%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP175-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : 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 01:25:32 PM UTC 2026
% Result : Unsatisfiable 6.65s 1.49s
% Output : CNFRefutation 6.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 15
% Syntax : Number of clauses : 77 ( 77 unt; 0 nHn; 51 RR)
% Number of literals : 77 ( 76 equ; 25 neg)
% Maximal clause size : 1 ( 1 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-2 aty)
% Number of variables : 52 ( 4 sgn)
% Comments :
%------------------------------------------------------------------------------
cnf(t2,axiom,
least_upper_bound(identity,b) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t87,plain,
least_upper_bound(identity,b) = b,
inference(orient,[status(thm)],[t2]) ).
cnf(t7,axiom,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t70,plain,
least_upper_bound(X1,X2) = least_upper_bound(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(t6,axiom,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t24,plain,
greatest_lower_bound(X1,least_upper_bound(X1,X2)) = X1,
inference(orient,[status(thm)],[t6]) ).
cnf(t89,plain,
identity = greatest_lower_bound(identity,b),
inference(cp,[status(thm)],[t24,t87]) ).
cnf(t109,plain,
greatest_lower_bound(identity,b) = identity,
inference(orient,[status(thm)],[t89]) ).
cnf(t73,plain,
X1 = greatest_lower_bound(X1,least_upper_bound(X2,X1)),
inference(cp,[status(thm)],[t24,t70]) ).
cnf(t131,plain,
greatest_lower_bound(X1,least_upper_bound(X2,X1)) = X1,
inference(orient,[status(thm)],[t73]) ).
cnf(t19,axiom,
sFlat3 = least_upper_bound(identity,multiply(inverse(a),multiply(b,a))),
introduced(definition) ).
cnf(t17,axiom,
sFlat1 = multiply(b,a),
introduced(definition) ).
cnf(t40,plain,
multiply(b,a) = sFlat1,
inference(orient,[status(thm)],[t17]) ).
cnf(t292,plain,
sFlat3 = least_upper_bound(identity,multiply(inverse(a),sFlat1)),
inference(step,[status(thm)],[t19,t40]) ).
cnf(t18,axiom,
sFlat2 = multiply(inverse(a),multiply(b,a)),
introduced(definition) ).
cnf(t291,plain,
sFlat2 = multiply(inverse(a),sFlat1),
inference(step,[status(thm)],[t18,t40]) ).
cnf(t60,plain,
multiply(inverse(a),sFlat1) = sFlat2,
inference(orient,[status(thm)],[t291]) ).
cnf(t293,plain,
sFlat3 = least_upper_bound(identity,sFlat2),
inference(step,[status(thm)],[t292,t60]) ).
cnf(t294,plain,
sFlat3 = least_upper_bound(sFlat2,identity),
inference(step,[status(thm)],[t293,t70]) ).
cnf(t84,plain,
least_upper_bound(sFlat2,identity) = sFlat3,
inference(orient,[status(thm)],[t294]) ).
cnf(t134,plain,
identity = greatest_lower_bound(identity,sFlat3),
inference(cp,[status(thm)],[t131,t84]) ).
cnf(t5,axiom,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t90,plain,
greatest_lower_bound(X1,X2) = greatest_lower_bound(X2,X1),
inference(orient,[status(thm)],[t5]) ).
cnf(t296,plain,
identity = greatest_lower_bound(sFlat3,identity),
inference(step,[status(thm)],[t134,t90]) ).
cnf(t137,plain,
greatest_lower_bound(sFlat3,identity) = identity,
inference(orient,[status(thm)],[t296]) ).
cnf(t9,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(t94,plain,
greatest_lower_bound(greatest_lower_bound(X1,X2),X3) = greatest_lower_bound(X1,greatest_lower_bound(X2,X3)),
inference(orient,[status(thm)],[t9]) ).
cnf(t16,axiom,
sFlat0 = inverse(a),
introduced(definition) ).
cnf(t104,plain,
inverse(a) = sFlat0,
inference(orient,[status(thm)],[t16]) ).
cnf(t10,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(t74,plain,
least_upper_bound(least_upper_bound(X1,X2),X3) = least_upper_bound(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t10]) ).
cnf(t85,plain,
least_upper_bound(sFlat2,least_upper_bound(identity,X1)) = least_upper_bound(sFlat3,X1),
inference(cp,[status(thm)],[t74,t84]) ).
cnf(t174,plain,
least_upper_bound(sFlat2,least_upper_bound(identity,X1)) = least_upper_bound(sFlat3,X1),
inference(orient,[status(thm)],[t85]) ).
cnf(t175,plain,
least_upper_bound(sFlat3,b) = least_upper_bound(sFlat2,b),
inference(cp,[status(thm)],[t174,t87]) ).
cnf(t183,plain,
least_upper_bound(sFlat3,b) = least_upper_bound(sFlat2,b),
inference(orient,[status(thm)],[t175]) ).
cnf(t186,plain,
sFlat3 = greatest_lower_bound(sFlat3,least_upper_bound(sFlat2,b)),
inference(cp,[status(thm)],[t24,t183]) ).
cnf(t199,plain,
greatest_lower_bound(sFlat3,least_upper_bound(sFlat2,b)) = sFlat3,
inference(orient,[status(thm)],[t186]) ).
cnf(t4,axiom,
multiply(inverse(X1),X1) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t50,plain,
multiply(inverse(X1),X1) = identity,
inference(orient,[status(thm)],[t4]) ).
