%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GRP486-1 : TPTP v9.3.1. Released v2.6.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 : Sun Sep 27 07:29:51 AM UTC 2026
% Result : Unsatisfiable 0.21s 10.55s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 34
% Number of leaves : 5
% Syntax : Number of formulae : 122 ( 122 unt; 0 def)
% Number of atoms : 122 ( 121 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 14 ( 14 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 2 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 193 ( 0 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(single_axiom,axiom,
! [VAR_0,VAR_1,VAR_2] : double_divide(double_divide(VAR_0,double_divide(double_divide(double_divide(VAR_0,VAR_1),VAR_2),double_divide(VAR_1,identity))),double_divide(identity,identity)) = VAR_2,
file('theBenchmark.p',single_axiom) ).
cnf(c_1,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,B),C),double_divide(B,identity))),double_divide(identity,identity)) = C,
inference(clausify,[status(thm)],[single_axiom]) ).
fof(multiply,axiom,
! [VAR_0,VAR_1] : multiply(VAR_0,VAR_1) = double_divide(double_divide(VAR_1,VAR_0),identity),
file('theBenchmark.p',multiply) ).
cnf(c_2,plain,
multiply(A,B) = double_divide(double_divide(B,A),identity),
inference(clausify,[status(thm)],[multiply]) ).
fof(inverse,axiom,
! [VAR_0] : inverse(VAR_0) = double_divide(VAR_0,identity),
file('theBenchmark.p',inverse) ).
cnf(c_3,plain,
inverse(A) = double_divide(A,identity),
inference(clausify,[status(thm)],[inverse]) ).
fof(identity,axiom,
! [VAR_0] : identity = double_divide(VAR_0,inverse(VAR_0)),
file('theBenchmark.p',identity) ).
cnf(c_4,plain,
identity = double_divide(A,inverse(A)),
inference(clausify,[status(thm)],[identity]) ).
cnf(c_304,plain,
identity = double_divide(A,double_divide(A,identity)),
inference(paramod,[status(thm)],[c_3,c_4]) ).
cnf(c_5,plain,
double_divide(A,double_divide(A,identity)) = identity,
inference(copy,[status(thm)],[c_304]) ).
fof(prove_these_axioms_3,axiom,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
file('theBenchmark.p',prove_these_axioms_3) ).
cnf(c_6,plain,
multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3)),
inference(clausify,[status(thm)],[prove_these_axioms_3]) ).
cnf(c_305,plain,
multiply(double_divide(double_divide(b3,a3),identity),c3) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_6]) ).
cnf(c_306,plain,
double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != multiply(a3,multiply(b3,c3)),
inference(paramod,[status(thm)],[c_2,c_305]) ).
cnf(c_307,plain,
double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity) != multiply(a3,double_divide(double_divide(c3,b3),identity)),
inference(paramod,[status(thm)],[c_2,c_306]) ).
cnf(c_308,plain,
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),
inference(paramod,[status(thm)],[c_2,c_307]) ).
cnf(c_7,plain,
double_divide(double_divide(double_divide(double_divide(c3,b3),identity),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(copy,[status(thm)],[c_308]) ).
cnf(c_309,plain,
double_divide(double_divide(A,B),double_divide(identity,identity)) = double_divide(double_divide(double_divide(double_divide(A,identity),C),B),double_divide(C,identity)),
inference(paramod,[status(thm)],[c_1,c_1]) ).
cnf(c_8,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),B),C),double_divide(B,identity)) = double_divide(double_divide(A,C),double_divide(identity,identity)),
inference(copy,[status(thm)],[c_309]) ).
cnf(c_9,plain,
double_divide(double_divide(A,double_divide(double_divide(identity,B),double_divide(double_divide(A,identity),identity))),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_10,plain,
double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),double_divide(identity,identity)) = double_divide(double_divide(A,B),identity),
inference(paramod,[status(thm)],[c_5,c_1]) ).
cnf(c_310,plain,
double_divide(A,double_divide(double_divide(double_divide(double_divide(double_divide(B,identity),C),A),double_divide(C,identity)),identity)) = double_divide(double_divide(B,double_divide(identity,identity)),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_1,c_8]) ).
cnf(c_13,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),double_divide(identity,identity)),identity)) = double_divide(double_divide(B,double_divide(identity,identity)),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_8,c_310]) ).
cnf(c_14,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,identity),identity),identity)) = double_divide(double_divide(B,A),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_311,plain,
double_divide(identity,double_divide(A,identity)) = double_divide(double_divide(B,double_divide(double_divide(double_divide(B,identity),A),identity)),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_5,c_8]) ).
