%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : GRP179-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 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 : Thu Sep 24 12:32:59 PM UTC 2026
% Result : Unsatisfiable 8.22s 1.47s
% Output : CNFRefutation 8.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 20
% Syntax : Number of formulae : 135 ( 135 unt; 5 def)
% Number of atoms : 135 ( 134 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 3 ( 3 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-2 aty)
% Number of variables : 131 ( 131 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : multiply(identity,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] : multiply(inverse(X),X) = identity,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y,Z] : multiply(multiply(X,Y),Z) = multiply(X,multiply(Y,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] : greatest_lower_bound(X,Y) = greatest_lower_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,Y] : least_upper_bound(X,Y) = least_upper_bound(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X,Y,Z] : greatest_lower_bound(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(greatest_lower_bound(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X,Y,Z] : least_upper_bound(X,least_upper_bound(Y,Z)) = least_upper_bound(least_upper_bound(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [X] : greatest_lower_bound(X,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [X,Y] : least_upper_bound(X,greatest_lower_bound(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [X,Y] : greatest_lower_bound(X,least_upper_bound(X,Y)) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [X,Y,Z] : multiply(X,least_upper_bound(Y,Z)) = least_upper_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X,Y,Z] : multiply(X,greatest_lower_bound(Y,Z)) = greatest_lower_bound(multiply(X,Y),multiply(X,Z)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Y,Z,X] : multiply(least_upper_bound(Y,Z),X) = least_upper_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Y,Z,X] : multiply(greatest_lower_bound(Y,Z),X) = greatest_lower_bound(multiply(Y,X),multiply(Z,X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
inverse(least_upper_bound(a,b)) != greatest_lower_bound(inverse(a),inverse(b)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,plain,
! [X0] : multiply(identity,X0) = X0,
inference(cnf_transformation,[status(thm)],[f1]) ).
fof(f18,plain,
! [X0] : multiply(inverse(X0),X0) = identity,
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f19,plain,
! [X0,X1,X2] : multiply(multiply(X0,X1),X2) = multiply(X0,multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f20,plain,
! [X0,X1] : greatest_lower_bound(X0,X1) = greatest_lower_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0,X1] : least_upper_bound(X0,X1) = least_upper_bound(X1,X0),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f22,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(greatest_lower_bound(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f23,plain,
! [X0,X1,X2] : least_upper_bound(X0,least_upper_bound(X1,X2)) = least_upper_bound(least_upper_bound(X0,X1),X2),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f25,plain,
! [X0] : greatest_lower_bound(X0,X0) = X0,
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f26,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f27,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X0,X1)) = X0,
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f28,plain,
! [X0,X1,X2] : multiply(X0,least_upper_bound(X1,X2)) = least_upper_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f29,plain,
! [X0,X1,X2] : multiply(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(multiply(X0,X1),multiply(X0,X2)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f30,plain,
! [X0,X1,X2] : multiply(least_upper_bound(X0,X1),X2) = least_upper_bound(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f31,plain,
! [X0,X1,X2] : multiply(greatest_lower_bound(X0,X1),X2) = greatest_lower_bound(multiply(X0,X2),multiply(X1,X2)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f32,plain,
inverse(least_upper_bound(a,b)) != greatest_lower_bound(inverse(a),inverse(b)),
inference(cnf_transformation,[status(thm)],[f16]) ).
fof(f33,definition,
sF1_fnc = least_upper_bound(a,b),
introduced(definition,[new_symbols(definition,[sF1_fnc])],[function_definition]) ).
fof(f34,definition,
sF0_fnc = inverse(sF1_fnc),
introduced(definition,[new_symbols(definition,[sF0_fnc])],[function_definition]) ).
fof(f35,definition,
sF3_fnc = inverse(a),
introduced(definition,[new_symbols(definition,[sF3_fnc])],[function_definition]) ).
