%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n017.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 5.28s 1.25s
% Output : Proof 5.28s
% Verified :
% SZS Type : Refutation
% Derivation depth : 53
% Number of leaves : 5
% Syntax : Number of formulae : 96 ( 92 unt; 0 def)
% Number of atoms : 104 ( 103 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 28 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 8 ( 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 : 135 ( 2 sgn 10 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f0,axiom,
double_divide(double_divide(identity,X),double_divide(double_divide(double_divide(Y,Z),double_divide(identity,identity)),double_divide(X,Z))) = Y,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',single_axiom) ).
fof(f0_nnf,plain,
! [X,Y,Z] : double_divide(double_divide(identity,X),double_divide(double_divide(double_divide(Y,Z),double_divide(identity,identity)),double_divide(X,Z))) = Y,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] : double_divide(double_divide(identity,X),double_divide(double_divide(double_divide(Y,Z),double_divide(identity,identity)),double_divide(X,Z))) = Y,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
double_divide(double_divide(identity,X0),double_divide(double_divide(double_divide(X1,X2),double_divide(identity,identity)),double_divide(X0,X2))) = X1,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t2,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(double_divide(X2,X3),double_divide(identity,identity)),double_divide(X1,X3))) = X2,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t4,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(double_divide(X2,X3),double_divide(identity,identity)),double_divide(X1,X3))) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(f3,axiom,
identity = double_divide(X,inverse(X)),
file('/export/starexec/sandbox2/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(u1,axiom,
identity = double_divide(X0,inverse(X0)),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f2,axiom,
inverse(X) = double_divide(X,identity),
file('/export/starexec/sandbox2/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(d1,axiom,
inverse(X0) = double_divide(X0,identity),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t0,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(definition_unfolding,[status(thm)],[u1,d1]) ).
cnf(t8,plain,
double_divide(X1,double_divide(X1,identity)) = identity,
inference(orient,[status(thm)],[t0]) ).
cnf(t11,plain,
X1 = double_divide(double_divide(identity,X2),double_divide(double_divide(identity,double_divide(identity,identity)),double_divide(X2,double_divide(X1,identity)))),
inference(cp,[status(thm)],[t4,t8]) ).
cnf(t2896,plain,
X1 = double_divide(double_divide(identity,X2),double_divide(identity,double_divide(X2,double_divide(X1,identity)))),
inference(step,[status(thm)],[t11,t8]) ).
cnf(t19,plain,
double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X1,double_divide(X2,identity)))) = X2,
inference(orient,[status(thm)],[t2896]) ).
cnf(t21,plain,
X1 = double_divide(double_divide(identity,X1),double_divide(identity,identity)),
inference(cp,[status(thm)],[t19,t8]) ).
cnf(t25,plain,
double_divide(double_divide(identity,X1),double_divide(identity,identity)) = X1,
inference(orient,[status(thm)],[t21]) ).
cnf(t26,plain,
double_divide(identity,identity) = double_divide(identity,double_divide(identity,identity)),
inference(cp,[status(thm)],[t25,t8]) ).
cnf(t2897,plain,
double_divide(identity,identity) = identity,
inference(step,[status(thm)],[t26,t8]) ).
cnf(t32,plain,
double_divide(identity,identity) = identity,
inference(orient,[status(thm)],[t2897]) ).
cnf(t1,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t7,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t1]) ).
cnf(t2898,plain,
double_divide(double_divide(identity,X1),identity) = X1,
inference(step,[status(thm)],[t25,t32]) ).
cnf(t35,plain,
double_divide(double_divide(identity,X1),identity) = X1,
inference(rw,[status(thm)],[t2898]) ).
cnf(t39,plain,
double_divide(double_divide(identity,X1),identity) = X1,
inference(orient,[status(thm)],[t35]) ).
cnf(t40,plain,
identity = double_divide(double_divide(identity,X1),X1),
inference(cp,[status(thm)],[t8,t39]) ).
