%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 01:24:55 PM UTC 2026
% Result : Unsatisfiable 10.52s 1.91s
% Output : Proof 10.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 12
% Syntax : Number of formulae : 118 ( 110 unt; 0 def)
% Number of atoms : 138 ( 97 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 50 ( 30 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 2 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 8 con; 0-4 aty)
% Number of variables : 183 ( 2 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(t10,axiom,
sFlat1 = inverse(a),
introduced(definition) ).
cnf(t76,plain,
inverse(a) = sFlat1,
inference(orient,[status(thm)],[t10]) ).
cnf(t9,axiom,
sFlat0 = inverse(b),
introduced(definition) ).
cnf(t79,plain,
inverse(b) = sFlat0,
inference(orient,[status(thm)],[t9]) ).
cnf(f5,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
fof(f5_nnf,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y,Z,W] :
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( X2 = X3
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(t6,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t15,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,X3,X4),X4) = X4,
inference(orient,[status(thm)],[t6]) ).
cnf(f4,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function1) ).
fof(f4_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(t5,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t17,plain,
product(X1,X2,multiply(X1,X2)) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t19,plain,
multiply(X1,X2) = ifeq(product(X1,X2,X3),true,ifeq(true,true,X3,multiply(X1,X2)),multiply(X1,X2)),
inference(cp,[status(thm)],[t15,t17]) ).
cnf(t2,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t2]) ).
cnf(t1068,plain,
multiply(X1,X2) = ifeq(product(X1,X2,X3),true,X3,multiply(X1,X2)),
inference(step,[status(thm)],[t19,t14]) ).
cnf(t235,plain,
ifeq(product(X1,X2,X3),true,X3,multiply(X1,X2)) = multiply(X1,X2),
inference(orient,[status(thm)],[t1068]) ).
cnf(f6,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity1) ).
fof(f6_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,U,Z,V,W] :
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(t8,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X2,X4,X5),true,ifeq(product(X3,X4,X6),true,product(X1,X5,X6),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t32,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(X2,X4,X5),true,ifeq(product(X3,X4,X6),true,product(X1,X5,X6),true),true),true) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(t33,plain,
true = ifeq(true,true,ifeq(product(X1,X2,X3),true,ifeq(product(multiply(X4,X1),X2,X5),true,product(X4,X3,X5),true),true),true),
inference(cp,[status(thm)],[t32,t17]) ).
cnf(t1084,plain,
true = ifeq(product(X1,X2,X3),true,ifeq(product(multiply(X4,X1),X2,X5),true,product(X4,X3,X5),true),true),
inference(step,[status(thm)],[t33,t14]) ).
cnf(t359,plain,
ifeq(product(X1,X2,X3),true,ifeq(product(multiply(X4,X1),X2,X5),true,product(X4,X3,X5),true),true) = true,
inference(orient,[status(thm)],[t1084]) ).
cnf(f3,axiom,
product(X,inverse(X),identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_inverse) ).
fof(f3_nnf,plain,
! [X] : product(X,inverse(X),identity),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X] : product(X,inverse(X),identity),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
product(X0,inverse(X0),identity),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t3,plain,
product(X1,inverse(X1),identity) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t20,plain,
product(X1,inverse(X1),identity) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(t13,axiom,
sFlat4 = inverse(multiply(a,b)),
introduced(definition) ).
cnf(t82,plain,
inverse(multiply(a,b)) = sFlat4,
inference(orient,[status(thm)],[t13]) ).
cnf(t12,axiom,
sFlat3 = multiply(a,b),
introduced(definition) ).
cnf(t87,plain,
multiply(a,b) = sFlat3,
inference(orient,[status(thm)],[t12]) ).
cnf(t1031,plain,
inverse(sFlat3) = sFlat4,
inference(step,[status(thm)],[t82,t87]) ).
cnf(t89,plain,
inverse(sFlat3) = sFlat4,
inference(rw,[status(thm)],[t1031]) ).
cnf(t90,plain,
inverse(sFlat3) = sFlat4,
inference(orient,[status(thm)],[t89]) ).
cnf(t92,plain,
true = product(sFlat3,sFlat4,identity),
inference(cp,[status(thm)],[t20,t90]) ).
cnf(t170,plain,
product(sFlat3,sFlat4,identity) = true,
inference(orient,[status(thm)],[t92]) ).
cnf(t363,plain,
true = ifeq(true,true,ifeq(product(multiply(X1,sFlat3),sFlat4,X2),true,product(X1,identity,X2),true),true),
inference(cp,[status(thm)],[t359,t170]) ).
cnf(t1086,plain,
true = ifeq(product(multiply(X1,sFlat3),sFlat4,X2),true,product(X1,identity,X2),true),
inference(step,[status(thm)],[t363,t14]) ).