fof(f36,definition,
sF4_fnc = inverse(b),
introduced(definition,[new_symbols(definition,[sF4_fnc])],[function_definition]) ).
fof(f37,definition,
sF2_fnc = greatest_lower_bound(sF3_fnc,sF4_fnc),
introduced(definition,[new_symbols(definition,[sF2_fnc])],[function_definition]) ).
fof(f38,plain,
sF0_fnc != sF2_fnc,
inference(definition_folding,[],[f32,f37,f36,f35,f34,f33]) ).
fof(f47,plain,
least_upper_bound(sF3_fnc,sF2_fnc) = sF3_fnc,
inference(paramodulation,[status(thm)],[f37,f26]) ).
fof(f49,plain,
! [X0,X1] : least_upper_bound(X0,greatest_lower_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f20,f26]) ).
fof(f51,plain,
greatest_lower_bound(a,sF1_fnc) = a,
inference(paramodulation,[status(thm)],[f33,f27]) ).
fof(f53,plain,
! [X0,X1] : greatest_lower_bound(X0,least_upper_bound(X1,X0)) = X0,
inference(paramodulation,[status(thm)],[f21,f27]) ).
fof(f63,plain,
least_upper_bound(sF4_fnc,sF2_fnc) = sF4_fnc,
inference(paramodulation,[status(thm)],[f37,f49]) ).
fof(f64,plain,
! [X0,X1] : least_upper_bound(least_upper_bound(X0,X1),X0) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f27,f49]) ).
fof(f70,plain,
least_upper_bound(sF1_fnc,a) = sF1_fnc,
inference(paramodulation,[status(thm)],[f51,f49]) ).
fof(f74,plain,
greatest_lower_bound(b,sF1_fnc) = b,
inference(paramodulation,[status(thm)],[f33,f53]) ).
fof(f88,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,greatest_lower_bound(X1,X2)) = greatest_lower_bound(X2,greatest_lower_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f20,f22]) ).
fof(f117,plain,
! [X0] : least_upper_bound(a,least_upper_bound(b,X0)) = least_upper_bound(sF1_fnc,X0),
inference(paramodulation,[status(thm)],[f33,f23]) ).
fof(f134,plain,
multiply(sF4_fnc,b) = identity,
inference(paramodulation,[status(thm)],[f36,f18]) ).
fof(f135,plain,
multiply(sF3_fnc,a) = identity,
inference(paramodulation,[status(thm)],[f35,f18]) ).
fof(f136,plain,
multiply(sF0_fnc,sF1_fnc) = identity,
inference(paramodulation,[status(thm)],[f34,f18]) ).
fof(f165,plain,
! [X0] : multiply(identity,X0) = multiply(sF3_fnc,multiply(a,X0)),
inference(paramodulation,[status(thm)],[f135,f19]) ).
fof(f167,plain,
! [X0,X1] : multiply(identity,X0) = multiply(inverse(X1),multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f19]) ).
fof(f172,plain,
! [X0] : X0 = multiply(sF3_fnc,multiply(a,X0)),
inference(forward_demodulation,[status(thm)],[f17,f165]) ).
fof(f174,plain,
! [X0,X1] : X0 = multiply(inverse(X1),multiply(X1,X0)),
inference(forward_demodulation,[status(thm)],[f17,f167]) ).
fof(f179,plain,
! [X0] : multiply(sF0_fnc,least_upper_bound(sF1_fnc,X0)) = least_upper_bound(identity,multiply(sF0_fnc,X0)),
inference(paramodulation,[status(thm)],[f136,f28]) ).
fof(f182,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X0,X1)) = least_upper_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f188,plain,
! [X0,X1] : multiply(inverse(X0),least_upper_bound(X1,X0)) = least_upper_bound(multiply(inverse(X0),X1),identity),
inference(paramodulation,[status(thm)],[f18,f28]) ).