cnf(c_15,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),B),identity)),double_divide(identity,identity)) = double_divide(identity,double_divide(B,identity)),
inference(copy,[status(thm)],[c_311]) ).
cnf(c_312,plain,
double_divide(double_divide(double_divide(A,B),double_divide(identity,identity)),double_divide(B,identity)) = double_divide(double_divide(double_divide(A,identity),double_divide(identity,identity)),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_8,c_8]) ).
cnf(c_16,plain,
double_divide(double_divide(double_divide(A,identity),double_divide(identity,identity)),double_divide(identity,identity)) = double_divide(double_divide(double_divide(A,B),double_divide(identity,identity)),double_divide(B,identity)),
inference(copy,[status(thm)],[c_312]) ).
cnf(c_17,plain,
double_divide(double_divide(identity,identity),double_divide(identity,identity)) = identity,
inference(paramod,[status(thm)],[c_5,c_9]) ).
cnf(c_19,plain,
double_divide(double_divide(A,identity),double_divide(identity,identity)) = double_divide(double_divide(A,identity),identity),
inference(paramod,[status(thm)],[c_5,c_10]) ).
cnf(c_313,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),B),identity) = double_divide(double_divide(A,double_divide(identity,double_divide(B,identity))),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_10,c_8]) ).
cnf(c_21,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),B),identity) = double_divide(double_divide(A,B),identity),
inference(paramod,[status(thm)],[c_10,c_313]) ).
cnf(c_22,plain,
double_divide(double_divide(identity,identity),identity) = identity,
inference(paramod,[status(thm)],[c_19,c_17]) ).
cnf(c_314,plain,
double_divide(double_divide(double_divide(A,identity),identity),double_divide(identity,identity)) = double_divide(double_divide(double_divide(A,B),double_divide(identity,identity)),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_19,c_16]) ).
cnf(c_23,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(double_divide(double_divide(A,B),double_divide(identity,identity)),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_19,c_314]) ).
cnf(c_24,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,double_divide(identity,identity)),B),identity)),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_22,c_1]) ).
cnf(c_315,plain,
double_divide(double_divide(double_divide(identity,A),B),double_divide(A,identity)) = double_divide(double_divide(double_divide(identity,identity),B),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_22,c_8]) ).
cnf(c_25,plain,
double_divide(double_divide(double_divide(identity,identity),A),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,B),A),double_divide(B,identity)),
inference(copy,[status(thm)],[c_315]) ).
cnf(c_316,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),double_divide(identity,identity)),B),identity) = double_divide(double_divide(A,B),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_22,c_8]) ).
cnf(c_317,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),identity),B),identity) = double_divide(double_divide(A,B),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_19,c_316]) ).
cnf(c_318,plain,
double_divide(double_divide(A,B),identity) = double_divide(double_divide(A,B),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_21,c_317]) ).
cnf(c_26,plain,
double_divide(double_divide(A,B),double_divide(identity,identity)) = double_divide(double_divide(A,B),identity),
inference(copy,[status(thm)],[c_318]) ).
cnf(c_319,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,A),double_divide(identity,identity))),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_22,c_9]) ).
cnf(c_320,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,A),identity)),double_divide(identity,identity)) = A,
inference(paramod,[status(thm)],[c_26,c_319]) ).
cnf(c_28,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(double_divide(identity,A),identity)),identity) = A,
inference(paramod,[status(thm)],[c_26,c_320]) ).
cnf(c_321,plain,
double_divide(double_divide(double_divide(identity,identity),double_divide(identity,double_divide(identity,identity))),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_22,c_10]) ).
cnf(c_322,plain,
double_divide(double_divide(double_divide(identity,identity),identity),double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_321]) ).
cnf(c_323,plain,
double_divide(identity,double_divide(identity,identity)) = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_22,c_322]) ).
cnf(c_324,plain,
identity = double_divide(identity,identity),
inference(paramod,[status(thm)],[c_5,c_323]) ).
cnf(c_30,plain,
double_divide(identity,identity) = identity,
inference(copy,[status(thm)],[c_324]) ).
cnf(c_325,plain,
double_divide(double_divide(identity,A),double_divide(identity,identity)) = double_divide(double_divide(double_divide(identity,B),A),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_30,c_25]) ).
cnf(c_326,plain,
double_divide(double_divide(identity,A),identity) = double_divide(double_divide(double_divide(identity,B),A),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_30,c_325]) ).
