%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP076-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 01:25:07 PM UTC 2026
% Result : Unsatisfiable 7.20s 11.48s
% Output : Proof 7.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 84
% Number of leaves : 6
% Syntax : Number of formulae : 188 ( 184 unt; 0 def)
% Number of atoms : 196 ( 195 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 22 ( 14 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 8 con; 0-4 aty)
% Number of variables : 288 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,negated_conjecture,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).
fof(f4_nnf,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
| multiply(identity,a2) != a2
| multiply(inverse(a1),a1) != identity ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t5,plain,
ifeq(multiply(inverse(a1),a1),identity,ifeq(multiply(identity,a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t18,plain,
ifeq(multiply(inverse(a1),a1),identity,ifeq(multiply(identity,a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true),true) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f1,axiom,
multiply(X,Y) = double_divide(double_divide(Y,X),identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).
fof(f1_nnf,plain,
! [X,Y] : multiply(X,Y) = double_divide(double_divide(Y,X),identity),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] : multiply(X,Y) = double_divide(double_divide(Y,X),identity),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
multiply(X0,X1) = double_divide(double_divide(X1,X0),identity),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t3,plain,
double_divide(double_divide(X1,X2),identity) = multiply(X2,X1),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f2,axiom,
inverse(X) = double_divide(X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).
fof(f2_nnf,plain,
! [X] : inverse(X) = double_divide(X,identity),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : inverse(X) = double_divide(X,identity),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
inverse(X0) = double_divide(X0,identity),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t0,plain,
double_divide(X1,identity) = inverse(X1),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t11,plain,
double_divide(X1,identity) = inverse(X1),
inference(orient,[status(thm)],[t0]) ).
cnf(t1608,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(step,[status(thm)],[t3,t11]) ).
cnf(t14,plain,
inverse(double_divide(X1,X2)) = multiply(X2,X1),
inference(orient,[status(thm)],[t1608]) ).
cnf(f3,axiom,
identity = double_divide(X,inverse(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity) ).
fof(f3_nnf,plain,
! [X] : identity = double_divide(X,inverse(X)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : identity = double_divide(X,inverse(X)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
identity = double_divide(X0,inverse(X0)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t1,plain,
double_divide(X1,inverse(X1)) = identity,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t13,plain,
double_divide(X1,inverse(X1)) = identity,
inference(orient,[status(thm)],[t1]) ).
cnf(t16,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(cp,[status(thm)],[t14,t13]) ).
cnf(t23,plain,
multiply(inverse(X1),X1) = inverse(identity),
inference(orient,[status(thm)],[t16]) ).
cnf(t1609,plain,
ifeq(inverse(identity),identity,ifeq(multiply(identity,a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true),true) = true,
inference(step,[status(thm)],[t18,t23]) ).
cnf(t26,plain,
ifeq(inverse(identity),identity,ifeq(multiply(identity,a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true),true) = true,
inference(rw,[status(thm)],[t1609]) ).
cnf(t17,plain,
identity = double_divide(double_divide(X1,X2),multiply(X2,X1)),
inference(cp,[status(thm)],[t13,t14]) ).
cnf(t40,plain,
double_divide(double_divide(X1,X2),multiply(X2,X1)) = identity,
inference(orient,[status(thm)],[t17]) ).
cnf(f0,axiom,
double_divide(double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),double_divide(Y,identity))),double_divide(identity,identity)) = Z,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).
fof(f0_nnf,plain,
! [X,Y,Z] : double_divide(double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),double_divide(Y,identity))),double_divide(identity,identity)) = Z,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] : double_divide(double_divide(X,double_divide(double_divide(double_divide(X,Y),Z),double_divide(Y,identity))),double_divide(identity,identity)) = Z,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
double_divide(double_divide(X0,double_divide(double_divide(double_divide(X0,X1),X2),double_divide(X1,identity))),double_divide(identity,identity)) = X2,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t4,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t6,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),double_divide(X2,identity))),double_divide(identity,identity)) = X3,
inference(orient,[status(thm)],[t4]) ).
