound(identity,b) = b,
inference(step,[status(thm)],[t3,t59]) ).
cnf(t79,plain,
least_upper_bound(identity,b) = b,
inference(orient,[status(thm)],[t1090]) ).
cnf(t81,plain,
identity = greatest_lower_bound(identity,b),
inference(cp,[status(thm)],[t23,t79]) ).
cnf(t100,plain,
greatest_lower_bound(identity,b) = identity,
inference(orient,[status(thm)],[t81]) ).
cnf(t1153,plain,
multiply(a,identity) = greatest_lower_bound(sFlat0,a),
inference(step,[status(thm)],[t1152,t100]) ).
cnf(t1154,plain,
a = greatest_lower_bound(sFlat0,a),
inference(step,[status(thm)],[t1153,t915]) ).
cnf(t1064,plain,
greatest_lower_bound(sFlat0,a) = a,
inference(orient,[status(thm)],[t1154]) ).
cnf(t1065,plain,
sFlat0 = least_upper_bound(sFlat0,a),
inference(cp,[status(thm)],[t21,t1064]) ).
cnf(t1155,plain,
sFlat0 = sFlat1,
inference(step,[status(thm)],[t1065,t73]) ).
cnf(t1070,plain,
sFlat1 = sFlat0,
inference(orient,[status(thm)],[t1155]) ).
cnf(t1156,plain,
least_upper_bound(sFlat0,a) = sFlat0,
inference(step,[status(thm)],[t73,t1070]) ).
cnf(t1071,plain,
least_upper_bound(sFlat0,a) = sFlat0,
inference(orient,[status(thm)],[t1156]) ).
cnf(goal_0,negated_conjecture,
least_upper_bound(a,multiply(a,b)) != multiply(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
least_upper_bound(a,sFlat0) != multiply(a,b),
inference(rw,[status(thm)],[goal_0,t39]) ).
cnf(g0_1,plain,
least_upper_bound(sFlat0,a) != multiply(a,b),
inference(rw,[status(thm)],[g0_0,t59]) ).
cnf(g0_2,plain,
sFlat0 != multiply(a,b),
inference(rw,[status(thm)],[g0_1,t1071]) ).
cnf(g0_3,plain,
sFlat0 != sFlat0,
inference(rw,[status(thm)],[g0_2,t39]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP166-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.37 % Computer : n015.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Wed Sep 23 13:58:24 UTC 2026
% 0.12/0.38 % CPUTime :
% 0.12/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.63/1.13 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.63/1.13 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------