cnf(c_31,plain,
double_divide(double_divide(double_divide(identity,A),B),double_divide(A,identity)) = double_divide(double_divide(identity,B),identity),
inference(copy,[status(thm)],[c_326]) ).
cnf(c_327,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),B),identity)),double_divide(identity,identity)) = B,
inference(paramod,[status(thm)],[c_30,c_24]) ).
cnf(c_32,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),B),identity)),identity) = B,
inference(paramod,[status(thm)],[c_30,c_327]) ).
cnf(c_33,plain,
double_divide(double_divide(double_divide(A,identity),identity),identity) = double_divide(double_divide(double_divide(A,B),identity),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_30,c_23]) ).
cnf(c_328,plain,
double_divide(double_divide(A,double_divide(double_divide(double_divide(A,identity),B),identity)),identity) = double_divide(identity,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_30,c_15]) ).
cnf(c_329,plain,
B = double_divide(identity,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_32,c_328]) ).
cnf(c_36,plain,
double_divide(identity,double_divide(A,identity)) = A,
inference(copy,[status(thm)],[c_329]) ).
cnf(c_37,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(double_divide(B,identity),identity),identity)) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_30,c_14]) ).
cnf(c_330,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),identity),identity)) = double_divide(double_divide(B,double_divide(identity,identity)),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_30,c_13]) ).
cnf(c_331,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),identity),identity)) = double_divide(double_divide(B,identity),double_divide(identity,identity)),
inference(paramod,[status(thm)],[c_30,c_330]) ).
cnf(c_38,plain,
double_divide(A,double_divide(double_divide(double_divide(B,A),identity),identity)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_30,c_331]) ).
cnf(c_42,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),B),C),double_divide(B,identity)) = double_divide(double_divide(A,C),identity),
inference(paramod,[status(thm)],[c_30,c_8]) ).
cnf(c_332,plain,
double_divide(double_divide(identity,double_divide(double_divide(identity,A),identity)),identity) = A,
inference(paramod,[status(thm)],[c_30,c_28]) ).
cnf(c_44,plain,
double_divide(double_divide(identity,A),identity) = A,
inference(paramod,[status(thm)],[c_36,c_332]) ).
cnf(c_45,plain,
double_divide(double_divide(double_divide(identity,A),B),double_divide(A,identity)) = B,
inference(paramod,[status(thm)],[c_44,c_31]) ).
cnf(c_46,plain,
double_divide(double_divide(identity,A),A) = identity,
inference(paramod,[status(thm)],[c_44,c_5]) ).
cnf(c_47,plain,
double_divide(double_divide(A,B),double_divide(double_divide(A,identity),identity)) = B,
inference(paramod,[status(thm)],[c_36,c_45]) ).
cnf(c_333,plain,
double_divide(identity,double_divide(double_divide(A,B),identity)) = double_divide(double_divide(double_divide(A,identity),identity),B),
inference(paramod,[status(thm)],[c_21,c_36]) ).
cnf(c_334,plain,
double_divide(A,B) = double_divide(double_divide(double_divide(A,identity),identity),B),
inference(paramod,[status(thm)],[c_36,c_333]) ).
cnf(c_50,plain,
double_divide(double_divide(double_divide(A,identity),identity),B) = double_divide(A,B),
inference(copy,[status(thm)],[c_334]) ).
cnf(c_53,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(double_divide(B,A),identity),
inference(paramod,[status(thm)],[c_50,c_37]) ).
cnf(c_335,plain,
double_divide(A,identity) = double_divide(double_divide(double_divide(A,B),identity),double_divide(B,identity)),
inference(paramod,[status(thm)],[c_50,c_33]) ).
cnf(c_54,plain,
double_divide(double_divide(double_divide(A,B),identity),double_divide(B,identity)) = double_divide(A,identity),
inference(copy,[status(thm)],[c_335]) ).
cnf(c_336,plain,
double_divide(double_divide(double_divide(A,identity),identity),double_divide(B,identity)) = double_divide(double_divide(double_divide(A,double_divide(identity,B)),identity),identity),
inference(paramod,[status(thm)],[c_38,c_45]) ).
cnf(c_337,plain,
double_divide(A,double_divide(B,identity)) = double_divide(double_divide(double_divide(A,double_divide(identity,B)),identity),identity),
inference(paramod,[status(thm)],[c_50,c_336]) ).
cnf(c_59,plain,
double_divide(double_divide(double_divide(A,double_divide(identity,B)),identity),identity) = double_divide(A,double_divide(B,identity)),
inference(copy,[status(thm)],[c_337]) ).