cnf(t1606,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),double_divide(identity,identity)) = X3,
inference(step,[status(thm)],[t6,t11]) ).
cnf(t1607,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),inverse(identity)) = X3,
inference(step,[status(thm)],[t1606,t11]) ).
cnf(t12,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),inverse(identity)) = X3,
inference(rw,[status(thm)],[t1607]) ).
cnf(t75,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),inverse(identity)) = X3,
inference(orient,[status(thm)],[t12]) ).
cnf(t76,plain,
multiply(X1,X2) = double_divide(double_divide(X2,double_divide(identity,inverse(X1))),inverse(identity)),
inference(cp,[status(thm)],[t75,t40]) ).
cnf(t96,plain,
double_divide(double_divide(X1,double_divide(identity,inverse(X2))),inverse(identity)) = multiply(X2,X1),
inference(orient,[status(thm)],[t76]) ).
cnf(t105,plain,
double_divide(identity,inverse(X1)) = double_divide(double_divide(X2,multiply(X1,double_divide(X2,identity))),inverse(identity)),
inference(cp,[status(thm)],[t75,t96]) ).
cnf(t1614,plain,
double_divide(identity,inverse(X1)) = double_divide(double_divide(X2,multiply(X1,inverse(X2))),inverse(identity)),
inference(step,[status(thm)],[t105,t11]) ).
cnf(t132,plain,
double_divide(double_divide(X1,multiply(X2,inverse(X1))),inverse(identity)) = double_divide(identity,inverse(X2)),
inference(orient,[status(thm)],[t1614]) ).
cnf(t143,plain,
multiply(X1,inverse(double_divide(X2,identity))) = double_divide(double_divide(X2,double_divide(identity,inverse(X1))),inverse(identity)),
inference(cp,[status(thm)],[t75,t132]) ).
cnf(t1618,plain,
multiply(X1,multiply(identity,X2)) = double_divide(double_divide(X2,double_divide(identity,inverse(X1))),inverse(identity)),
inference(step,[status(thm)],[t143,t14]) ).
cnf(t1619,plain,
multiply(X1,multiply(identity,X2)) = multiply(X1,X2),
inference(step,[status(thm)],[t1618,t96]) ).
cnf(t153,plain,
multiply(X1,multiply(identity,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t1619]) ).
cnf(t97,plain,
multiply(identity,X1) = double_divide(double_divide(X1,identity),inverse(identity)),
inference(cp,[status(thm)],[t96,t13]) ).
cnf(t1610,plain,
multiply(identity,X1) = double_divide(inverse(X1),inverse(identity)),
inference(step,[status(thm)],[t97,t11]) ).
cnf(t108,plain,
double_divide(inverse(X1),inverse(identity)) = multiply(identity,X1),
inference(orient,[status(thm)],[t1610]) ).
cnf(t115,plain,
multiply(inverse(identity),inverse(X1)) = inverse(multiply(identity,X1)),
inference(cp,[status(thm)],[t14,t108]) ).
cnf(t15,plain,
multiply(identity,X1) = inverse(inverse(X1)),
inference(cp,[status(thm)],[t14,t11]) ).
cnf(t19,plain,
inverse(inverse(X1)) = multiply(identity,X1),
inference(orient,[status(thm)],[t15]) ).
cnf(t22,plain,
multiply(identity,inverse(X1)) = inverse(multiply(identity,X1)),
inference(cp,[status(thm)],[t19,t19]) ).
cnf(t27,plain,
inverse(multiply(identity,X1)) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t22]) ).
cnf(t1611,plain,
multiply(inverse(identity),inverse(X1)) = multiply(identity,inverse(X1)),
inference(step,[status(thm)],[t115,t27]) ).
cnf(t117,plain,
multiply(inverse(identity),inverse(X1)) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t1611]) ).
cnf(t119,plain,
multiply(identity,inverse(double_divide(X1,X2))) = multiply(inverse(identity),multiply(X2,X1)),
inference(cp,[status(thm)],[t117,t14]) ).
cnf(t1613,plain,
multiply(identity,multiply(X2,X1)) = multiply(inverse(identity),multiply(X2,X1)),
inference(step,[status(thm)],[t119,t14]) ).