cnf(t42,plain,
double_divide(double_divide(identity,X1),X1) = identity,
inference(orient,[status(thm)],[t40]) ).
cnf(t43,plain,
X1 = double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),double_divide(identity,identity)),
inference(cp,[status(thm)],[t19,t42]) ).
cnf(t2903,plain,
X1 = double_divide(double_divide(identity,double_divide(identity,double_divide(X1,identity))),identity),
inference(step,[status(thm)],[t43,t32]) ).
cnf(t2904,plain,
X1 = double_divide(identity,double_divide(X1,identity)),
inference(step,[status(thm)],[t2903,t39]) ).
cnf(t45,plain,
double_divide(identity,double_divide(X1,identity)) = X1,
inference(orient,[status(thm)],[t2904]) ).
cnf(t47,plain,
X1 = double_divide(double_divide(identity,identity),double_divide(identity,X1)),
inference(cp,[status(thm)],[t19,t45]) ).
cnf(t2905,plain,
X1 = double_divide(identity,double_divide(identity,X1)),
inference(step,[status(thm)],[t47,t32]) ).
cnf(t48,plain,
double_divide(identity,double_divide(identity,X1)) = X1,
inference(orient,[status(thm)],[t2905]) ).
cnf(t49,plain,
double_divide(X1,identity) = double_divide(identity,X1),
inference(cp,[status(thm)],[t48,t45]) ).
cnf(t61,plain,
double_divide(X1,identity) = double_divide(identity,X1),
inference(orient,[status(thm)],[t49]) ).
cnf(t62,plain,
X1 = double_divide(double_divide(identity,X2),double_divide(identity,double_divide(X2,double_divide(identity,X1)))),
inference(cp,[status(thm)],[t19,t61]) ).
cnf(t76,plain,
double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X1,double_divide(identity,X2)))) = X2,
inference(orient,[status(thm)],[t62]) ).
cnf(t88,plain,
double_divide(X1,identity) = double_divide(double_divide(identity,X2),double_divide(identity,double_divide(X2,X1))),
inference(cp,[status(thm)],[t76,t45]) ).
cnf(t92,plain,
double_divide(double_divide(identity,X1),double_divide(identity,double_divide(X1,X2))) = double_divide(X2,identity),
inference(orient,[status(thm)],[t88]) ).
cnf(t2899,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(double_divide(X2,X3),identity),double_divide(X1,X3))) = X2,
inference(step,[status(thm)],[t4,t32]) ).
cnf(t36,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(double_divide(X2,X3),identity),double_divide(X1,X3))) = X2,
inference(rw,[status(thm)],[t2899]) ).
cnf(t2912,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(identity,double_divide(X2,X3)),double_divide(X1,X3))) = X2,
inference(step,[status(thm)],[t36,t61]) ).
cnf(t158,plain,
double_divide(double_divide(identity,X1),double_divide(double_divide(identity,double_divide(X2,X3)),double_divide(X1,X3))) = X2,
inference(orient,[status(thm)],[t2912]) ).
cnf(t169,plain,
X1 = double_divide(double_divide(identity,X2),double_divide(X1,double_divide(X2,identity))),
inference(cp,[status(thm)],[t158,t45]) ).
cnf(t202,plain,
double_divide(double_divide(identity,X1),double_divide(X2,double_divide(X1,identity))) = X2,
inference(orient,[status(thm)],[t169]) ).
cnf(t212,plain,
double_divide(double_divide(X1,double_divide(X2,identity)),identity) = double_divide(double_divide(identity,double_divide(identity,X2)),double_divide(identity,X1)),
inference(cp,[status(thm)],[t92,t202]) ).
cnf(t2913,plain,
double_divide(identity,double_divide(X1,double_divide(X2,identity))) = double_divide(double_divide(identity,double_divide(identity,X2)),double_divide(identity,X1)),
inference(step,[status(thm)],[t212,t61]) ).
