%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP013-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:24:56 PM UTC 2026
% Result : Unsatisfiable 7.80s 1.45s
% Output : Proof 7.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 9
% Syntax : Number of formulae : 69 ( 61 unt; 0 def)
% Number of atoms : 81 ( 42 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 31 ( 19 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 81 ( 2 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t10,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)],[t10]) ).
cnf(f9,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b_is_c) ).
fof(f9_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(t2,plain,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t38,plain,
product(a,b,c) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(t39,plain,
X1 = ifeq(true,true,ifeq(product(a,b,X1),true,c,X1),X1),
inference(cp,[status(thm)],[t15,t38]) ).
cnf(t4,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t14,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t4]) ).
cnf(t231,plain,
X1 = ifeq(product(a,b,X1),true,c,X1),
inference(step,[status(thm)],[t39,t14]) ).
cnf(t207,plain,
ifeq(product(a,b,X1),true,c,X1) = X1,
inference(orient,[status(thm)],[t231]) ).
cnf(f10,hypothesis,
product(inverse(a),inverse(b),d),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverse_a_times_inverse_b_is_d) ).
fof(f10_nnf,plain,
product(inverse(a),inverse(b),d),
inference(nnf_transformation,[status(thm)],[f10]) ).
cnf(c10,plain,
product(inverse(a),inverse(b),d),
inference(cnf_transformation,[status(esa)],[f10_nnf]) ).
cnf(t8,plain,
product(inverse(a),inverse(b),d) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t35,plain,
product(inverse(a),inverse(b),d) = true,
inference(orient,[status(thm)],[t8]) ).
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(t1,plain,
product(X1,identity,X1) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t23,plain,
product(X1,identity,X1) = true,
inference(orient,[status(thm)],[t1]) ).
cnf(t24,plain,
X1 = ifeq(true,true,ifeq(product(X2,identity,X1),true,X2,X1),X1),
inference(cp,[status(thm)],[t15,t23]) ).
cnf(t220,plain,
X1 = ifeq(product(X2,identity,X1),true,X2,X1),
inference(step,[status(thm)],[t24,t14]) ).
cnf(t177,plain,
ifeq(product(X1,identity,X2),true,X1,X2) = X2,
inference(orient,[status(thm)],[t220]) ).
cnf(f11,hypothesis,
( product(A,C,B)
| ~ product(inverse(A),inverse(B),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inverses_have_property) ).
fof(f11_nnf,plain,
! [A,B,C] :
( product(A,C,B)
| ~ product(inverse(A),inverse(B),C) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [A,B,C] :
( product(A,C,B)
| ~ product(inverse(A),inverse(B),C) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( product(X0,X2,X1)
| ~ product(inverse(X0),inverse(X1),X2) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(t9,plain,
ifeq(product(inverse(X1),inverse(X2),X3),true,product(X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(t109,plain,
ifeq(product(inverse(X1),inverse(X2),X3),true,product(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t9]) ).
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(t5,plain,
product(X1,inverse(X1),identity) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t26,plain,
product(X1,inverse(X1),identity) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t112,plain,
true = ifeq(true,true,product(X1,identity,inverse(X1)),true),
inference(cp,[status(thm)],[t109,t26]) ).
cnf(t215,plain,
true = product(X1,identity,inverse(X1)),
inference(step,[status(thm)],[t112,t14]) ).
cnf(t158,plain,
product(X1,identity,inverse(X1)) = true,
inference(orient,[status(thm)],[t215]) ).
cnf(t178,plain,
inverse(X1) = ifeq(true,true,X1,inverse(X1)),
inference(cp,[status(thm)],[t177,t158]) ).
cnf(t221,plain,
inverse(X1) = X1,
inference(step,[status(thm)],[t178,t14]) ).
cnf(t185,plain,
inverse(X1) = X1,
inference(orient,[status(thm)],[t221]) ).
cnf(t222,plain,
product(a,inverse(b),d) = true,
inference(step,[status(thm)],[t35,t185]) ).
cnf(t223,plain,
product(a,b,d) = true,
inference(step,[status(thm)],[t222,t185]) ).
cnf(t186,plain,
product(a,b,d) = true,
inference(rw,[status(thm)],[t223]) ).
cnf(t189,plain,
product(a,b,d) = true,
inference(orient,[status(thm)],[t186]) ).
cnf(t208,plain,
d = ifeq(true,true,c,d),
inference(cp,[status(thm)],[t207,t189]) ).
cnf(t232,plain,
d = c,
inference(step,[status(thm)],[t208,t14]) ).
cnf(t210,plain,
c = d,
inference(orient,[status(thm)],[t232]) ).
cnf(f8,hypothesis,
product(A,A,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',squareness) ).
fof(f8_nnf,plain,
! [A] : product(A,A,identity),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] : product(A,A,identity),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
product(X0,X0,identity),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(t0,plain,
product(X1,X1,identity) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t20,plain,
product(X1,X1,identity) = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f12,negated_conjecture,
~ product(c,d,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_c_times_d_is_identity) ).
fof(f12_nnf,plain,
~ product(c,d,identity),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
~ product(c,d,identity),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
~ product(c,d,identity),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(goal_0,negated_conjecture,
product(c,d,identity) != true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(g0_0,plain,
product(d,d,identity) != true,
inference(rw,[status(thm)],[goal_0,t210]) ).
cnf(g0_1,plain,
true != true,
inference(rw,[status(thm)],[g0_0,t20]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP013-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n007.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 : Wed Sep 23 13:12:06 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 7.80/1.45 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 7.80/1.45 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------