%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GRP025-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/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 01:24:58 PM UTC 2026
% Result : Unsatisfiable 27.82s 19.04s
% Output : Proof 27.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 15
% Syntax : Number of formulae : 106 ( 57 unt; 0 def)
% Number of atoms : 181 ( 89 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 124 ( 49 ~; 75 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-3 aty)
% Number of variables : 40 ( 0 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f25,hypothesis,
an_isomorphism(a) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_maps_to_c) ).
fof(f25_nnf,plain,
an_isomorphism(a) = c,
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
an_isomorphism(a) = c,
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(f15,hypothesis,
( X = b
| X = a
| ~ group_member(X,g1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_and_b_only_members_of_group1) ).
fof(f15_nnf,plain,
! [X] :
( X = b
| X = a
| ~ group_member(X,g1) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X] :
( X = b
| X = a
| ~ group_member(X,g1) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( X0 = b
| X0 = a
| ~ group_member(X0,g1) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(f28,hypothesis,
group_member(d2,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2_member_of_group1) ).
fof(f28_nnf,plain,
group_member(d2,g1),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
group_member(d2,g1),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(p176,plain,
( d2 = b
| d2 = a ),
inference(resolution,[status(thm)],[c15,c28]) ).
cnf(f27,hypothesis,
group_member(d1,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_member_of_group1) ).
fof(f27_nnf,plain,
group_member(d1,g1),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
group_member(d1,g1),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(p175,plain,
( d1 = b
| d1 = a ),
inference(resolution,[status(thm)],[c15,c27]) ).
cnf(f29,hypothesis,
group_member(d3,g1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_member_of_group1) ).
fof(f29_nnf,plain,
group_member(d3,g1),
inference(nnf_transformation,[status(thm)],[f29]) ).
cnf(c29,plain,
group_member(d3,g1),
inference(cnf_transformation,[status(esa)],[f29_nnf]) ).
cnf(p177,plain,
( d3 = b
| d3 = a ),
inference(resolution,[status(thm)],[c15,c29]) ).
cnf(f30,hypothesis,
product(g1,d1,d2,d3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_times_d2_is_d3) ).
fof(f30_nnf,plain,
product(g1,d1,d2,d3),
inference(nnf_transformation,[status(thm)],[f30]) ).
cnf(c30,plain,
product(g1,d1,d2,d3),
inference(cnf_transformation,[status(esa)],[f30_nnf]) ).
cnf(p218,plain,
( product(g1,d1,d2,b)
| d3 = a ),
inference(superposition,[status(thm)],[p177,c30]) ).
cnf(f8,axiom,
( W = Z
| ~ product(Xg,X,Y,W)
| ~ product(Xg,X,Y,Z) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).
fof(f8_nnf,plain,
! [Xg,X,Y,Z,W] :
( W = Z
| ~ product(Xg,X,Y,W)
| ~ product(Xg,X,Y,Z) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [Xg,X,Y,Z,W] :
( W = Z
| ~ product(Xg,X,Y,W)
| ~ product(Xg,X,Y,Z) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( X4 = X3
| ~ product(X0,X1,X2,X4)
| ~ product(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p119,plain,
( X0 = d3
| ~ product(g1,d1,d2,X0) ),
inference(resolution,[status(thm)],[c8,c30]) ).
cnf(p701,plain,
( b = d3
| d3 = a ),
inference(resolution,[status(thm)],[p218,p119]) ).
cnf(f31,negated_conjecture,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_holds_in_group2) ).
fof(f31_nnf,plain,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c31,plain,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),an_isomorphism(d3)),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(p197,plain,
( ~ product(g2,d,an_isomorphism(d2),an_isomorphism(d3))
| d1 = a ),
inference(superposition,[status(thm)],[p175,c31]) ).
cnf(p203,plain,
( ~ product(g2,d,d,an_isomorphism(d3))
| d1 = a
| d2 = a ),
inference(superposition,[status(thm)],[p176,p197]) ).
cnf(p706,plain,
( ~ product(g2,d,d,c)
| d1 = a
| d2 = a
| b = d3 ),
inference(superposition,[status(thm)],[p701,p203]) ).
cnf(f24,hypothesis,
product(g2,d,d,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_d_is_c) ).
fof(f24_nnf,plain,
product(g2,d,d,c),
inference(nnf_transformation,[status(thm)],[f24]) ).
cnf(c24,plain,
product(g2,d,d,c),
inference(cnf_transformation,[status(esa)],[f24_nnf]) ).
cnf(p751,plain,
( d1 = a
| d2 = a
| b = d3 ),
inference(resolution,[status(thm)],[p706,c24]) ).
cnf(f6,axiom,
( product(Xg,X,Y,multiply(Xg,X,Y))
| ~ group_member(Y,Xg)
| ~ group_member(X,Xg) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1_1) ).