fof(f215,plain,
! [X0,X1] : multiply(inverse(X0),greatest_lower_bound(X0,X1)) = greatest_lower_bound(identity,multiply(inverse(X0),X1)),
inference(paramodulation,[status(thm)],[f18,f29]) ).
fof(f287,plain,
! [X0,X1] : least_upper_bound(X0,least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(forward_demodulation,[status(thm)],[f23,f64]) ).
fof(f308,plain,
! [X0,X1] : greatest_lower_bound(least_upper_bound(X0,X1),least_upper_bound(X1,X0)) = least_upper_bound(X0,X1),
inference(paramodulation,[status(thm)],[f287,f53]) ).
fof(f385,plain,
! [X0,X1] : multiply(least_upper_bound(identity,X0),X1) = least_upper_bound(X1,multiply(X0,X1)),
inference(paramodulation,[status(thm)],[f17,f30]) ).
fof(f417,plain,
! [X0] : multiply(greatest_lower_bound(sF0_fnc,X0),sF1_fnc) = greatest_lower_bound(identity,multiply(X0,sF1_fnc)),
inference(paramodulation,[status(thm)],[f136,f31]) ).
fof(f422,plain,
! [X0,X1] : multiply(greatest_lower_bound(inverse(X0),X1),X0) = greatest_lower_bound(identity,multiply(X1,X0)),
inference(paramodulation,[status(thm)],[f18,f31]) ).
fof(f457,plain,
! [X0] : multiply(a,X0) = multiply(inverse(sF3_fnc),X0),
inference(paramodulation,[status(thm)],[f172,f174]) ).
fof(f458,plain,
a = multiply(inverse(sF3_fnc),identity),
inference(paramodulation,[status(thm)],[f135,f174]) ).
fof(f460,plain,
b = multiply(inverse(sF4_fnc),identity),
inference(paramodulation,[status(thm)],[f134,f174]) ).
fof(f461,plain,
! [X0,X1] : multiply(X0,X1) = multiply(inverse(inverse(X0)),X1),
inference(paramodulation,[status(thm)],[f174,f174]) ).
fof(f462,plain,
! [X0] : X0 = multiply(inverse(inverse(X0)),identity),
inference(paramodulation,[status(thm)],[f18,f174]) ).
fof(f503,plain,
identity = multiply(inverse(inverse(sF3_fnc)),a),
inference(paramodulation,[status(thm)],[f458,f174]) ).
fof(f514,plain,
identity = multiply(inverse(inverse(sF4_fnc)),b),
inference(paramodulation,[status(thm)],[f460,f174]) ).
fof(f954,plain,
! [X0] : greatest_lower_bound(X0,sF2_fnc) = greatest_lower_bound(sF4_fnc,greatest_lower_bound(X0,sF3_fnc)),
inference(paramodulation,[status(thm)],[f37,f88]) ).
fof(f961,plain,
! [X0,X1,X2] : greatest_lower_bound(X0,X1) = greatest_lower_bound(least_upper_bound(X2,X1),greatest_lower_bound(X0,X1)),
inference(paramodulation,[status(thm)],[f53,f88]) ).
fof(f2266,plain,
multiply(a,sF3_fnc) = identity,
inference(paramodulation,[status(thm)],[f18,f457]) ).
fof(f2625,plain,
a = multiply(inverse(inverse(inverse(sF3_fnc))),identity),
inference(paramodulation,[status(thm)],[f503,f174]) ).
fof(f2635,plain,
a = inverse(sF3_fnc),
inference(forward_demodulation,[status(thm)],[f462,f2625]) ).
fof(f2643,plain,
b = multiply(inverse(inverse(inverse(sF4_fnc))),identity),
inference(paramodulation,[status(thm)],[f514,f174]) ).
fof(f2653,plain,
b = inverse(sF4_fnc),
inference(forward_demodulation,[status(thm)],[f462,f2643]) ).
fof(f3024,plain,
! [X0] : X0 = multiply(X0,identity),
inference(backward_demodulation,[status(thm)],[f461,f462]) ).