cnf(c_338,plain,
double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),identity)) = double_divide(double_divide(double_divide(double_divide(identity,A),B),identity),identity),
inference(paramod,[status(thm)],[c_45,c_38]) ).
cnf(c_60,plain,
double_divide(double_divide(double_divide(double_divide(identity,A),B),identity),identity) = double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),identity)),
inference(copy,[status(thm)],[c_338]) ).
cnf(c_339,plain,
double_divide(double_divide(double_divide(double_divide(A,B),identity),identity),double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),identity)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_38,c_38]) ).
cnf(c_340,plain,
double_divide(double_divide(double_divide(double_divide(A,B),identity),identity),double_divide(double_divide(A,identity),identity)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_50,c_339]) ).
cnf(c_341,plain,
double_divide(double_divide(A,B),double_divide(double_divide(A,identity),identity)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_50,c_340]) ).
cnf(c_342,plain,
B = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_47,c_341]) ).
cnf(c_61,plain,
double_divide(double_divide(A,identity),identity) = A,
inference(copy,[status(thm)],[c_342]) ).
cnf(c_343,plain,
double_divide(double_divide(double_divide(double_divide(A,B),identity),identity),double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),identity)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_38,c_38]) ).
cnf(c_344,plain,
double_divide(double_divide(A,B),double_divide(double_divide(double_divide(double_divide(A,identity),identity),identity),identity)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_61,c_343]) ).
cnf(c_345,plain,
double_divide(double_divide(A,B),double_divide(double_divide(A,identity),identity)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_61,c_344]) ).
cnf(c_346,plain,
double_divide(double_divide(A,B),A) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_61,c_345]) ).
cnf(c_62,plain,
double_divide(double_divide(A,B),A) = B,
inference(paramod,[status(thm)],[c_61,c_346]) ).
cnf(c_347,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(A,identity),double_divide(double_divide(B,identity),identity)),
inference(paramod,[status(thm)],[c_61,c_60]) ).
cnf(c_63,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(A,identity),B),
inference(paramod,[status(thm)],[c_61,c_347]) ).
cnf(c_348,plain,
double_divide(double_divide(identity,double_divide(A,double_divide(identity,B))),identity) = double_divide(A,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_63,c_59]) ).
cnf(c_64,plain,
double_divide(A,double_divide(identity,B)) = double_divide(A,double_divide(B,identity)),
inference(paramod,[status(thm)],[c_62,c_348]) ).
cnf(c_349,plain,
double_divide(A,double_divide(double_divide(identity,double_divide(B,A)),identity)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_63,c_38]) ).
cnf(c_350,plain,
double_divide(A,double_divide(B,A)) = double_divide(double_divide(B,identity),identity),
inference(paramod,[status(thm)],[c_62,c_349]) ).
cnf(c_66,plain,
double_divide(A,double_divide(B,A)) = B,
inference(paramod,[status(thm)],[c_61,c_350]) ).
cnf(c_67,plain,
double_divide(double_divide(identity,double_divide(A,B)),double_divide(B,identity)) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_63,c_54]) ).
cnf(c_351,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),a3),identity) != double_divide(double_divide(c3,double_divide(double_divide(b3,a3),identity)),identity),
inference(paramod,[status(thm)],[c_63,c_7]) ).
cnf(c_68,plain,
double_divide(double_divide(double_divide(identity,double_divide(c3,b3)),a3),identity) != double_divide(double_divide(c3,double_divide(identity,double_divide(b3,a3))),identity),
inference(paramod,[status(thm)],[c_64,c_351]) ).
cnf(c_72,plain,
double_divide(identity,A) = double_divide(A,identity),
inference(paramod,[status(thm)],[c_5,c_62]) ).
cnf(c_73,plain,
double_divide(identity,double_divide(identity,A)) = A,
inference(paramod,[status(thm)],[c_46,c_62]) ).
cnf(c_352,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(double_divide(c3,double_divide(identity,double_divide(b3,a3))),identity),
inference(paramod,[status(thm)],[c_72,c_68]) ).
cnf(c_76,plain,
double_divide(identity,double_divide(double_divide(identity,double_divide(c3,b3)),a3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_72,c_352]) ).
cnf(c_77,plain,
double_divide(double_divide(identity,A),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_72,c_53]) ).
cnf(c_80,plain,
double_divide(double_divide(double_divide(double_divide(A,identity),B),C),double_divide(B,identity)) = double_divide(identity,double_divide(A,C)),
inference(paramod,[status(thm)],[c_72,c_42]) ).