cnf(t105,plain,
identity = multiply(sFlat0,a),
inference(cp,[status(thm)],[t50,t104]) ).
cnf(t111,plain,
multiply(sFlat0,a) = identity,
inference(orient,[status(thm)],[t105]) ).
cnf(t14,axiom,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t26,plain,
least_upper_bound(multiply(X1,X2),multiply(X1,X3)) = multiply(X1,least_upper_bound(X2,X3)),
inference(orient,[status(thm)],[t14]) ).
cnf(t15,axiom,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t29,plain,
least_upper_bound(multiply(X1,X2),multiply(X3,X2)) = multiply(least_upper_bound(X1,X3),X2),
inference(orient,[status(thm)],[t15]) ).
cnf(t3,axiom,
multiply(identity,X1) = X1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(t20,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t3]) ).
cnf(t30,plain,
multiply(least_upper_bound(identity,X1),X2) = least_upper_bound(X2,multiply(X1,X2)),
inference(cp,[status(thm)],[t29,t20]) ).
cnf(t271,plain,
least_upper_bound(X1,multiply(X2,X1)) = multiply(least_upper_bound(identity,X2),X1),
inference(orient,[status(thm)],[t30]) ).
cnf(t88,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(b,X1),
inference(cp,[status(thm)],[t74,t87]) ).
cnf(t206,plain,
least_upper_bound(identity,least_upper_bound(b,X1)) = least_upper_bound(b,X1),
inference(orient,[status(thm)],[t88]) ).
cnf(goal_0,negated_conjecture,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(b,a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
cnf(g0_0,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(least_upper_bound(identity,b),a)),
inference(rw,[status(thm)],[goal_0,t87]) ).
cnf(g0_1,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(least_upper_bound(b,identity),a)),
inference(rw,[status(thm)],[g0_0,t70]) ).
cnf(g0_2,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(least_upper_bound(b,greatest_lower_bound(identity,b)),a)),
inference(rw,[status(thm)],[g0_1,t109]) ).
cnf(g0_3,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(least_upper_bound(b,greatest_lower_bound(greatest_lower_bound(sFlat3,identity),b)),a)),
inference(rw,[status(thm)],[g0_2,t137]) ).
cnf(g0_4,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(least_upper_bound(b,greatest_lower_bound(greatest_lower_bound(identity,sFlat3),b)),a)),
inference(rw,[status(thm)],[g0_3,t90]) ).
cnf(g0_5,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(inverse(a),multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(sFlat3,b))),a)),
inference(rw,[status(thm)],[g0_4,t94]) ).
cnf(g0_6,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(sFlat3,b))),a)),
inference(rw,[status(thm)],[g0_5,t104]) ).
cnf(g0_7,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(sFlat3,least_upper_bound(sFlat2,b)),b))),a)),
inference(rw,[status(thm)],[g0_6,t199]) ).
cnf(g0_8,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(least_upper_bound(sFlat2,b),sFlat3),b))),a)),
inference(rw,[status(thm)],[g0_7,t90]) ).
cnf(g0_9,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(b,a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_8,t94]) ).
cnf(g0_10,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(least_upper_bound(identity,b),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_9,t87]) ).
cnf(g0_11,plain,
least_upper_bound(identity,multiply(inverse(a),multiply(least_upper_bound(b,identity),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_10,t70]) ).
cnf(g0_12,plain,
least_upper_bound(identity,multiply(sFlat0,multiply(least_upper_bound(b,identity),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_11,t104]) ).
cnf(g0_13,plain,
least_upper_bound(identity,multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,b)),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_12,t109]) ).
cnf(g0_14,plain,
least_upper_bound(multiply(sFlat0,a),multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,b)),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_13,t111]) ).
cnf(g0_15,plain,
multiply(sFlat0,least_upper_bound(a,multiply(least_upper_bound(b,greatest_lower_bound(identity,b)),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_14,t26]) ).
cnf(g0_16,plain,
multiply(sFlat0,least_upper_bound(a,multiply(least_upper_bound(b,greatest_lower_bound(greatest_lower_bound(sFlat3,identity),b)),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_15,t137]) ).
cnf(g0_17,plain,
multiply(sFlat0,least_upper_bound(a,multiply(least_upper_bound(b,greatest_lower_bound(greatest_lower_bound(identity,sFlat3),b)),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_16,t90]) ).
cnf(g0_18,plain,
multiply(sFlat0,least_upper_bound(a,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(sFlat3,b))),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_17,t94]) ).
cnf(g0_19,plain,
multiply(sFlat0,least_upper_bound(a,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(sFlat3,least_upper_bound(sFlat2,b)),b))),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_18,t199]) ).
cnf(g0_20,plain,
multiply(sFlat0,least_upper_bound(a,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(greatest_lower_bound(least_upper_bound(sFlat2,b),sFlat3),b))),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_19,t90]) ).
cnf(g0_21,plain,
multiply(sFlat0,least_upper_bound(a,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a))) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_20,t94]) ).
cnf(g0_22,plain,
multiply(sFlat0,multiply(least_upper_bound(identity,least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b))))),a)) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_21,t271]) ).
cnf(g0_23,plain,
multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)) != multiply(sFlat0,multiply(least_upper_bound(b,greatest_lower_bound(identity,greatest_lower_bound(least_upper_bound(sFlat2,b),greatest_lower_bound(sFlat3,b)))),a)),
inference(rw,[status(thm)],[g0_22,t206]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP175-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Wed Sep 23 13:58:35 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.65/1.49 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.65/1.49 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------