fof(f6_nnf,plain,
! [X,Xg,Y] :
( product(Xg,X,Y,multiply(Xg,X,Y))
| ~ group_member(Y,Xg)
| ~ group_member(X,Xg) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Xg,Y] :
( product(Xg,X,Y,multiply(Xg,X,Y))
| ~ group_member(Y,Xg)
| ~ group_member(X,Xg) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( product(X1,X0,X2,multiply(X1,X0,X2))
| ~ group_member(X2,X1)
| ~ group_member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p55,plain,
( product(g1,d1,X0,multiply(g1,d1,X0))
| ~ group_member(X0,g1) ),
inference(resolution,[status(thm)],[c6,c27]) ).
cnf(p407,plain,
product(g1,d1,d2,multiply(g1,d1,d2)),
inference(resolution,[status(thm)],[p55,c28]) ).
cnf(p622,plain,
multiply(g1,d1,d2) = d3,
inference(resolution,[status(thm)],[p119,p407]) ).
cnf(p774,plain,
( multiply(g1,d1,a) = d3
| d1 = a
| b = d3 ),
inference(superposition,[status(thm)],[p751,p622]) ).
cnf(p845,plain,
( b = d3
| d1 = a
| b = d3
| d1 = a ),
inference(superposition,[status(thm)],[p175,p774]) ).
cnf(p847,plain,
( b = d3
| b = d3
| d1 = a ),
inference(factoring,[status(thm)],[p845]) ).
cnf(p871,plain,
( b = d3
| d1 = a ),
inference(factoring,[status(thm)],[p847]) ).
cnf(p894,plain,
( multiply(g1,a,d2) = d3
| b = d3 ),
inference(superposition,[status(thm)],[p871,p622]) ).
cnf(p923,plain,
( b = d3
| b = d3
| d2 = a ),
inference(superposition,[status(thm)],[p176,p894]) ).
cnf(p935,plain,
( b = d3
| d2 = a ),
inference(factoring,[status(thm)],[p923]) ).
cnf(p702,plain,
( ~ product(g2,an_isomorphism(d1),an_isomorphism(d2),c)
| b = d3 ),
inference(superposition,[status(thm)],[p701,c31]) ).
cnf(p896,plain,
( ~ product(g2,c,an_isomorphism(d2),c)
| b = d3
| b = d3 ),
inference(superposition,[status(thm)],[p871,p702]) ).
cnf(p2557,plain,
( ~ product(g2,c,an_isomorphism(d2),c)
| b = d3 ),
inference(factoring,[status(thm)],[p896]) ).
cnf(p2558,plain,
( ~ product(g2,c,c,c)
| b = d3
| b = d3 ),
inference(superposition,[status(thm)],[p935,p2557]) ).
cnf(p2582,plain,
( ~ product(g2,c,c,c)
| b = d3 ),
inference(factoring,[status(thm)],[p2558]) ).
cnf(f21,hypothesis,
product(g2,c,c,c),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_c_is_c) ).
fof(f21_nnf,plain,
product(g2,c,c,c),
inference(nnf_transformation,[status(thm)],[f21]) ).
cnf(c21,plain,
product(g2,c,c,c),
inference(cnf_transformation,[status(esa)],[f21_nnf]) ).
cnf(p2583,plain,
b = d3,
inference(resolution,[status(thm)],[p2582,c21]) ).
cnf(p2609,plain,
d3 = b,
inference(superposition,[status(thm)],[p2583,p622]) ).
cnf(p408,plain,
product(g1,d1,d3,multiply(g1,d1,d3)),
inference(resolution,[status(thm)],[p55,c29]) ).
cnf(p513,plain,
( product(g1,d1,d3,multiply(g1,b,d3))
| d1 = a ),
inference(superposition,[status(thm)],[p175,p408]) ).
cnf(p2629,plain,
( product(g1,d1,b,multiply(g1,b,b))
| d1 = a ),
inference(demodulation,[status(thm)],[p2609,p513]) ).
cnf(p2737,plain,
( X0 = a
| ~ product(g1,d1,b,X0)
| d1 = a ),
inference(resolution,[status(thm)],[p2629,c8]) ).
cnf(p2814,plain,
( ~ product(g1,d1,b,d1)
| d1 = a ),
inference(factoring,[status(thm)],[p2737]) ).
cnf(p2816,plain,
( ~ product(g1,d1,b,b)
| d1 = a
| d1 = a ),
inference(superposition,[status(thm)],[p175,p2814]) ).
cnf(p2889,plain,
( ~ product(g1,d1,b,b)
| d1 = a ),
inference(factoring,[status(thm)],[p2816]) ).