cnf(t127,plain,
multiply(inverse(identity),multiply(X1,X2)) = multiply(identity,multiply(X1,X2)),
inference(orient,[status(thm)],[t1613]) ).
cnf(t155,plain,
multiply(inverse(identity),X1) = multiply(identity,multiply(identity,X1)),
inference(cp,[status(thm)],[t153,t127]) ).
cnf(t1625,plain,
multiply(inverse(identity),X1) = multiply(identity,X1),
inference(step,[status(thm)],[t155,t153]) ).
cnf(t163,plain,
multiply(inverse(identity),X1) = multiply(identity,X1),
inference(orient,[status(thm)],[t1625]) ).
cnf(t164,plain,
multiply(identity,identity) = inverse(identity),
inference(cp,[status(thm)],[t163,t23]) ).
cnf(t168,plain,
multiply(identity,identity) = inverse(identity),
inference(orient,[status(thm)],[t164]) ).
cnf(t172,plain,
identity = double_divide(double_divide(identity,identity),inverse(identity)),
inference(cp,[status(thm)],[t40,t168]) ).
cnf(t1628,plain,
identity = double_divide(inverse(identity),inverse(identity)),
inference(step,[status(thm)],[t172,t11]) ).
cnf(t1629,plain,
identity = multiply(identity,identity),
inference(step,[status(thm)],[t1628,t108]) ).
cnf(t1630,plain,
identity = inverse(identity),
inference(step,[status(thm)],[t1629,t168]) ).
cnf(t177,plain,
inverse(identity) = identity,
inference(orient,[status(thm)],[t1630]) ).
cnf(t1677,plain,
ifeq(identity,identity,ifeq(multiply(identity,a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true),true) = true,
inference(step,[status(thm)],[t26,t177]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t10,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t1678,plain,
ifeq(multiply(identity,a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true) = true,
inference(step,[status(thm)],[t1677,t10]) ).
cnf(t297,plain,
ifeq(multiply(identity,a2),a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true) = true,
inference(orient,[status(thm)],[t1678]) ).
cnf(t1645,plain,
double_divide(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2))),identity) = X3,
inference(step,[status(thm)],[t75,t177]) ).
cnf(t1646,plain,
inverse(double_divide(X1,double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2)))) = X3,
inference(step,[status(thm)],[t1645,t11]) ).
cnf(t1647,plain,
multiply(double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2)),X1) = X3,
inference(step,[status(thm)],[t1646,t14]) ).
cnf(t188,plain,
multiply(double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2)),X1) = X3,
inference(rw,[status(thm)],[t1647]) ).
cnf(t1042,plain,
multiply(double_divide(double_divide(double_divide(X1,X2),X3),inverse(X2)),X1) = X3,
inference(orient,[status(thm)],[t188]) ).
cnf(t1057,plain,
X1 = multiply(double_divide(double_divide(inverse(X2),X1),inverse(identity)),X2),
inference(cp,[status(thm)],[t1042,t11]) ).
cnf(t1718,plain,
X1 = multiply(double_divide(double_divide(inverse(X2),X1),identity),X2),
inference(step,[status(thm)],[t1057,t177]) ).
cnf(t1719,plain,
X1 = multiply(inverse(double_divide(inverse(X2),X1)),X2),
inference(step,[status(thm)],[t1718,t11]) ).
cnf(t1720,plain,
X1 = multiply(multiply(X1,inverse(X2)),X2),
inference(step,[status(thm)],[t1719,t14]) ).
cnf(t1639,plain,
double_divide(double_divide(X1,multiply(X2,inverse(X1))),identity) = double_divide(identity,inverse(X2)),
inference(step,[status(thm)],[t132,t177]) ).
cnf(t1640,plain,
inverse(double_divide(X1,multiply(X2,inverse(X1)))) = double_divide(identity,inverse(X2)),
inference(step,[status(thm)],[t1639,t11]) ).
cnf(t1641,plain,
multiply(multiply(X2,inverse(X1)),X1) = double_divide(identity,inverse(X2)),
inference(step,[status(thm)],[t1640,t14]) ).
