%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL098-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 01:02:02 PM UTC 2026
% Result : Unsatisfiable 0.07s 6.00s
% Output : Proof 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 13
% Syntax : Number of formulae : 71 ( 43 unt; 0 def)
% Number of atoms : 115 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 106 ( 62 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 101 ( 11 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f14,hypothesis,
( member(pair(y,sk2(YP)),r)
| ~ member(pair(x,YP),r) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h6) ).
fof(f14_nnf,plain,
! [YP] :
( member(pair(y,sk2(YP)),r)
| ~ member(pair(x,YP),r) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [YP] :
( member(pair(y,sk2(YP)),r)
| ~ member(pair(x,YP),r) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( member(pair(y,sk2(X0)),r)
| ~ member(pair(x,X0),r) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi11,axiom,
ifeq(member(pair(x,X0),r),true,member(pair(y,sk2(X0)),r),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f15,negated_conjecture,
member(pair(x,sk3),r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD_2c1) ).
fof(f15_nnf,plain,
member(pair(x,sk3),r),
inference(nnf_transformation,[status(thm)],[f15]) ).
cnf(c15,plain,
member(pair(x,sk3),r),
inference(cnf_transformation,[status(esa)],[f15_nnf]) ).
cnf(hi12,negated_conjecture,
member(pair(x,sk3),r) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h2,plain,
member(pair(y,sk2(sk3)),r) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi12]) ).
cnf(f9,hypothesis,
( member(pair(Y,sk1(X,Y,YP)),r)
| ~ member(pair(X,YP),r)
| ~ member(pair(X,Y),r) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h1) ).
fof(f9_nnf,plain,
! [X,Y,YP] :
( member(pair(Y,sk1(X,Y,YP)),r)
| ~ member(pair(X,YP),r)
| ~ member(pair(X,Y),r) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X,Y,YP] :
( member(pair(Y,sk1(X,Y,YP)),r)
| ~ member(pair(X,YP),r)
| ~ member(pair(X,Y),r) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( member(pair(X1,sk1(X0,X1,X2)),r)
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),r) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi6,axiom,
ifeq(member(pair(X0,X1),r),true,ifeq(member(pair(X0,X2),r),true,member(pair(X1,sk1(X0,X1,X2)),r),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(f12,hypothesis,
member(pair(y,z),r),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h4) ).
fof(f12_nnf,plain,
member(pair(y,z),r),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
member(pair(y,z),r),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi9,axiom,
member(pair(y,z),r) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h41,plain,
member(pair(z,sk1(y,z,sk2(sk3))),r) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi9,h2]) ).
cnf(f10,hypothesis,
( member(pair(YP,sk1(X,Y,YP)),r)
| ~ member(pair(X,YP),r)
| ~ member(pair(X,Y),r) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h2) ).
fof(f10_nnf,plain,
! [X,Y,YP] :
( member(pair(YP,sk1(X,Y,YP)),r)
| ~ member(pair(X,YP),r)
| ~ member(pair(X,Y),r) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y,YP] :
( member(pair(YP,sk1(X,Y,YP)),r)
| ~ member(pair(X,YP),r)
| ~ member(pair(X,Y),r) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( member(pair(X2,sk1(X0,X1,X2)),r)
| ~ member(pair(X0,X2),r)
| ~ member(pair(X0,X1),r) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi7,axiom,
ifeq(member(pair(X0,X1),r),true,ifeq(member(pair(X0,X2),r),true,member(pair(X2,sk1(X0,X1,X2)),r),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h39,plain,
member(pair(sk2(sk3),sk1(y,z,sk2(sk3))),r) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi9,h2]) ).
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(h81,plain,
member(pair(sk2(sk3),sk1(y,z,sk2(sk3))),trancl(r)) = true,
inference(hyper_resolution,[status(thm)],[hi3,h39]) ).
cnf(f13,hypothesis,
( member(pair(YP,sk2(YP)),trancl(r))
| ~ member(pair(x,YP),r) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD_2h5) ).
fof(f13_nnf,plain,
! [YP] :
( member(pair(YP,sk2(YP)),trancl(r))
| ~ member(pair(x,YP),r) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [YP] :
( member(pair(YP,sk2(YP)),trancl(r))
| ~ member(pair(x,YP),r) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( member(pair(X0,sk2(X0)),trancl(r))
| ~ member(pair(x,X0),r) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi10,axiom,
ifeq(member(pair(x,X0),r),true,member(pair(X0,sk2(X0)),trancl(r)),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h3,plain,
member(pair(sk3,sk2(sk3)),trancl(r)) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi12]) ).
cnf(f8,axiom,
( member(pair(A,C),R)
| ~ member(pair(B,C),R)
| ~ member(pair(A,B),R)
| ~ trans(R) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transD) ).
fof(f8_nnf,plain,
! [R,A,B,C] :
( member(pair(A,C),R)
| ~ member(pair(B,C),R)
| ~ member(pair(A,B),R)
| ~ trans(R) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [R,A,B,C] :
( member(pair(A,C),R)
| ~ member(pair(B,C),R)
| ~ member(pair(A,B),R)
| ~ trans(R) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( member(pair(X1,X3),X0)
| ~ member(pair(X2,X3),X0)
| ~ member(pair(X1,X2),X0)
| ~ trans(X0) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi5,axiom,
ifeq(trans(X0),true,ifeq(member(pair(X1,X2),X0),true,ifeq(member(pair(X2,X3),X0),true,member(pair(X1,X3),X0),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f7,axiom,
trans(trancl(R)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',trans_trancl) ).
fof(f7_nnf,plain,
! [R] : trans(trancl(R)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [R] : trans(trancl(R)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
trans(trancl(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi4,axiom,
trans(trancl(X0)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h106,plain,
member(pair(sk3,sk1(y,z,sk2(sk3))),trancl(r)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi4,h3,h81]) ).
cnf(f16,negated_conjecture,
( ~ member(pair(z,ZA),r)
| ~ member(pair(sk3,ZA),trancl(r)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diamond_strip_lemmaD_2c2) ).
fof(f16_nnf,plain,
! [ZA] :
( ~ member(pair(z,ZA),r)
| ~ member(pair(sk3,ZA),trancl(r)) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [ZA] :
( ~ member(pair(z,ZA),r)
| ~ member(pair(sk3,ZA),trancl(r)) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ member(pair(z,X0),r)
| ~ member(pair(sk3,X0),trancl(r)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,negated_conjecture,
ifeq(member(pair(sk3,X0),trancl(r)),true,ifeq(member(pair(z,X0),r),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi16,h106,h41]) ).
cnf(t546,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,c16]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t546]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL098-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/5.32 % Computer : n012.cluster.edu
% 0.03/5.32 % Model : x86_64 x86_64
% 0.03/5.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.32 % Memory : 8046.5625MB
% 0.03/5.32 % OS : Linux 6.8.0-71-generic
% 0.03/5.32 % CPULimit : 300
% 0.03/5.32 % WCLimit : 300
% 0.03/5.32 % DateTime : Fri Sep 25 07:34:14 UTC 2026
% 0.03/5.32 % CPUTime :
% 0.03/5.32 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/6.00 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/6.00 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------