%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 14.65s 12.33s
% Output : CNFRefutation 14.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of clauses : 60 ( 60 unt; 0 nHn; 27 RR)
% Number of literals : 60 ( 59 equ; 8 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 5 ( 2 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 : 56 ( 2 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t17,axiom,
sFlat1 = inverse(b),
introduced(definition) ).
cnf(t76,plain,
inverse(b) = sFlat1,
inference(orient,[status(thm)],[t17]) ).
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(t601,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(step,[status(thm)],[t48,t19]) ).
cnf(t150,plain,
multiply(inverse(X1),multiply(X1,X2)) = X2,
inference(orient,[status(thm)],[t601]) ).
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(t28,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(t79,plain,
inverse(a) = sFlat0,
inference(orient,[status(thm)],[t16]) ).
cnf(t80,plain,
identity = multiply(sFlat0,a),
inference(cp,[status(thm)],[t39,t79]) ).
cnf(t91,plain,
multiply(sFlat0,a) = identity,
inference(orient,[status(thm)],[t80]) ).
cnf(t94,plain,
multiply(greatest_lower_bound(sFlat0,X1),a) = greatest_lower_bound(identity,multiply(X1,a)),
inference(cp,[status(thm)],[t28,t91]) ).
cnf(t563,plain,
greatest_lower_bound(identity,multiply(X1,a)) = multiply(greatest_lower_bound(sFlat0,X1),a),
inference(orient,[status(thm)],[t94]) ).
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(t25,plain,
greatest_lower_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t12]) ).
cnf(t77,plain,
identity = multiply(sFlat1,b),
inference(cp,[status(thm)],[t39,t76]) ).
cnf(t81,plain,
multiply(sFlat1,b) = identity,
inference(orient,[status(thm)],[t77]) ).
cnf(t88,plain,
multiply(sFlat1,greatest_lower_bound(b,X1)) = greatest_lower_bound(identity,multiply(sFlat1,X1)),
inference(cp,[status(thm)],[t25,t81]) ).
cnf(t554,plain,
greatest_lower_bound(identity,multiply(sFlat1,X1)) = multiply(sFlat1,greatest_lower_bound(b,X1)),
inference(orient,[status(thm)],[t88]) ).
cnf(t564,plain,
multiply(greatest_lower_bound(sFlat0,sFlat1),a) = multiply(sFlat1,greatest_lower_bound(b,a)),
inference(cp,[status(thm)],[t563,t554]) ).
cnf(t1,axiom,
greatest_lower_bound(a,b) = b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t5,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t49,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t586,plain,
greatest_lower_bound(b,a) = b,
inference(step,[status(thm)],[t1,t49]) ).
cnf(t60,plain,
greatest_lower_bound(b,a) = b,
inference(orient,[status(thm)],[t586]) ).
cnf(t621,plain,
multiply(greatest_lower_bound(sFlat0,sFlat1),a) = multiply(sFlat1,b),
inference(step,[status(thm)],[t564,t60]) ).
cnf(t622,plain,
multiply(greatest_lower_bound(sFlat0,sFlat1),a) = identity,
inference(step,[status(thm)],[t621,t81]) ).
cnf(t566,plain,
multiply(greatest_lower_bound(sFlat0,sFlat1),a) = identity,
inference(orient,[status(thm)],[t622]) ).
cnf(t569,plain,
a = multiply(inverse(greatest_lower_bound(sFlat0,sFlat1)),identity),
inference(cp,[status(thm)],[t150,t566]) ).
cnf(t155,plain,
X1 = multiply(inverse(inverse(X1)),identity),
inference(cp,[status(thm)],[t150,t39]) ).
cnf(t264,plain,
multiply(inverse(inverse(X1)),identity) = X1,
inference(orient,[status(thm)],[t155]) ).
cnf(t158,plain,
multiply(X1,X2) = multiply(inverse(inverse(X1)),X2),
inference(cp,[status(thm)],[t150,t150]) ).
cnf(t327,plain,
multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t158]) ).
cnf(t606,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t264,t327]) ).
cnf(t336,plain,
multiply(X1,identity) = X1,
inference(rw,[status(thm)],[t606]) ).
cnf(t382,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t336]) ).
cnf(t623,plain,
a = inverse(greatest_lower_bound(sFlat0,sFlat1)),
inference(step,[status(thm)],[t569,t382]) ).
cnf(t581,plain,
inverse(greatest_lower_bound(sFlat0,sFlat1)) = a,
inference(orient,[status(thm)],[t623]) ).
cnf(t7,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t62,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t383,plain,
inverse(inverse(X1)) = multiply(X1,identity),
inference(cp,[status(thm)],[t382,t327]) ).
cnf(t608,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t383,t382]) ).
cnf(t395,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t608]) ).
cnf(t8,axiom,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(t23,plain,
least_upper_bound(X1,greatest_lower_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(goal_0,negated_conjecture,
least_upper_bound(inverse(a),inverse(b)) != inverse(b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
sFlat1 != inverse(b),
inference(rw,[status(thm)],[goal_0,t76]) ).
cnf(g0_1,plain,
sFlat1 != least_upper_bound(inverse(inverse(greatest_lower_bound(sFlat0,sFlat1))),inverse(b)),
inference(rw,[status(thm)],[g0_0,t581]) ).
cnf(g0_2,plain,
sFlat1 != least_upper_bound(inverse(inverse(greatest_lower_bound(sFlat1,sFlat0))),inverse(b)),
inference(rw,[status(thm)],[g0_1,t49]) ).
cnf(g0_3,plain,
sFlat1 != least_upper_bound(inverse(b),inverse(inverse(greatest_lower_bound(sFlat1,sFlat0)))),
inference(rw,[status(thm)],[g0_2,t62]) ).
cnf(g0_4,plain,
sFlat1 != least_upper_bound(inverse(b),greatest_lower_bound(sFlat1,sFlat0)),
inference(rw,[status(thm)],[g0_3,t395]) ).
cnf(g0_5,plain,
sFlat1 != least_upper_bound(sFlat1,greatest_lower_bound(sFlat1,sFlat0)),
inference(rw,[status(thm)],[g0_4,t76]) ).
cnf(g0_6,plain,
sFlat1 != sFlat1,
inference(rw,[status(thm)],[g0_5,t23]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP191-2 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/10.40 % Computer : n002.cluster.edu
% 0.11/10.40 % Model : x86_64 x86_64
% 0.11/10.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.40 % Memory : 8046.5625MB
% 0.11/10.40 % OS : Linux 6.8.0-71-generic
% 0.11/10.40 % CPULimit : 300
% 0.16/10.40 % WCLimit : 300
% 0.16/10.40 % DateTime : Wed Sep 23 14:08:31 UTC 2026
% 0.16/10.40 % CPUTime :
% 0.16/10.40 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.65/12.33 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.65/12.33 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------