cnf(t186,plain,
multiply(multiply(X2,inverse(X1)),X1) = double_divide(identity,inverse(X2)),
inference(rw,[status(thm)],[t1641]) ).
cnf(t197,plain,
multiply(multiply(X1,inverse(X2)),X2) = double_divide(identity,inverse(X1)),
inference(orient,[status(thm)],[t186]) ).
cnf(t1642,plain,
double_divide(double_divide(X1,double_divide(identity,inverse(X2))),identity) = multiply(X2,X1),
inference(step,[status(thm)],[t96,t177]) ).
cnf(t1643,plain,
inverse(double_divide(X1,double_divide(identity,inverse(X2)))) = multiply(X2,X1),
inference(step,[status(thm)],[t1642,t11]) ).
cnf(t1644,plain,
multiply(double_divide(identity,inverse(X2)),X1) = multiply(X2,X1),
inference(step,[status(thm)],[t1643,t14]) ).
cnf(t187,plain,
multiply(double_divide(identity,inverse(X2)),X1) = multiply(X2,X1),
inference(rw,[status(thm)],[t1644]) ).
cnf(t191,plain,
multiply(double_divide(identity,inverse(X1)),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t187]) ).
cnf(t198,plain,
double_divide(identity,inverse(double_divide(identity,inverse(X1)))) = multiply(multiply(X1,inverse(X2)),X2),
inference(cp,[status(thm)],[t197,t191]) ).
cnf(t1659,plain,
double_divide(identity,multiply(inverse(X1),identity)) = multiply(multiply(X1,inverse(X2)),X2),
inference(step,[status(thm)],[t198,t14]) ).
cnf(t1660,plain,
double_divide(identity,multiply(inverse(X1),identity)) = double_divide(identity,inverse(X1)),
inference(step,[status(thm)],[t1659,t197]) ).
cnf(t240,plain,
double_divide(identity,multiply(inverse(X1),identity)) = double_divide(identity,inverse(X1)),
inference(orient,[status(thm)],[t1660]) ).
cnf(t245,plain,
multiply(multiply(inverse(X1),identity),identity) = inverse(double_divide(identity,inverse(X1))),
inference(cp,[status(thm)],[t14,t240]) ).
cnf(t201,plain,
double_divide(identity,inverse(X1)) = multiply(multiply(X1,identity),identity),
inference(cp,[status(thm)],[t197,t177]) ).
cnf(t207,plain,
multiply(multiply(X1,identity),identity) = double_divide(identity,inverse(X1)),
inference(orient,[status(thm)],[t201]) ).
cnf(t1661,plain,
double_divide(identity,inverse(inverse(X1))) = inverse(double_divide(identity,inverse(X1))),
inference(step,[status(thm)],[t245,t207]) ).
cnf(t1662,plain,
double_divide(identity,multiply(identity,X1)) = inverse(double_divide(identity,inverse(X1))),
inference(step,[status(thm)],[t1661,t19]) ).
cnf(t25,plain,
inverse(identity) = multiply(multiply(identity,X1),inverse(X1)),
inference(cp,[status(thm)],[t23,t19]) ).
cnf(t37,plain,
multiply(multiply(identity,X1),inverse(X1)) = inverse(identity),
inference(orient,[status(thm)],[t25]) ).
cnf(t1633,plain,
multiply(multiply(identity,X1),inverse(X1)) = identity,
inference(step,[status(thm)],[t37,t177]) ).
cnf(t180,plain,
multiply(multiply(identity,X1),inverse(X1)) = identity,
inference(orient,[status(thm)],[t1633]) ).
cnf(t199,plain,
double_divide(identity,inverse(multiply(identity,X1))) = multiply(identity,X1),
inference(cp,[status(thm)],[t197,t180]) ).
cnf(t1650,plain,
double_divide(identity,multiply(identity,inverse(X1))) = multiply(identity,X1),
inference(step,[status(thm)],[t199,t27]) ).
cnf(t213,plain,
double_divide(identity,multiply(identity,inverse(X1))) = multiply(identity,X1),
inference(orient,[status(thm)],[t1650]) ).
