%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL099-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 01:02:03 PM UTC 2026
% Result : Unsatisfiable 6.90s 1.42s
% Output : Proof 6.90s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 52 ( 36 unt; 0 def)
% Number of atoms : 84 ( 26 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 82 ( 50 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-4 aty)
% Number of variables : 76 ( 8 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f10,axiom,
( member(pair(Y,diamond_strip_lemmaD_sk1(X,Y,YP,R)),R)
| ~ member(pair(X,YP),R)
| ~ member(pair(X,Y),trancl(R))
| ~ diamond(R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD2) ).
fof(f10_nnf,plain,
! [R,X,Y,YP] :
( member(pair(Y,diamond_strip_lemmaD_sk1(X,Y,YP,R)),R)
| ~ member(pair(X,YP),R)
| ~ member(pair(X,Y),trancl(R))
| ~ diamond(R) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [R,X,Y,YP] :
( member(pair(Y,diamond_strip_lemmaD_sk1(X,Y,YP,R)),R)
| ~ member(pair(X,YP),R)
| ~ member(pair(X,Y),trancl(R))
| ~ diamond(R) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( member(pair(X2,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),X0)
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ~ diamond(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi7,axiom,
ifeq(diamond(X0),true,ifeq(member(pair(X1,X2),trancl(X0)),true,ifeq(member(pair(X1,X3),X0),true,member(pair(X2,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f11,hypothesis,
diamond(r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1h1) ).
fof(f11_nnf,plain,
diamond(r),
inference(nnf_transformation,[status(thm)],[f11]) ).
cnf(c11,plain,
diamond(r),
inference(cnf_transformation,[status(esa)],[f11_nnf]) ).
cnf(hi8,axiom,
diamond(r) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(f13,negated_conjecture,
member(pair(y,yp),trancl(r)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1c1) ).
fof(f13_nnf,plain,
member(pair(y,yp),trancl(r)),
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
member(pair(y,yp),trancl(r)),
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(hi10,negated_conjecture,
member(pair(y,yp),trancl(r)) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(f12,hypothesis,
member(pair(y,ya),r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1h2) ).
fof(f12_nnf,plain,
member(pair(y,ya),r),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
member(pair(y,ya),r),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi9,axiom,
member(pair(y,ya),r) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h21,plain,
member(pair(yp,diamond_strip_lemmaD_sk1(y,yp,ya,r)),r) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi8,hi10,hi9]) ).
cnf(f6,axiom,
( member(pair(A,B),trancl(R))
| ~ member(pair(A,B),R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r_into_trancl) ).
fof(f6_nnf,plain,
! [A,B,R] :
( member(pair(A,B),trancl(R))
| ~ member(pair(A,B),R) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,R] :
( member(pair(A,B),trancl(R))
| ~ member(pair(A,B),R) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( member(pair(X0,X1),trancl(X2))
| ~ member(pair(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi3,axiom,
ifeq(member(pair(X0,X1),X2),true,member(pair(X0,X1),trancl(X2)),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h59,plain,
member(pair(yp,diamond_strip_lemmaD_sk1(y,yp,ya,r)),trancl(r)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h21]) ).
cnf(f9,axiom,
( member(pair(YP,diamond_strip_lemmaD_sk1(X,Y,YP,R)),trancl(R))
| ~ member(pair(X,YP),R)
| ~ member(pair(X,Y),trancl(R))
| ~ diamond(R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD1) ).
fof(f9_nnf,plain,
! [R,X,Y,YP] :
( member(pair(YP,diamond_strip_lemmaD_sk1(X,Y,YP,R)),trancl(R))
| ~ member(pair(X,YP),R)
| ~ member(pair(X,Y),trancl(R))
| ~ diamond(R) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [R,X,Y,YP] :
( member(pair(YP,diamond_strip_lemmaD_sk1(X,Y,YP,R)),trancl(R))
| ~ member(pair(X,YP),R)
| ~ member(pair(X,Y),trancl(R))
| ~ diamond(R) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( member(pair(X3,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),trancl(X0))
| ~ member(pair(X1,X3),X0)
| ~ member(pair(X1,X2),trancl(X0))
| ~ diamond(X0) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi6,axiom,
ifeq(diamond(X0),true,ifeq(member(pair(X1,X2),trancl(X0)),true,ifeq(member(pair(X1,X3),X0),true,member(pair(X3,diamond_strip_lemmaD_sk1(X1,X2,X3,X0)),trancl(X0)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h22,plain,
member(pair(ya,diamond_strip_lemmaD_sk1(y,yp,ya,r)),trancl(r)) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi8,hi10,hi9]) ).
cnf(f14,negated_conjecture,
( ~ member(pair(yp,Z),trancl(r))
| ~ member(pair(ya,Z),trancl(r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_trancl_1c2) ).
fof(f14_nnf,plain,
! [Z] :
( ~ member(pair(yp,Z),trancl(r))
| ~ member(pair(ya,Z),trancl(r)) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [Z] :
( ~ member(pair(yp,Z),trancl(r))
| ~ member(pair(ya,Z),trancl(r)) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ member(pair(yp,X0),trancl(r))
| ~ member(pair(ya,X0),trancl(r)) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,negated_conjecture,
ifeq(member(pair(ya,X0),trancl(r)),true,ifeq(member(pair(yp,X0),trancl(r)),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi14,h22,h59]) ).
cnf(t267,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(f0,axiom,
combK != combS,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_s) ).
fof(f0_nnf,plain,
combK != combS,
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
combK != combS,
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
combK != combS,
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(f1,axiom,
combK != comb_app(P,Q),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',k_app) ).
fof(f1_nnf,plain,
! [P,Q] : combK != comb_app(P,Q),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [P,Q] : combK != comb_app(P,Q),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
combK != comb_app(X0,X1),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(f2,axiom,
combS != comb_app(P,Q),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',s_app) ).
fof(f2_nnf,plain,
! [P,Q] : combS != comb_app(P,Q),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [P,Q] : combS != comb_app(P,Q),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
combS != comb_app(X0,X1),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c1,c2,c14]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t267]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : COL099-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n019.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 : Fri Sep 25 07:35:04 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 6.90/1.42 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 6.90/1.42 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------