%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : RNG006-2 : 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 02:37:24 PM UTC 2026
% Result : Unsatisfiable 4.69s 6.23s
% Output : Proof 4.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 28 unt; 0 def)
% Number of atoms : 56 ( 11 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-4 aty)
% Number of variables : 50 ( 0 sgn 20 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f28,axiom,
( product(A,additive_inverse(B),additive_inverse(C))
| ~ product(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',product_lemma1) ).
fof(f28_nnf,plain,
! [A,B,C] :
( product(A,additive_inverse(B),additive_inverse(C))
| ~ product(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A,B,C] :
( product(A,additive_inverse(B),additive_inverse(C))
| ~ product(A,B,C) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( product(X0,additive_inverse(X1),additive_inverse(X2))
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi28,axiom,
ifeq(product(X0,X1,X2),true,product(X0,additive_inverse(X1),additive_inverse(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(f33,hypothesis,
product(a,c,aPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_c) ).
fof(f33_nnf,plain,
product(a,c,aPc),
inference(nnf_transformation,[status(thm)],[f33]) ).
cnf(c33,plain,
product(a,c,aPc),
inference(cnf_transformation,[status(esa)],[f33_nnf]) ).
cnf(hi33,axiom,
product(a,c,aPc) = true,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(h12,plain,
product(a,additive_inverse(c),additive_inverse(aPc)) = true,
inference(hyper_resolution,[status(thm)],[hi28,hi33]) ).
cnf(f21,axiom,
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
fof(f21_nnf,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X,Y,V1,Z,V2,V3,V4] :
( product(X,V3,V4)
| ~ sum(V1,V2,V4)
| ~ sum(Y,Z,V3)
| ~ product(X,Z,V2)
| ~ product(X,Y,V1) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( product(X0,X5,X6)
| ~ sum(X2,X4,X6)
| ~ sum(X1,X3,X5)
| ~ product(X0,X3,X4)
| ~ product(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
ifeq(product(X0,X1,X2),true,ifeq(product(X0,X3,X4),true,ifeq(sum(X1,X3,X5),true,ifeq(sum(X2,X4,X6),true,product(X0,X5,X6),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(f32,hypothesis,
product(a,b,aPb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_times_b) ).
fof(f32_nnf,plain,
product(a,b,aPb),
inference(nnf_transformation,[status(thm)],[f32]) ).
cnf(c32,plain,
product(a,b,aPb),
inference(cnf_transformation,[status(esa)],[f32_nnf]) ).
cnf(hi32,axiom,
product(a,b,aPb) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(f31,hypothesis,
sum(b,additive_inverse(c),bS_Ic),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_plus_inverse_c) ).
fof(f31_nnf,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c31,plain,
sum(b,additive_inverse(c),bS_Ic),
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(hi31,axiom,
sum(b,additive_inverse(c),bS_Ic) = true,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(f34,hypothesis,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',aPb_plus_IaPc) ).
fof(f34_nnf,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(nnf_transformation,[status(thm)],[f34]) ).
cnf(c34,plain,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc),
inference(cnf_transformation,[status(esa)],[f34_nnf]) ).
cnf(hi34,axiom,
sum(aPb,additive_inverse(aPc),aPb_S_IaPc) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(t5,plain,
product(a,bS_Ic,aPb_S_IaPc) = true,
inference(hyper_resolution,[status(thm)],[hi21,hi32,h12,hi31,hi34]) ).
cnf(t313,plain,
product(a,bS_Ic,aPb_S_IaPc) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f35,negated_conjecture,
~ product(a,bS_Ic,aPb_S_IaPc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_times_bS_Ic_is_aPb_S__IaPc) ).
fof(f35_nnf,plain,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c35,plain,
~ product(a,bS_Ic,aPb_S_IaPc),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
cnf(goal_0,negated_conjecture,
product(a,bS_Ic,aPb_S_IaPc) != true,
inference(equality_encoding,[status(esa)],[c35]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t313]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : RNG006-2 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.60 % Computer : n017.cluster.edu
% 0.11/5.60 % Model : x86_64 x86_64
% 0.11/5.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.60 % Memory : 8046.5625MB
% 0.11/5.60 % OS : Linux 6.8.0-71-generic
% 0.11/5.60 % CPULimit : 300
% 0.11/5.60 % WCLimit : 300
% 0.11/5.60 % DateTime : Thu Sep 24 07:38:08 UTC 2026
% 0.11/5.60 % CPUTime :
% 0.11/5.60 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 4.69/6.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 4.69/6.23 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------