fof(f3026,plain,
! [X0] : multiply(X0,inverse(X0)) = identity,
inference(paramodulation,[status(thm)],[f18,f461]) ).
fof(f3069,plain,
! [X0] : inverse(inverse(X0)) = multiply(X0,identity),
inference(paramodulation,[status(thm)],[f461,f3024]) ).
fof(f3092,plain,
! [X0] : inverse(inverse(X0)) = X0,
inference(forward_demodulation,[status(thm)],[f3024,f3069]) ).
fof(f4206,plain,
multiply(sF0_fnc,sF1_fnc) = least_upper_bound(identity,multiply(sF0_fnc,a)),
inference(paramodulation,[status(thm)],[f70,f179]) ).
fof(f4240,plain,
identity = least_upper_bound(identity,multiply(sF0_fnc,a)),
inference(forward_demodulation,[status(thm)],[f136,f4206]) ).
fof(f4814,plain,
multiply(inverse(sF4_fnc),sF4_fnc) = least_upper_bound(identity,multiply(inverse(sF4_fnc),sF2_fnc)),
inference(paramodulation,[status(thm)],[f63,f182]) ).
fof(f4823,plain,
multiply(inverse(sF3_fnc),sF3_fnc) = least_upper_bound(identity,multiply(inverse(sF3_fnc),sF2_fnc)),
inference(paramodulation,[status(thm)],[f47,f182]) ).
fof(f4898,plain,
identity = least_upper_bound(identity,multiply(inverse(sF4_fnc),sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f18,f4814]) ).
fof(f4899,plain,
identity = least_upper_bound(identity,multiply(b,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f2653,f4898]) ).
fof(f4907,plain,
identity = least_upper_bound(identity,multiply(inverse(sF3_fnc),sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f18,f4823]) ).
fof(f4908,plain,
identity = least_upper_bound(identity,multiply(a,sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f2635,f4907]) ).
fof(f8021,plain,
multiply(inverse(b),b) = greatest_lower_bound(identity,multiply(inverse(b),sF1_fnc)),
inference(paramodulation,[status(thm)],[f74,f215]) ).
fof(f8097,plain,
identity = greatest_lower_bound(identity,multiply(inverse(b),sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f18,f8021]) ).
fof(f8098,plain,
identity = greatest_lower_bound(identity,multiply(sF4_fnc,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f36,f8097]) ).
fof(f10508,plain,
! [X0,X1] : greatest_lower_bound(X0,X0) = greatest_lower_bound(least_upper_bound(X1,X0),X0),
inference(paramodulation,[status(thm)],[f25,f961]) ).
fof(f10639,plain,
! [X0,X1] : X0 = greatest_lower_bound(least_upper_bound(X1,X0),X0),
inference(forward_demodulation,[status(thm)],[f25,f10508]) ).
fof(f11010,plain,
! [X0] : multiply(identity,X0) = least_upper_bound(X0,multiply(multiply(a,sF2_fnc),X0)),
inference(paramodulation,[status(thm)],[f4908,f385]) ).
fof(f11011,plain,
! [X0] : multiply(identity,X0) = least_upper_bound(X0,multiply(multiply(b,sF2_fnc),X0)),
inference(paramodulation,[status(thm)],[f4899,f385]) ).
fof(f11012,plain,
! [X0] : multiply(identity,X0) = least_upper_bound(X0,multiply(multiply(sF0_fnc,a),X0)),
inference(paramodulation,[status(thm)],[f4240,f385]) ).
fof(f11027,plain,
! [X0,X1] : multiply(identity,X0) = least_upper_bound(X0,multiply(greatest_lower_bound(X1,identity),X0)),
inference(paramodulation,[status(thm)],[f49,f385]) ).
fof(f11115,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(multiply(a,sF2_fnc),X0)),
inference(forward_demodulation,[status(thm)],[f17,f11010]) ).