cnf(t2914,plain,
double_divide(identity,double_divide(X1,double_divide(X2,identity))) = double_divide(X2,double_divide(identity,X1)),
inference(step,[status(thm)],[t2913,t48]) ).
cnf(t218,plain,
double_divide(identity,double_divide(X1,double_divide(X2,identity))) = double_divide(X2,double_divide(identity,X1)),
inference(orient,[status(thm)],[t2914]) ).
cnf(t220,plain,
double_divide(X1,double_divide(identity,X2)) = double_divide(identity,double_divide(X2,double_divide(identity,X1))),
inference(cp,[status(thm)],[t218,t61]) ).
cnf(t237,plain,
double_divide(identity,double_divide(X1,double_divide(identity,X2))) = double_divide(X2,double_divide(identity,X1)),
inference(orient,[status(thm)],[t220]) ).
cnf(t100,plain,
double_divide(X1,identity) = double_divide(double_divide(X2,identity),double_divide(identity,double_divide(X2,X1))),
inference(cp,[status(thm)],[t92,t61]) ).
cnf(t140,plain,
double_divide(double_divide(X1,identity),double_divide(identity,double_divide(X1,X2))) = double_divide(X2,identity),
inference(orient,[status(thm)],[t100]) ).
cnf(t241,plain,
double_divide(double_divide(X1,X2),double_divide(identity,double_divide(X1,identity))) = double_divide(identity,double_divide(X2,identity)),
inference(cp,[status(thm)],[t237,t140]) ).
cnf(t2915,plain,
double_divide(double_divide(X1,X2),X1) = double_divide(identity,double_divide(X2,identity)),
inference(step,[status(thm)],[t241,t45]) ).
cnf(t2916,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(step,[status(thm)],[t2915,t45]) ).
cnf(t265,plain,
double_divide(double_divide(X1,X2),X1) = X2,
inference(orient,[status(thm)],[t2916]) ).
cnf(t95,plain,
double_divide(X1,identity) = double_divide(X2,double_divide(identity,double_divide(double_divide(identity,X2),X1))),
inference(cp,[status(thm)],[t92,t48]) ).
cnf(t126,plain,
double_divide(X1,double_divide(identity,double_divide(double_divide(identity,X1),X2))) = double_divide(X2,identity),
inference(orient,[status(thm)],[t95]) ).
cnf(t268,plain,
double_divide(identity,double_divide(double_divide(identity,X1),X2)) = double_divide(double_divide(X2,identity),X1),
inference(cp,[status(thm)],[t265,t126]) ).
cnf(t367,plain,
double_divide(identity,double_divide(double_divide(identity,X1),X2)) = double_divide(double_divide(X2,identity),X1),
inference(orient,[status(thm)],[t268]) ).
cnf(t275,plain,
double_divide(double_divide(identity,double_divide(X1,X2)),double_divide(X3,X2)) = double_divide(X1,double_divide(identity,X3)),
inference(cp,[status(thm)],[t265,t158]) ).
cnf(t418,plain,
double_divide(double_divide(identity,double_divide(X1,X2)),double_divide(X3,X2)) = double_divide(X1,double_divide(identity,X3)),
inference(orient,[status(thm)],[t275]) ).
cnf(t436,plain,
double_divide(X1,double_divide(identity,double_divide(X2,X3))) = double_divide(double_divide(identity,double_divide(X1,X2)),X3),
inference(cp,[status(thm)],[t418,t265]) ).
cnf(t454,plain,
double_divide(double_divide(identity,double_divide(X1,X2)),X3) = double_divide(X1,double_divide(identity,double_divide(X2,X3))),
inference(orient,[status(thm)],[t436]) ).
cnf(t481,plain,
double_divide(double_divide(X1,identity),double_divide(X2,X3)) = double_divide(identity,double_divide(X2,double_divide(identity,double_divide(X3,X1)))),
inference(cp,[status(thm)],[t367,t454]) ).
cnf(t2977,plain,
double_divide(double_divide(X1,identity),double_divide(X2,X3)) = double_divide(double_divide(X3,X1),double_divide(identity,X2)),
inference(step,[status(thm)],[t481,t237]) ).
cnf(t2766,plain,
double_divide(double_divide(X1,identity),double_divide(X2,X3)) = double_divide(double_divide(X3,X1),double_divide(identity,X2)),
inference(orient,[status(thm)],[t2977]) ).
