%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n016.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 01:25:01 PM UTC 2026
% Result : Unsatisfiable 38.93s 5.45s
% Output : Proof 38.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 14
% Syntax : Number of formulae : 85 ( 31 unt; 0 def)
% Number of atoms : 189 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 178 ( 74 ~; 104 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 122 ( 0 sgn 52 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f17,axiom,
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',property_of_O2) ).
fof(f17_nnf,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| product(A,element_in_O2(A,B),B) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( subgroup_member(X0)
| subgroup_member(X1)
| product(X0,element_in_O2(X0,X1),X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(f14,axiom,
( equalish(D,B)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_right_cancellation) ).
fof(f14_nnf,plain,
! [A,B,C,D] :
( equalish(D,B)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C,D] :
( equalish(D,B)
| ~ product(A,D,C)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( equalish(X3,X1)
| ~ product(X0,X3,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(f20,negated_conjecture,
product(a,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_c_is_d) ).
fof(f20_nnf,plain,
product(a,c,d),
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
product(a,c,d),
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(p104,plain,
( equalish(X0,c)
| ~ product(a,X0,d) ),
inference(resolution,[status(thm)],[c14,c20]) ).
cnf(p143,plain,
( equalish(element_in_O2(a,d),c)
| subgroup_member(a)
| subgroup_member(d) ),
inference(resolution,[status(thm)],[c17,p104]) ).
cnf(f0,axiom,
( subgroup_member(B)
| ~ subgroup_member(A)
| ~ equalish(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subgroup_member_substitution) ).
fof(f0_nnf,plain,
! [A,B] :
( subgroup_member(B)
| ~ subgroup_member(A)
| ~ equalish(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( subgroup_member(B)
| ~ subgroup_member(A)
| ~ equalish(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( subgroup_member(X1)
| ~ subgroup_member(X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p256,plain,
( subgroup_member(c)
| ~ subgroup_member(element_in_O2(a,d))
| subgroup_member(a)
| subgroup_member(d) ),
inference(resolution,[status(thm)],[p143,c0]) ).
cnf(f16,axiom,
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',an_element_in_O2) ).
fof(f16_nnf,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B] :
( subgroup_member(A)
| subgroup_member(B)
| subgroup_member(element_in_O2(A,B)) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( subgroup_member(X0)
| subgroup_member(X1)
| subgroup_member(element_in_O2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p360,plain,
( subgroup_member(a)
| subgroup_member(d)
| subgroup_member(c)
| subgroup_member(a)
| subgroup_member(d) ),
inference(resolution,[status(thm)],[p256,c16]) ).
cnf(p3508,plain,
( subgroup_member(a)
| subgroup_member(c)
| subgroup_member(a)
| subgroup_member(d) ),
inference(factoring,[status(thm)],[p360]) ).
cnf(p4020,plain,
( subgroup_member(c)
| subgroup_member(a)
| subgroup_member(d) ),
inference(factoring,[status(thm)],[p3508]) ).
cnf(f21,negated_conjecture,
~ subgroup_member(d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_d_is_in_subgroup) ).
fof(f21_nnf,plain,
~ subgroup_member(d),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
~ subgroup_member(d),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
~ subgroup_member(d),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p4021,plain,
( subgroup_member(c)
| subgroup_member(a) ),
inference(resolution,[status(thm)],[p4020,c21]) ).
cnf(f5,axiom,
( subgroup_member(C)
| ~ product(A,B,C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_product) ).
fof(f5_nnf,plain,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,B,C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( subgroup_member(C)
| ~ product(A,B,C)
| ~ subgroup_member(B)
| ~ subgroup_member(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( subgroup_member(X2)
| ~ product(X0,X1,X2)
| ~ subgroup_member(X1)
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(f4,axiom,
( subgroup_member(inverse(X))
| ~ subgroup_member(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',closure_of_inverse) ).
fof(f4_nnf,plain,
! [X] :
( subgroup_member(inverse(X))
| ~ subgroup_member(X) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X] :
( subgroup_member(inverse(X))
| ~ subgroup_member(X) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( subgroup_member(inverse(X0))
| ~ subgroup_member(X0) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(f18,negated_conjecture,
subgroup_member(b),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_is_in_subgroup) ).
fof(f18_nnf,plain,
subgroup_member(b),
inference(nnf_transformation,[status(thm)],[f18]) ).
cnf(c18,plain,
subgroup_member(b),
inference(cnf_transformation,[status(esa)],[f18_nnf]) ).
cnf(p22,plain,
subgroup_member(inverse(b)),
inference(resolution,[status(thm)],[c4,c18]) ).
cnf(p37,plain,
( subgroup_member(X1)
| ~ product(inverse(b),X0,X1)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[c5,p22]) ).
cnf(p4025,plain,
( subgroup_member(X0)
| ~ product(inverse(b),c,X0)
| subgroup_member(a) ),
inference(resolution,[status(thm)],[p4021,p37]) ).
