%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP044-2 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 01:25:02 PM UTC 2026
% Result : Unsatisfiable 6.25s 1.22s
% Output : Proof 6.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 45 ( 33 unt; 0 def)
% Number of atoms : 77 ( 14 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 : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-4 aty)
% Number of variables : 95 ( 0 sgn 38 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,hypothesis,
product(a,c,result),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_with_a) ).
fof(f8_nnf,plain,
product(a,c,result),
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
product(a,c,result),
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(hi8,axiom,
product(a,c,result) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h0,plain,
product(a,c,result) = true,
inference(hyper_resolution,[status(thm)],[hi8]) ).
cnf(f4,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(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(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(f2,axiom,
product(X,Y,multiply(X,Y)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).
fof(f2_nnf,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : product(X,Y,multiply(X,Y)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
product(X0,X1,multiply(X0,X1)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
product(X0,X1,multiply(X0,X1)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h1,plain,
product(identity,multiply(a,c),result) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi0,hi2,h0]) ).
cnf(f6,axiom,
( product(W,Z,Y)
| ~ product(W,Z,X)
| ~ equalish(X,Y) ),
file('/export/starexec/sandbox/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/sandbox/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(h2,plain,
product(identity,a,b) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi7,hi0]) ).
cnf(f5,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(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(t2,plain,
product(b,c,result) = true,
inference(hyper_resolution,[status(thm)],[hi5,h2,hi2,h1]) ).
cnf(t14,plain,
product(b,c,result) = true,
inference(orient,[status(thm)],[t2]) ).
cnf(f9,negated_conjecture,
~ product(b,c,result),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_with_b) ).
fof(f9_nnf,plain,
~ product(b,c,result),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
~ product(b,c,result),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
~ product(b,c,result),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(goal_0,negated_conjecture,
product(b,c,result) != true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t14]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP044-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.36 % Computer : n026.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Wed Sep 23 13:25:23 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.25/1.22 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.25/1.22 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------