%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 10.08s 1.87s
% Output : Proof 10.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 55 ( 43 unt; 0 def)
% Number of atoms : 87 ( 24 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 70 ( 38 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 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 : 100 ( 0 sgn 40 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( product(X,V,W)
| ~ product(U,Z,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/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(hi6,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X2,X3,X5),true,product(X0,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f2,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f2_nnf,plain,
! [X] : product(inverse(X),X,identity),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X] : product(inverse(X),X,identity),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
product(inverse(X0),X0,identity) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f8,hypothesis,
product(a,b,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_multiply_b_is_c) ).
fof(f8_nnf,plain,
product(a,b,c),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
product(a,b,c),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(hi8,axiom,
product(a,b,c) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f0,axiom,
product(identity,X,X),
file('/export/starexec/sandbox/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(hi0,axiom,
product(identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h4,plain,
product(inverse(a),c,b) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi2,hi8,hi0]) ).
cnf(f7,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).
fof(f7_nnf,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y,U,Z,V,W] :
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X1,X3,X4),true,ifeq(product(X0,X4,X5),true,product(X2,X3,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f9,hypothesis,
product(inverse(b),inverse(a),d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse_b_multiply_inverse_a_is_d) ).
fof(f9_nnf,plain,
product(inverse(b),inverse(a),d),
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
product(inverse(b),inverse(a),d),
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(hi9,axiom,
product(inverse(b),inverse(a),d) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h240,plain,
product(d,c,identity) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi9,h4,hi2]) ).
cnf(f3,axiom,
product(X,inverse(X),identity),
file('/export/starexec/sandbox/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(hi3,axiom,
product(X0,inverse(X0),identity) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f1,axiom,
product(X,identity,X),
file('/export/starexec/sandbox/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(hi1,axiom,
product(X0,identity,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h276,plain,
product(identity,inverse(c),d) = true,
inference(hyper_resolution,[status(thm)],[hi7,h240,hi3,hi1]) ).
cnf(f5,axiom,
( Z = W
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox/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(hi5,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,X2,X3),X3) = X3,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t0,plain,
inverse(c) = d,
inference(hyper_resolution,[status(thm)],[hi5,hi0,h276]) ).
cnf(t268,plain,
inverse(c) = d,
inference(orient,[status(thm)],[t0]) ).
cnf(f10,negated_conjecture,
inverse(c) != d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_c_inverse_equals_d) ).
fof(f10_nnf,plain,
inverse(c) != d,
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
inverse(c) != d,
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
inverse(c) != d,
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(goal_0,negated_conjecture,
inverse(c) != d,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(g0_0,plain,
d != d,
inference(rw,[status(thm)],[goal_0,t268]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP012-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n009.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 13:13:13 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 10.08/1.87 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.08/1.87 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------