%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% 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 01:25:03 PM UTC 2026
% Result : Unsatisfiable 5.83s 1.20s
% Output : Proof 5.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 50 ( 34 unt; 0 def)
% Number of atoms : 90 ( 18 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 86 ( 46 ~; 40 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-4 aty)
% Number of variables : 112 ( 0 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,axiom,
( product(W,Z,Y)
| ~ product(W,Z,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_substitution3) ).
fof(f6_nnf,plain,
! [X,Y,W,Z] :
( product(W,Z,Y)
| ~ product(W,Z,X)
| ~ equalish(X,Y) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,W,Z] :
( product(W,Z,Y)
| ~ product(W,Z,X)
| ~ equalish(X,Y) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( product(X2,X3,X1)
| ~ product(X2,X3,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(equalish(X0,X1),true,ifeq(product(X2,X3,X0),true,product(X2,X3,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f7,hypothesis,
equalish(a,b),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).
fof(f7_nnf,plain,
equalish(a,b),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
equalish(a,b),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(hi7,axiom,
equalish(a,b) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
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(hi0,axiom,
product(identity,X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
product(identity,a,b) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi7,hi0]) ).
cnf(f4,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(f4_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)],[f4]) ).
fof(f4_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)],[f4_nnf]) ).
cnf(c4,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,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)],[c4]) ).
cnf(h2,plain,
product(identity,b,a) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi0,h0,hi0]) ).
cnf(f1,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_inverse) ).
fof(f1_nnf,plain,
! [X] : product(inverse(X),X,identity),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X] : product(inverse(X),X,identity),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
product(inverse(X0),X0,identity) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h4,plain,
product(inverse(inverse(b)),identity,a) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi1,hi1,h2]) ).
cnf(f5,axiom,
( product(U,Z,W)
| ~ product(X,V,W)
| ~ product(Y,Z,V)
| ~ product(X,Y,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',associativity2) ).
fof(f5_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)],[f5]) ).
fof(f5_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)],[f5_nnf]) ).
cnf(c5,plain,
( product(X2,X3,X5)
| ~ product(X0,X4,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,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)],[c5]) ).
cnf(h154,plain,
product(a,inverse(b),identity) = true,
inference(hyper_resolution,[status(thm)],[hi5,h4,hi0,hi1]) ).
cnf(h334,plain,
product(inverse(a),identity,inverse(b)) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi1,h154,hi0]) ).
cnf(h6,plain,
product(inverse(inverse(V0)),identity,V0) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi1,hi1,hi0]) ).
cnf(h530,plain,
product(V0,identity,V0) = true,
inference(hyper_resolution,[status(thm)],[hi5,h6,hi0,h6]) ).
cnf(f3,axiom,
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',total_function2) ).
fof(f3_nnf,plain,
! [X,Y,Z,W] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z,W] :
( equalish(Z,W)
| ~ product(X,Y,W)
| ~ product(X,Y,Z) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( equalish(X2,X3)
| ~ product(X0,X1,X3)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X1,X3),true,equalish(X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t14,plain,
equalish(inverse(a),inverse(b)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h530,h334]) ).
cnf(t378,plain,
equalish(inverse(a),inverse(b)) = true,
inference(orient,[status(thm)],[t14]) ).
cnf(f8,negated_conjecture,
~ equalish(inverse(a),inverse(b)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_inverse_substitution) ).
fof(f8_nnf,plain,
~ equalish(inverse(a),inverse(b)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ equalish(inverse(a),inverse(b)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ equalish(inverse(a),inverse(b)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
equalish(inverse(a),inverse(b)) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t378]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP048-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n017.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 13:19:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.83/1.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.83/1.20 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------