cnf(t215,plain,
multiply(identity,inverse(X1)) = double_divide(identity,multiply(identity,multiply(identity,X1))),
inference(cp,[status(thm)],[t213,t19]) ).
cnf(t1651,plain,
multiply(identity,inverse(X1)) = double_divide(identity,multiply(identity,X1)),
inference(step,[status(thm)],[t215,t153]) ).
cnf(t220,plain,
double_divide(identity,multiply(identity,X1)) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t1651]) ).
cnf(t1663,plain,
multiply(identity,inverse(X1)) = inverse(double_divide(identity,inverse(X1))),
inference(step,[status(thm)],[t1662,t220]) ).
cnf(t1664,plain,
multiply(identity,inverse(X1)) = multiply(inverse(X1),identity),
inference(step,[status(thm)],[t1663,t14]) ).
cnf(t247,plain,
multiply(inverse(X1),identity) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t1664]) ).
cnf(t1665,plain,
double_divide(identity,multiply(identity,inverse(X1))) = double_divide(identity,inverse(X1)),
inference(step,[status(thm)],[t240,t247]) ).
cnf(t1666,plain,
multiply(identity,X1) = double_divide(identity,inverse(X1)),
inference(step,[status(thm)],[t1665,t213]) ).
cnf(t251,plain,
multiply(identity,X1) = double_divide(identity,inverse(X1)),
inference(rw,[status(thm)],[t1666]) ).
cnf(t252,plain,
double_divide(identity,inverse(X1)) = multiply(identity,X1),
inference(orient,[status(thm)],[t251]) ).
cnf(t1667,plain,
multiply(multiply(X1,inverse(X2)),X2) = multiply(identity,X1),
inference(step,[status(thm)],[t197,t252]) ).
cnf(t253,plain,
multiply(multiply(X1,inverse(X2)),X2) = multiply(identity,X1),
inference(orient,[status(thm)],[t1667]) ).
cnf(t1721,plain,
X1 = multiply(identity,X1),
inference(step,[status(thm)],[t1720,t253]) ).
cnf(t1110,plain,
multiply(identity,X1) = X1,
inference(orient,[status(thm)],[t1721]) ).
cnf(t1741,plain,
ifeq(a2,a2,ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true),true) = true,
inference(step,[status(thm)],[t297,t1110]) ).
cnf(t1742,plain,
ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true) = true,
inference(step,[status(thm)],[t1741,t10]) ).
cnf(t1147,plain,
ifeq(multiply(multiply(a3,b3),c3),multiply(a3,multiply(b3,c3)),false,true) = true,
inference(rw,[status(thm)],[t1742]) ).
cnf(t203,plain,
double_divide(identity,inverse(X1)) = multiply(multiply(X1,multiply(identity,X2)),inverse(X2)),
inference(cp,[status(thm)],[t197,t19]) ).
cnf(t1681,plain,
multiply(identity,X1) = multiply(multiply(X1,multiply(identity,X2)),inverse(X2)),
inference(step,[status(thm)],[t203,t252]) ).
cnf(t1682,plain,
multiply(identity,X1) = multiply(multiply(X1,X2),inverse(X2)),
inference(step,[status(thm)],[t1681,t153]) ).
cnf(t345,plain,
multiply(multiply(X1,X2),inverse(X2)) = multiply(identity,X1),
inference(orient,[status(thm)],[t1682]) ).
cnf(t1730,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(step,[status(thm)],[t345,t1110]) ).
cnf(t1119,plain,
multiply(multiply(X1,X2),inverse(X2)) = X1,
inference(orient,[status(thm)],[t1730]) ).
cnf(t1058,plain,
X1 = multiply(double_divide(double_divide(identity,X1),inverse(inverse(X2))),X2),
inference(cp,[status(thm)],[t1042,t13]) ).
cnf(t1672,plain,
multiply(multiply(identity,X1),X2) = multiply(X1,X2),
inference(step,[status(thm)],[t191,t252]) ).
cnf(t259,plain,
multiply(multiply(identity,X1),X2) = multiply(X1,X2),
inference(rw,[status(thm)],[t1672]) ).