cnf(p202,plain,
( product(g1,d1,b,d3)
| d2 = a ),
inference(superposition,[status(thm)],[p176,c30]) ).
cnf(p2617,plain,
( product(g1,d1,b,b)
| d2 = a ),
inference(demodulation,[status(thm)],[p2609,p202]) ).
cnf(p2891,plain,
( d2 = a
| d1 = a ),
inference(resolution,[status(thm)],[p2889,p2617]) ).
cnf(p2586,plain,
( ~ product(g2,d,an_isomorphism(d2),d)
| d1 = a ),
inference(superposition,[status(thm)],[p2583,p197]) ).
cnf(p2908,plain,
( ~ product(g2,d,c,d)
| d1 = a
| d1 = a ),
inference(superposition,[status(thm)],[p2891,p2586]) ).
cnf(p3174,plain,
( ~ product(g2,d,c,d)
| d1 = a ),
inference(factoring,[status(thm)],[p2908]) ).
cnf(f23,hypothesis,
product(g2,d,c,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d_times_c_is_d) ).
fof(f23_nnf,plain,
product(g2,d,c,d),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
product(g2,d,c,d),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(p3175,plain,
d1 = a,
inference(resolution,[status(thm)],[p3174,c23]) ).
cnf(p2584,plain,
~ product(g2,an_isomorphism(d1),an_isomorphism(d2),d),
inference(superposition,[status(thm)],[p2583,c31]) ).
cnf(p3183,plain,
~ product(g2,an_isomorphism(a),an_isomorphism(d2),d),
inference(demodulation,[status(thm)],[p3175,p2584]) ).
cnf(p3222,plain,
( ~ product(g2,c,d,d)
| d2 = a ),
inference(superposition,[status(thm)],[p176,p3183]) ).
cnf(f22,hypothesis,
product(g2,c,d,d),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c_times_d_is_d) ).
fof(f22_nnf,plain,
product(g2,c,d,d),
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
product(g2,c,d,d),
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(p3230,plain,
d2 = a,
inference(resolution,[status(thm)],[p3222,c22]) ).
cnf(p2585,plain,
product(g1,d1,d2,b),
inference(superposition,[status(thm)],[p2583,c30]) ).
cnf(p3184,plain,
product(g1,a,d2,b),
inference(demodulation,[status(thm)],[p3175,p2585]) ).
cnf(p3232,plain,
product(g1,a,a,b),
inference(demodulation,[status(thm)],[p3230,p3184]) ).
cnf(f17,hypothesis,
product(g1,a,a,a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_times_a_is_a) ).
fof(f17_nnf,plain,
product(g1,a,a,a),
inference(nnf_transformation,[status(thm)],[f17]) ).
cnf(c17,plain,
product(g1,a,a,a),
inference(cnf_transformation,[status(esa)],[f17_nnf]) ).
cnf(p110,plain,
( X0 = a
| ~ product(g1,a,a,X0) ),
inference(resolution,[status(thm)],[c8,c17]) ).
cnf(p3247,plain,
b = a,
inference(resolution,[status(thm)],[p3232,p110]) ).
cnf(f26,hypothesis,
an_isomorphism(b) = d,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_maps_to_d) ).
fof(f26_nnf,plain,
an_isomorphism(b) = d,
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
an_isomorphism(b) = d,
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(p3249,plain,
an_isomorphism(a) = d,
inference(demodulation,[status(thm)],[p3247,c26]) ).
cnf(p3271,plain,
d = c,
inference(superposition,[status(thm)],[p3249,c25]) ).
cnf(p3221,plain,
~ product(g2,c,an_isomorphism(d2),d),
inference(superposition,[status(thm)],[c25,p3183]) ).
cnf(p3245,plain,
~ product(g2,c,an_isomorphism(a),d),
inference(demodulation,[status(thm)],[p3230,p3221]) ).
cnf(p3291,plain,
~ product(g2,c,an_isomorphism(a),c),
inference(demodulation,[status(thm)],[p3271,p3245]) ).
cnf(p3292,plain,
~ product(g2,c,c,c),
inference(superposition,[status(thm)],[c25,p3291]) ).
cnf(p3297,plain,
$false,
inference(resolution,[status(thm)],[p3292,c21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GRP025-1 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/15.38 % Computer : n017.cluster.edu
% 0.09/15.38 % Model : x86_64 x86_64
% 0.09/15.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/15.38 % Memory : 8046.5625MB
% 0.09/15.38 % OS : Linux 6.8.0-71-generic
% 0.09/15.38 % CPULimit : 300
% 0.09/15.38 % WCLimit : 300
% 0.09/15.38 % DateTime : Wed Sep 23 13:12:17 UTC 2026
% 0.09/15.38 % CPUTime :
% 0.09/15.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 27.82/19.04 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 27.82/19.04 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------