cnf(c_84,plain,
double_divide(double_divide(identity,A),double_divide(B,double_divide(A,identity))) = B,
inference(paramod,[status(thm)],[c_63,c_66]) ).
cnf(c_353,plain,
double_divide(double_divide(identity,A),double_divide(double_divide(B,identity),identity)) = double_divide(double_divide(double_divide(identity,B),A),identity),
inference(paramod,[status(thm)],[c_45,c_67]) ).
cnf(c_354,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(B,identity))) = double_divide(double_divide(double_divide(identity,B),A),identity),
inference(paramod,[status(thm)],[c_72,c_353]) ).
cnf(c_355,plain,
double_divide(double_divide(identity,A),B) = double_divide(double_divide(double_divide(identity,B),A),identity),
inference(paramod,[status(thm)],[c_66,c_354]) ).
cnf(c_89,plain,
double_divide(double_divide(identity,A),B) = double_divide(identity,double_divide(double_divide(identity,B),A)),
inference(paramod,[status(thm)],[c_72,c_355]) ).
cnf(c_92,plain,
double_divide(double_divide(A,identity),double_divide(B,identity)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_67,c_66]) ).
cnf(c_356,plain,
double_divide(double_divide(identity,a3),double_divide(double_divide(identity,double_divide(c3,b3)),identity)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_77,c_76]) ).
cnf(c_357,plain,
double_divide(double_divide(identity,a3),double_divide(identity,double_divide(identity,double_divide(c3,b3)))) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_72,c_356]) ).
cnf(c_110,plain,
double_divide(double_divide(identity,a3),double_divide(c3,b3)) != double_divide(identity,double_divide(c3,double_divide(identity,double_divide(b3,a3)))),
inference(paramod,[status(thm)],[c_73,c_357]) ).
cnf(c_118,plain,
double_divide(double_divide(A,identity),double_divide(identity,B)) = double_divide(identity,double_divide(B,A)),
inference(paramod,[status(thm)],[c_72,c_92]) ).
cnf(c_232,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(identity,double_divide(double_divide(double_divide(C,identity),double_divide(identity,B)),A)),
inference(paramod,[status(thm)],[c_118,c_89]) ).
cnf(c_358,plain,
double_divide(double_divide(identity,A),double_divide(identity,double_divide(B,C))) = double_divide(double_divide(double_divide(B,identity),A),C),
inference(paramod,[status(thm)],[c_80,c_84]) ).
cnf(c_295,plain,
double_divide(double_divide(double_divide(A,identity),B),C) = double_divide(double_divide(identity,B),double_divide(identity,double_divide(A,C))),
inference(copy,[status(thm)],[c_358]) ).
cnf(c_359,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(identity,double_divide(double_divide(identity,double_divide(identity,B)),double_divide(identity,double_divide(C,A)))),
inference(paramod,[status(thm)],[c_295,c_232]) ).
cnf(c_302,plain,
double_divide(double_divide(identity,A),double_divide(B,C)) = double_divide(identity,double_divide(B,double_divide(identity,double_divide(C,A)))),
inference(paramod,[status(thm)],[c_73,c_359]) ).
cnf(c_303,plain,
$false,
inference(resolve,[status(thm)],[c_302,c_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GRP486-1 : TPTP v9.3.1. Released v2.6.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/10.44 % Computer : n001.cluster.edu
% 0.17/10.44 % Model : x86_64 x86_64
% 0.17/10.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.44 % Memory : 8046.5625MB
% 0.17/10.44 % OS : Linux 6.8.0-71-generic
% 0.17/10.44 % CPULimit : 300
% 0.17/10.44 % WCLimit : 300
% 0.17/10.44 % DateTime : Fri Sep 25 15:02:36 UTC 2026
% 0.17/10.44 % CPUTime :
% 0.17/10.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/10.45 % Process 3612566 was started by sandbox2 on n001,
% 0.17/10.45 % Fri Sep 25 15:02:36 2026
% 0.17/10.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/10.45
% 0.17/10.45 % From the command line: assign(max_seconds, 300).
% 0.21/10.55
% 0.21/10.55 % SZS status Unsatisfiable for theBenchmark
% 0.21/10.55
% 0.21/10.55 % Proof 1 at 0.06 (+ 0.02) seconds.
% 0.21/10.55 % Length of proof is 61.
% 0.21/10.55 % Level of proof is 18.
% 0.21/10.55 % Maximum clause weight is 83.000.
% 0.21/10.55 % Given clauses 48.
% 0.21/10.55
% 0.21/10.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------