fof(f11116,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(a,multiply(sF2_fnc,X0))),
inference(forward_demodulation,[status(thm)],[f19,f11115]) ).
fof(f11117,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(multiply(b,sF2_fnc),X0)),
inference(forward_demodulation,[status(thm)],[f17,f11011]) ).
fof(f11118,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(b,multiply(sF2_fnc,X0))),
inference(forward_demodulation,[status(thm)],[f19,f11117]) ).
fof(f11119,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(multiply(sF0_fnc,a),X0)),
inference(forward_demodulation,[status(thm)],[f17,f11012]) ).
fof(f11120,plain,
! [X0] : X0 = least_upper_bound(X0,multiply(sF0_fnc,multiply(a,X0))),
inference(forward_demodulation,[status(thm)],[f19,f11119]) ).
fof(f11126,plain,
! [X0,X1] : X0 = least_upper_bound(X0,multiply(greatest_lower_bound(X1,identity),X0)),
inference(forward_demodulation,[status(thm)],[f17,f11027]) ).
fof(f12724,plain,
! [X0,X1] : greatest_lower_bound(least_upper_bound(multiply(greatest_lower_bound(X0,identity),X1),X1),X1) = least_upper_bound(multiply(greatest_lower_bound(X0,identity),X1),X1),
inference(paramodulation,[status(thm)],[f11126,f308]) ).
fof(f12780,plain,
! [X0,X1] : X0 = least_upper_bound(multiply(greatest_lower_bound(X1,identity),X0),X0),
inference(forward_demodulation,[status(thm)],[f10639,f12724]) ).
fof(f14034,plain,
! [X0] : X0 = least_upper_bound(greatest_lower_bound(identity,multiply(identity,X0)),X0),
inference(paramodulation,[status(thm)],[f422,f12780]) ).
fof(f14094,plain,
! [X0] : X0 = least_upper_bound(greatest_lower_bound(identity,X0),X0),
inference(forward_demodulation,[status(thm)],[f17,f14034]) ).
fof(f14523,plain,
inverse(sF2_fnc) = least_upper_bound(inverse(sF2_fnc),multiply(a,identity)),
inference(paramodulation,[status(thm)],[f3026,f11116]) ).
fof(f14587,plain,
inverse(sF2_fnc) = least_upper_bound(inverse(sF2_fnc),a),
inference(forward_demodulation,[status(thm)],[f3024,f14523]) ).
fof(f14623,plain,
inverse(sF2_fnc) = least_upper_bound(a,inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f21,f14587]) ).
fof(f16665,plain,
inverse(sF2_fnc) = least_upper_bound(inverse(sF2_fnc),multiply(b,identity)),
inference(paramodulation,[status(thm)],[f3026,f11118]) ).
fof(f16729,plain,
inverse(sF2_fnc) = least_upper_bound(inverse(sF2_fnc),b),
inference(forward_demodulation,[status(thm)],[f3024,f16665]) ).
fof(f16765,plain,
inverse(sF2_fnc) = least_upper_bound(b,inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f21,f16729]) ).
fof(f16943,plain,
least_upper_bound(a,inverse(sF2_fnc)) = least_upper_bound(sF1_fnc,inverse(sF2_fnc)),
inference(paramodulation,[status(thm)],[f16765,f117]) ).
fof(f16972,plain,
inverse(sF2_fnc) = least_upper_bound(sF1_fnc,inverse(sF2_fnc)),
inference(forward_demodulation,[status(thm)],[f14623,f16943]) ).
fof(f17486,plain,
multiply(inverse(inverse(sF2_fnc)),inverse(sF2_fnc)) = least_upper_bound(multiply(inverse(inverse(sF2_fnc)),sF1_fnc),identity),
inference(paramodulation,[status(thm)],[f16972,f188]) ).