cnf(t494,plain,
ifeq(product(multiply(X1,sFlat3),sFlat4,X2),true,product(X1,identity,X2),true) = true,
inference(orient,[status(thm)],[t1086]) ).
cnf(t495,plain,
true = ifeq(true,true,product(X1,identity,multiply(multiply(X1,sFlat3),sFlat4)),true),
inference(cp,[status(thm)],[t494,t17]) ).
cnf(t1087,plain,
true = product(X1,identity,multiply(multiply(X1,sFlat3),sFlat4)),
inference(step,[status(thm)],[t495,t14]) ).
cnf(t504,plain,
product(X1,identity,multiply(multiply(X1,sFlat3),sFlat4)) = true,
inference(orient,[status(thm)],[t1087]) ).
cnf(t508,plain,
multiply(X1,identity) = ifeq(true,true,multiply(multiply(X1,sFlat3),sFlat4),multiply(X1,identity)),
inference(cp,[status(thm)],[t235,t504]) ).
cnf(f1,axiom,
product(X,identity,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_identity) ).
fof(f1_nnf,plain,
! [X] : product(X,identity,X),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : product(X,identity,X),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
product(X0,identity,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t0,plain,
product(X1,identity,X1) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t23,plain,
product(X1,identity,X1) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(t24,plain,
X1 = ifeq(true,true,ifeq(product(X2,identity,X1),true,X2,X1),X1),
inference(cp,[status(thm)],[t15,t23]) ).
cnf(t1032,plain,
X1 = ifeq(product(X2,identity,X1),true,X2,X1),
inference(step,[status(thm)],[t24,t14]) ).
cnf(t181,plain,
ifeq(product(X1,identity,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t1032]) ).
cnf(t182,plain,
multiply(X1,identity) = ifeq(true,true,X1,multiply(X1,identity)),
inference(cp,[status(thm)],[t181,t17]) ).
cnf(t1034,plain,
multiply(X1,identity) = X1,
inference(step,[status(thm)],[t182,t14]) ).
cnf(t189,plain,
multiply(X1,identity) = X1,
inference(orient,[status(thm)],[t1034]) ).
cnf(t1088,plain,
X1 = ifeq(true,true,multiply(multiply(X1,sFlat3),sFlat4),multiply(X1,identity)),
inference(step,[status(thm)],[t508,t189]) ).
cnf(t1089,plain,
X1 = multiply(multiply(X1,sFlat3),sFlat4),
inference(step,[status(thm)],[t1088,t14]) ).
cnf(t528,plain,
multiply(multiply(X1,sFlat3),sFlat4) = X1,
inference(orient,[status(thm)],[t1089]) ).
cnf(t35,plain,
true = ifeq(true,true,ifeq(product(inverse(X1),X2,X3),true,ifeq(product(identity,X2,X4),true,product(X1,X3,X4),true),true),true),
inference(cp,[status(thm)],[t32,t20]) ).
cnf(t1095,plain,
true = ifeq(product(inverse(X1),X2,X3),true,ifeq(product(identity,X2,X4),true,product(X1,X3,X4),true),true),
inference(step,[status(thm)],[t35,t14]) ).
cnf(t612,plain,
ifeq(product(inverse(X1),X2,X3),true,ifeq(product(identity,X2,X4),true,product(X1,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t1095]) ).
cnf(f0,axiom,
product(identity,X,X),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_identity) ).
fof(f0_nnf,plain,
! [X] : product(identity,X,X),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X] : product(identity,X,X),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
product(identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t1,plain,
product(identity,X1,X1) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t29,plain,
product(identity,X1,X1) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t633,plain,
true = ifeq(product(inverse(X1),X2,X3),true,ifeq(true,true,product(X1,X3,X2),true),true),
inference(cp,[status(thm)],[t612,t29]) ).
cnf(t1105,plain,
true = ifeq(product(inverse(X1),X2,X3),true,product(X1,X3,X2),true),
inference(step,[status(thm)],[t633,t14]) ).
cnf(t787,plain,
ifeq(product(inverse(X1),X2,X3),true,product(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t1105]) ).
cnf(t788,plain,
true = ifeq(true,true,product(X1,multiply(inverse(X1),X2),X2),true),
inference(cp,[status(thm)],[t787,t17]) ).
cnf(t1111,plain,
true = product(X1,multiply(inverse(X1),X2),X2),
inference(step,[status(thm)],[t788,t14]) ).
cnf(t885,plain,
product(X1,multiply(inverse(X1),X2),X2) = true,
inference(orient,[status(thm)],[t1111]) ).