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/sandbox2/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(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(g0_0,plain,
true != ifeq(double_divide(identity,identity),identity,ifeq(double_divide(double_divide(a2,identity),identity),a2,ifeq(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),false,true),true),true),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
true != ifeq(double_divide(identity,identity),double_divide(identity,identity),ifeq(double_divide(double_divide(a2,identity),identity),a2,ifeq(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),false,true),true),true),
inference(rw,[status(thm)],[g0_0,t32]) ).
cnf(g0_2,plain,
true != ifeq(double_divide(identity,identity),double_divide(identity,identity),ifeq(a2,a2,ifeq(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),false,true),true),true),
inference(rw,[status(thm)],[g0_1]) ).
cnf(g0_3,plain,
true != ifeq(double_divide(identity,identity),double_divide(identity,identity),ifeq(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity),false,true),true),
inference(rw,[status(thm)],[g0_2,t7]) ).
cnf(g0_4,plain,
true != ifeq(double_divide(identity,identity),double_divide(identity,identity),ifeq(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),a3),identity),false,true),true),
inference(rw,[status(thm)],[g0_3,t61]) ).
cnf(g0_5,plain,
true != ifeq(double_divide(identity,identity),double_divide(identity,identity),ifeq(double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)),false,true),true),
inference(rw,[status(thm)],[g0_4,t61]) ).
cnf(g0_6,plain,
true != ifeq(double_divide(identity,identity),double_divide(identity,identity),ifeq(double_divide(double_divide(c3,double_divide(identity,double_divide(b3,a3))),identity),double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)),false,true),true),
inference(rw,[status(thm)],[g0_5,t61]) ).
cnf(g0_7,plain,
true != ifeq(double_divide(identity,identity),double_divide(identity,identity),ifeq(double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)),false,true),true),
inference(rw,[status(thm)],[g0_6,t61]) ).
cnf(g0_8,plain,
true != ifeq(double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)),false,true),
inference(rw,[status(thm)],[g0_7,t7]) ).
cnf(g0_9,plain,
true != ifeq(double_divide(double_divide(b3,a3),double_divide(identity,c3)),double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)),false,true),
inference(rw,[status(thm)],[g0_8,t237]) ).
cnf(g0_10,plain,
true != ifeq(double_divide(double_divide(b3,a3),double_divide(identity,c3)),double_divide(double_divide(a3,identity),double_divide(c3,b3)),false,true),
inference(rw,[status(thm)],[g0_9,t367]) ).
cnf(g0_11,plain,
true != ifeq(double_divide(double_divide(b3,a3),double_divide(identity,c3)),double_divide(double_divide(identity,a3),double_divide(c3,b3)),false,true),
inference(rw,[status(thm)],[g0_10,t61]) ).
cnf(g0_12,plain,
true != ifeq(double_divide(double_divide(a3,identity),double_divide(c3,b3)),double_divide(double_divide(identity,a3),double_divide(c3,b3)),false,true),
inference(rw,[status(thm)],[g0_11,t2766]) ).
cnf(g0_13,plain,
true != ifeq(double_divide(double_divide(a3,identity),double_divide(c3,b3)),double_divide(double_divide(a3,identity),double_divide(c3,b3)),false,true),
inference(rw,[status(thm)],[g0_12,t61]) ).
cnf(g0_14,plain,
true != false,
inference(rw,[status(thm)],[g0_13,t7]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP079-1 : TPTP v9.3.1. Bugfixed v2.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 13:23:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.28/1.25 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.28/1.25 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------