%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL221-1 : TPTP v9.3.1. Released v1.1.0.
% 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 02:01:25 PM UTC 2026
% Result : Unsatisfiable 81.50s 20.77s
% Output : Proof 81.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 61 ( 49 unt; 0 def)
% Number of atoms : 81 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 119 ( 3 sgn 34 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f5,axiom,
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
fof(f5_nnf,plain,
! [X] :
( ~ axiom(X)
| theorem(X) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X] :
( ~ axiom(X)
| theorem(X) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ axiom(X0)
| theorem(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,axiom,
ifeq(axiom(X0),true,theorem(X0),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f0,axiom,
axiom(or(not(or(A,A)),A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f0_nnf,plain,
! [A] : axiom(or(not(or(A,A)),A)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A] : axiom(or(not(or(A,A)),A)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
axiom(or(not(or(X0,X0)),X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
axiom(or(not(or(X0,X0)),X0)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
theorem(or(not(or(V0,V0)),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi0]) ).
cnf(f7,axiom,
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_3) ).
fof(f7_nnf,plain,
! [X,Z,Y] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Z,Y] :
( ~ theorem(or(not(Y),Z))
| ~ axiom(or(not(X),Y))
| theorem(or(not(X),Z)) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ theorem(or(not(X2),X1))
| ~ axiom(or(not(X0),X2))
| theorem(or(not(X0),X1)) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(axiom(or(not(X0),X1)),true,ifeq(theorem(or(not(X1),X2)),true,theorem(or(not(X0),X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(f1,axiom,
axiom(or(not(A),or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f1_nnf,plain,
! [A,B] : axiom(or(not(A),or(B,A))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : axiom(or(not(A),or(B,A))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
axiom(or(not(X0),or(X1,X0))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
axiom(or(not(X0),or(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h2,plain,
theorem(or(not(V0),V0)) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,h0]) ).
cnf(f2,axiom,
axiom(or(not(or(A,B)),or(B,A))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f2_nnf,plain,
! [A,B] : axiom(or(not(or(A,B)),or(B,A))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : axiom(or(not(or(A,B)),or(B,A))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
axiom(or(not(or(X0,X1)),or(X1,X0))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,axiom,
axiom(or(not(or(X0,X1)),or(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h10,plain,
theorem(or(not(or(V0,V1)),or(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi2,h2]) ).
cnf(h44,plain,
theorem(or(not(or(or(V0,V1),or(V0,V1))),or(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi0,h10]) ).
cnf(f3,axiom,
axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f3_nnf,plain,
! [A,B,C] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] : axiom(or(not(or(A,or(B,C))),or(B,or(A,C)))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
axiom(or(not(or(X0,or(X1,X2))),or(X1,or(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h917,plain,
theorem(or(not(or(V0,or(or(V0,V1),V1))),or(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,h44]) ).
cnf(h1859,plain,
theorem(or(not(or(or(V0,V1),V1)),or(V1,V0))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi1,h917]) ).
cnf(f6,axiom,
( ~ theorem(Y)
| ~ axiom(or(not(Y),X))
| theorem(X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
fof(f6_nnf,plain,
! [X,Y] :
( ~ theorem(Y)
| ~ axiom(or(not(Y),X))
| theorem(X) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y] :
( ~ theorem(Y)
| ~ axiom(or(not(Y),X))
| theorem(X) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ theorem(X1)
| ~ axiom(or(not(X1),X0))
| theorem(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(axiom(or(not(X0),X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f4,axiom,
axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f4_nnf,plain,
! [A,B,C] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : axiom(or(not(or(not(A),B)),or(not(or(C,A)),or(C,B)))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
axiom(or(not(or(not(X0),X1)),or(not(or(X2,X0)),or(X2,X1)))) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h3459,plain,
theorem(or(not(or(V0,or(or(V1,V2),V2))),or(V0,or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi4,h1859]) ).
cnf(h7751,plain,
theorem(or(not(or(not(V0),V1)),or(not(or(or(V2,V1),V0)),or(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi4,h3459]) ).
cnf(h7759,plain,
theorem(or(not(or(or(V0,V1),V2)),or(not(or(not(V2),V1)),or(V1,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3,h7751]) ).
cnf(h29310,plain,
theorem(or(not(or(V0,or(V1,V2))),or(not(or(not(V0),V2)),or(V2,V1)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi2,h7759]) ).
cnf(h50275,plain,
theorem(or(not(or(V0,or(V1,V2))),or(not(or(not(V1),V2)),or(V2,V0)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi3,h29310]) ).
cnf(h64200,plain,
theorem(or(not(or(or(V0,V1),V2)),or(not(or(not(V0),V1)),or(V1,V2)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi2,h50275]) ).
cnf(t8,plain,
theorem(or(not(or(not(X1),X2)),or(not(or(or(X1,X2),X3)),or(X2,X3)))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3,h64200]) ).
cnf(t400,plain,
theorem(or(not(or(not(X1),X2)),or(not(or(or(X1,X2),X3)),or(X2,X3)))) = true,
inference(orient,[status(thm)],[t8]) ).
cnf(f8,negated_conjecture,
~ theorem(or(not(or(not(p),q)),or(not(or(or(p,q),r)),or(q,r)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f8_nnf,plain,
~ theorem(or(not(or(not(p),q)),or(not(or(or(p,q),r)),or(q,r)))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ theorem(or(not(or(not(p),q)),or(not(or(or(p,q),r)),or(q,r)))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ theorem(or(not(or(not(p),q)),or(not(or(or(p,q),r)),or(q,r)))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
theorem(or(not(or(not(p),q)),or(not(or(or(p,q),r)),or(q,r)))) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t400]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL221-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/10.38 % Computer : n017.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Wed Sep 23 22:21:27 UTC 2026
% 0.10/10.39 % CPUTime :
% 0.10/10.39 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 81.50/20.77 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 81.50/20.77 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------