cnf(t789,plain,
true = ifeq(true,true,product(X1,identity,inverse(inverse(X1))),true),
inference(cp,[status(thm)],[t787,t20]) ).
cnf(t1106,plain,
true = product(X1,identity,inverse(inverse(X1))),
inference(step,[status(thm)],[t789,t14]) ).
cnf(t802,plain,
product(X1,identity,inverse(inverse(X1))) = true,
inference(orient,[status(thm)],[t1106]) ).
cnf(t807,plain,
multiply(X1,identity) = ifeq(true,true,inverse(inverse(X1)),multiply(X1,identity)),
inference(cp,[status(thm)],[t235,t802]) ).
cnf(t1107,plain,
X1 = ifeq(true,true,inverse(inverse(X1)),multiply(X1,identity)),
inference(step,[status(thm)],[t807,t189]) ).
cnf(t1108,plain,
X1 = inverse(inverse(X1)),
inference(step,[status(thm)],[t1107,t14]) ).
cnf(t832,plain,
inverse(inverse(X1)) = X1,
inference(orient,[status(thm)],[t1108]) ).
cnf(t833,plain,
a = inverse(sFlat1),
inference(cp,[status(thm)],[t832,t76]) ).
cnf(t872,plain,
inverse(sFlat1) = a,
inference(orient,[status(thm)],[t833]) ).
cnf(t887,plain,
true = product(sFlat1,multiply(a,X1),X1),
inference(cp,[status(thm)],[t885,t872]) ).
cnf(t951,plain,
product(sFlat1,multiply(a,X1),X1) = true,
inference(orient,[status(thm)],[t887]) ).
cnf(t952,plain,
true = product(sFlat1,sFlat3,b),
inference(cp,[status(thm)],[t951,t87]) ).
cnf(t974,plain,
product(sFlat1,sFlat3,b) = true,
inference(orient,[status(thm)],[t952]) ).
cnf(t975,plain,
multiply(sFlat1,sFlat3) = ifeq(true,true,b,multiply(sFlat1,sFlat3)),
inference(cp,[status(thm)],[t235,t974]) ).
cnf(t1113,plain,
multiply(sFlat1,sFlat3) = b,
inference(step,[status(thm)],[t975,t14]) ).
cnf(t995,plain,
multiply(sFlat1,sFlat3) = b,
inference(orient,[status(thm)],[t1113]) ).
cnf(t997,plain,
sFlat1 = multiply(b,sFlat4),
inference(cp,[status(thm)],[t528,t995]) ).
cnf(t1011,plain,
multiply(b,sFlat4) = sFlat1,
inference(orient,[status(thm)],[t997]) ).
cnf(t834,plain,
b = inverse(sFlat0),
inference(cp,[status(thm)],[t832,t79]) ).
cnf(t878,plain,
inverse(sFlat0) = b,
inference(orient,[status(thm)],[t834]) ).
cnf(t886,plain,
true = product(sFlat0,multiply(b,X1),X1),
inference(cp,[status(thm)],[t885,t878]) ).
cnf(t919,plain,
product(sFlat0,multiply(b,X1),X1) = true,
inference(orient,[status(thm)],[t886]) ).
cnf(t921,plain,
multiply(sFlat0,multiply(b,X1)) = ifeq(true,true,X1,multiply(sFlat0,multiply(b,X1))),
inference(cp,[status(thm)],[t235,t919]) ).
cnf(t1112,plain,
multiply(sFlat0,multiply(b,X1)) = X1,
inference(step,[status(thm)],[t921,t14]) ).
cnf(t942,plain,
multiply(sFlat0,multiply(b,X1)) = X1,
inference(orient,[status(thm)],[t1112]) ).
cnf(f8,negated_conjecture,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_of_product_is_product_of_inverses) ).
fof(f8_nnf,plain,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
inverse(multiply(a,b)) != multiply(inverse(b),inverse(a)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
multiply(inverse(b),inverse(a)) != inverse(multiply(a,b)),
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
sFlat4 != inverse(multiply(a,b)),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
sFlat4 != multiply(inverse(b),sFlat1),
inference(rw,[status(thm)],[g0_0,t76]) ).
cnf(g0_2,plain,
sFlat4 != multiply(sFlat0,sFlat1),
inference(rw,[status(thm)],[g0_1,t79]) ).
cnf(g0_3,plain,
sFlat4 != multiply(sFlat0,multiply(b,sFlat4)),
inference(rw,[status(thm)],[g0_2,t1011]) ).
cnf(g0_4,plain,
sFlat4 != sFlat4,
inference(rw,[status(thm)],[g0_3,t942]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP012-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n019.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 13:13:34 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 10.52/1.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.52/1.91 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------