fof(f17510,plain,
identity = least_upper_bound(multiply(inverse(inverse(sF2_fnc)),sF1_fnc),identity),
inference(forward_demodulation,[status(thm)],[f18,f17486]) ).
fof(f17511,plain,
identity = least_upper_bound(multiply(sF2_fnc,sF1_fnc),identity),
inference(forward_demodulation,[status(thm)],[f3092,f17510]) ).
fof(f17662,plain,
identity = least_upper_bound(identity,multiply(sF2_fnc,sF1_fnc)),
inference(paramodulation,[status(thm)],[f21,f17511]) ).
fof(f18181,plain,
sF3_fnc = least_upper_bound(sF3_fnc,multiply(sF0_fnc,identity)),
inference(paramodulation,[status(thm)],[f2266,f11120]) ).
fof(f18250,plain,
sF3_fnc = least_upper_bound(sF3_fnc,sF0_fnc),
inference(forward_demodulation,[status(thm)],[f3024,f18181]) ).
fof(f18514,plain,
greatest_lower_bound(sF0_fnc,sF3_fnc) = sF0_fnc,
inference(paramodulation,[status(thm)],[f18250,f53]) ).
fof(f18610,plain,
greatest_lower_bound(sF0_fnc,sF2_fnc) = greatest_lower_bound(sF4_fnc,sF0_fnc),
inference(paramodulation,[status(thm)],[f18514,f954]) ).
fof(f20157,plain,
greatest_lower_bound(sF0_fnc,sF2_fnc) = greatest_lower_bound(sF0_fnc,sF4_fnc),
inference(paramodulation,[status(thm)],[f20,f18610]) ).
fof(f20511,plain,
multiply(greatest_lower_bound(sF0_fnc,sF2_fnc),sF1_fnc) = greatest_lower_bound(identity,multiply(sF4_fnc,sF1_fnc)),
inference(paramodulation,[status(thm)],[f20157,f417]) ).
fof(f20576,plain,
greatest_lower_bound(identity,multiply(sF2_fnc,sF1_fnc)) = greatest_lower_bound(identity,multiply(sF4_fnc,sF1_fnc)),
inference(forward_demodulation,[status(thm)],[f417,f20511]) ).
fof(f20577,plain,
greatest_lower_bound(identity,multiply(sF2_fnc,sF1_fnc)) = identity,
inference(forward_demodulation,[status(thm)],[f8098,f20576]) ).
fof(f20625,plain,
multiply(sF2_fnc,sF1_fnc) = least_upper_bound(identity,multiply(sF2_fnc,sF1_fnc)),
inference(paramodulation,[status(thm)],[f20577,f14094]) ).
fof(f20656,plain,
multiply(sF2_fnc,sF1_fnc) = identity,
inference(forward_demodulation,[status(thm)],[f17662,f20625]) ).
fof(f20696,plain,
sF1_fnc = multiply(inverse(sF2_fnc),identity),
inference(paramodulation,[status(thm)],[f20656,f174]) ).
fof(f20712,plain,
sF1_fnc = inverse(sF2_fnc),
inference(forward_demodulation,[status(thm)],[f3024,f20696]) ).
fof(f20736,plain,
inverse(sF1_fnc) = sF2_fnc,
inference(paramodulation,[status(thm)],[f20712,f3092]) ).
fof(f20749,plain,
sF0_fnc = sF2_fnc,
inference(forward_demodulation,[status(thm)],[f34,f20736]) ).
fof(f20750,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f20749,f38]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP179-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.37 % Computer : n013.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sun Sep 20 20:04:07 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.38 % Drodi V4.1.1
% 8.22/1.47 % Refutation found
% 8.22/1.47 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 8.22/1.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 10.90/2.71 % Elapsed time: 2.122780 seconds
% 10.90/2.71 % CPU time: 7.126681 seconds
% 10.90/2.71 % Total memory used: 111.552 MB
% 10.90/2.71 % Net memory used: 109.273 MB
%------------------------------------------------------------------------------