cnf(f10,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(f10_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)],[f10]) ).
fof(f10_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)],[f10_nnf]) ).
cnf(c10,plain,
( product(X0,X4,X5)
| ~ product(X2,X3,X5)
| ~ product(X1,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(f8,axiom,
product(inverse(X),X,identity),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).
fof(f8_nnf,plain,
! [X] : product(inverse(X),X,identity),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X] : product(inverse(X),X,identity),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
product(inverse(X0),X0,identity),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p66,plain,
( product(inverse(X0),X2,X3)
| ~ product(identity,X1,X3)
| ~ product(X0,X1,X2) ),
inference(resolution,[status(thm)],[c10,c8]) ).
cnf(f19,negated_conjecture,
product(b,inverse(a),c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_times_a_inverse_is_c) ).
fof(f19_nnf,plain,
product(b,inverse(a),c),
inference(nnf_transformation,[status(thm)],[f19]) ).
cnf(c19,plain,
product(b,inverse(a),c),
inference(cnf_transformation,[status(esa)],[f19_nnf]) ).
cnf(p426,plain,
( product(inverse(b),c,X0)
| ~ product(identity,inverse(a),X0) ),
inference(resolution,[status(thm)],[p66,c19]) ).
cnf(f6,axiom,
product(identity,X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).
fof(f6_nnf,plain,
! [X] : product(identity,X,X),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] : product(identity,X,X),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
product(identity,X0,X0),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p448,plain,
product(inverse(b),c,inverse(a)),
inference(resolution,[status(thm)],[p426,c6]) ).
cnf(p6198,plain,
( subgroup_member(inverse(a))
| subgroup_member(a) ),
inference(resolution,[status(thm)],[p4025,p448]) ).
cnf(p6201,plain,
( subgroup_member(inverse(inverse(a)))
| subgroup_member(a) ),
inference(resolution,[status(thm)],[p6198,c4]) ).
cnf(p425,plain,
( product(inverse(a),d,X0)
| ~ product(identity,c,X0) ),
inference(resolution,[status(thm)],[p66,c20]) ).
cnf(p433,plain,
product(inverse(a),d,c),
inference(resolution,[status(thm)],[p425,c6]) ).
cnf(p441,plain,
( product(inverse(inverse(a)),c,X0)
| ~ product(identity,d,X0) ),
inference(resolution,[status(thm)],[p433,p66]) ).
cnf(p481,plain,
product(inverse(inverse(a)),c,d),
inference(resolution,[status(thm)],[p441,c6]) ).
cnf(f15,axiom,
( equalish(D,A)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_left_cancellation) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( equalish(D,A)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( equalish(D,A)
| ~ product(D,B,C)
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( equalish(X3,X0)
| ~ product(X3,X1,X2)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p117,plain,
( equalish(X0,a)
| ~ product(X0,c,d) ),
inference(resolution,[status(thm)],[c15,c20]) ).
cnf(p487,plain,
equalish(inverse(inverse(a)),a),
inference(resolution,[status(thm)],[p481,p117]) ).
cnf(p499,plain,
( subgroup_member(a)
| ~ subgroup_member(inverse(inverse(a))) ),
inference(resolution,[status(thm)],[p487,c0]) ).
cnf(p6234,plain,
( subgroup_member(a)
| subgroup_member(a) ),
inference(resolution,[status(thm)],[p6201,p499]) ).
cnf(p6240,plain,
subgroup_member(a),
inference(factoring,[status(thm)],[p6234]) ).
cnf(p6246,plain,
( subgroup_member(X1)
| ~ product(a,X0,X1)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[p6240,c5]) ).
cnf(p6245,plain,
subgroup_member(inverse(a)),
inference(resolution,[status(thm)],[p6240,c4]) ).
cnf(p35,plain,
( subgroup_member(X1)
| ~ product(b,X0,X1)
| ~ subgroup_member(X0) ),
inference(resolution,[status(thm)],[c5,c18]) ).
cnf(p6267,plain,
( subgroup_member(X0)
| ~ product(b,inverse(a),X0) ),
inference(resolution,[status(thm)],[p6245,p35]) ).
cnf(p6402,plain,
subgroup_member(c),
inference(resolution,[status(thm)],[p6267,c19]) ).
cnf(p6673,plain,
( subgroup_member(X0)
| ~ product(a,c,X0) ),
inference(resolution,[status(thm)],[p6246,p6402]) ).
cnf(p6717,plain,
subgroup_member(d),
inference(resolution,[status(thm)],[p6673,c20]) ).
cnf(p6721,plain,
$false,
inference(resolution,[status(thm)],[p6717,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GRP039-6 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n016.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Wed Sep 23 13:26:40 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 38.93/5.45 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 38.93/5.45 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------