cnf(t270,plain,
multiply(multiply(identity,X1),X2) = multiply(X1,X2),
inference(orient,[status(thm)],[t259]) ).
cnf(t20,plain,
multiply(identity,double_divide(X1,X2)) = inverse(multiply(X2,X1)),
inference(cp,[status(thm)],[t19,t14]) ).
cnf(t35,plain,
multiply(identity,double_divide(X1,X2)) = inverse(multiply(X2,X1)),
inference(orient,[status(thm)],[t20]) ).
cnf(t272,plain,
multiply(double_divide(X1,X2),X3) = multiply(inverse(multiply(X2,X1)),X3),
inference(cp,[status(thm)],[t270,t35]) ).
cnf(t424,plain,
multiply(inverse(multiply(X1,X2)),X3) = multiply(double_divide(X2,X1),X3),
inference(orient,[status(thm)],[t272]) ).
cnf(t156,plain,
multiply(X1,double_divide(X2,X3)) = multiply(X1,inverse(multiply(X3,X2))),
inference(cp,[status(thm)],[t153,t35]) ).
cnf(t358,plain,
multiply(X1,inverse(multiply(X2,X3))) = multiply(X1,double_divide(X3,X2)),
inference(orient,[status(thm)],[t156]) ).
cnf(t225,plain,
multiply(multiply(identity,X1),identity) = inverse(multiply(identity,inverse(X1))),
inference(cp,[status(thm)],[t14,t220]) ).
cnf(t1652,plain,
multiply(multiply(identity,X1),identity) = multiply(identity,inverse(inverse(X1))),
inference(step,[status(thm)],[t225,t27]) ).
cnf(t1653,plain,
multiply(multiply(identity,X1),identity) = multiply(identity,multiply(identity,X1)),
inference(step,[status(thm)],[t1652,t19]) ).
cnf(t1654,plain,
multiply(multiply(identity,X1),identity) = multiply(identity,X1),
inference(step,[status(thm)],[t1653,t153]) ).
cnf(t226,plain,
multiply(multiply(identity,X1),identity) = multiply(identity,X1),
inference(orient,[status(thm)],[t1654]) ).
cnf(t1673,plain,
multiply(X1,identity) = multiply(identity,X1),
inference(step,[status(thm)],[t226,t270]) ).
cnf(t275,plain,
multiply(X1,identity) = multiply(identity,X1),
inference(rw,[status(thm)],[t1673]) ).
cnf(t279,plain,
multiply(X1,identity) = multiply(identity,X1),
inference(orient,[status(thm)],[t275]) ).
cnf(t292,plain,
multiply(identity,inverse(X1)) = inverse(multiply(X1,identity)),
inference(cp,[status(thm)],[t27,t279]) ).
cnf(t298,plain,
inverse(multiply(X1,identity)) = multiply(identity,inverse(X1)),
inference(orient,[status(thm)],[t292]) ).
cnf(t361,plain,
multiply(X1,double_divide(identity,X2)) = multiply(X1,multiply(identity,inverse(X2))),
inference(cp,[status(thm)],[t358,t298]) ).
cnf(t1684,plain,
multiply(X1,double_divide(identity,X2)) = multiply(X1,inverse(X2)),
inference(step,[status(thm)],[t361,t153]) ).
cnf(t382,plain,
multiply(X1,double_divide(identity,X2)) = multiply(X1,inverse(X2)),
inference(orient,[status(thm)],[t1684]) ).
cnf(t426,plain,
multiply(double_divide(double_divide(identity,X1),X2),X3) = multiply(inverse(multiply(X2,inverse(X1))),X3),
inference(cp,[status(thm)],[t424,t382]) ).
cnf(t1716,plain,
multiply(double_divide(double_divide(identity,X1),X2),X3) = multiply(double_divide(inverse(X1),X2),X3),
inference(step,[status(thm)],[t426,t424]) ).
cnf(t1000,plain,
multiply(double_divide(double_divide(identity,X1),X2),X3) = multiply(double_divide(inverse(X1),X2),X3),
inference(orient,[status(thm)],[t1716]) ).
cnf(t1750,plain,
X1 = multiply(double_divide(inverse(X1),inverse(inverse(X2))),X2),
inference(step,[status(thm)],[t1058,t1000]) ).
cnf(t1722,plain,
inverse(inverse(X1)) = X1,
inference(step,[status(thm)],[t19,t1110]) ).
cnf(t1111,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t1722]) ).
cnf(t1751,plain,
X1 = multiply(double_divide(inverse(X1),X2),X2),
inference(step,[status(thm)],[t1750,t1111]) ).
cnf(t1188,plain,
multiply(double_divide(inverse(X1),X2),X2) = X1,
inference(orient,[status(thm)],[t1751]) ).
cnf(t1193,plain,
double_divide(inverse(X1),X2) = multiply(X1,inverse(X2)),
inference(cp,[status(thm)],[t1119,t1188]) ).
cnf(t1202,plain,
double_divide(inverse(X1),X2) = multiply(X1,inverse(X2)),
inference(orient,[status(thm)],[t1193]) ).
cnf(t1205,plain,
multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2),
inference(cp,[status(thm)],[t1202,t1111]) ).
cnf(t1214,plain,
multiply(inverse(X1),inverse(X2)) = double_divide(X1,X2),
inference(orient,[status(thm)],[t1205]) ).
cnf(t1219,plain,
double_divide(X1,inverse(X2)) = multiply(inverse(X1),X2),
inference(cp,[status(thm)],[t1214,t1111]) ).
cnf(t1225,plain,
double_divide(X1,inverse(X2)) = multiply(inverse(X1),X2),
inference(orient,[status(thm)],[t1219]) ).
cnf(t1756,plain,
multiply(multiply(inverse(double_divide(double_divide(X1,X2),X3)),X2),X1) = X3,
inference(step,[status(thm)],[t1042,t1225]) ).
cnf(t1757,plain,
multiply(multiply(multiply(X3,double_divide(X1,X2)),X2),X1) = X3,
inference(step,[status(thm)],[t1756,t14]) ).
cnf(t1231,plain,
multiply(multiply(multiply(X3,double_divide(X1,X2)),X2),X1) = X3,
inference(rw,[status(thm)],[t1757]) ).
cnf(t1320,plain,
multiply(multiply(multiply(X1,double_divide(X2,X3)),X3),X2) = X1,
inference(orient,[status(thm)],[t1231]) ).
cnf(t1724,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(step,[status(thm)],[t253,t1110]) ).
cnf(t1113,plain,
multiply(multiply(X1,inverse(X2)),X2) = X1,
inference(orient,[status(thm)],[t1724]) ).
cnf(t1325,plain,
multiply(X1,inverse(double_divide(X2,X3))) = multiply(multiply(X1,X3),X2),
inference(cp,[status(thm)],[t1320,t1113]) ).
cnf(t1762,plain,
multiply(X1,multiply(X3,X2)) = multiply(multiply(X1,X3),X2),
inference(step,[status(thm)],[t1325,t14]) ).
cnf(t1351,plain,
multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
inference(orient,[status(thm)],[t1762]) ).
cnf(t1783,plain,
ifeq(multiply(a3,multiply(b3,c3)),multiply(a3,multiply(b3,c3)),false,true) = true,
inference(step,[status(thm)],[t1147,t1351]) ).
cnf(t1784,plain,
false = true,
inference(step,[status(thm)],[t1783,t10]) ).
cnf(t1605,plain,
false = true,
inference(orient,[status(thm)],[t1784]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1605]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP076-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/10.38 % Computer : n007.cluster.edu
% 0.09/10.38 % Model : x86_64 x86_64
% 0.09/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.38 % Memory : 8046.5625MB
% 0.09/10.38 % OS : Linux 6.8.0-71-generic
% 0.09/10.38 % CPULimit : 300
% 0.09/10.38 % WCLimit : 300
% 0.09/10.38 % DateTime : Wed Sep 23 13:26:17 UTC 2026
% 0.09/10.38 % CPUTime :
% 0.09/10.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.20/11.48 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.20/11.48 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------