%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL224-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n013.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 02:01:26 PM UTC 2026
% Result : Unsatisfiable 237.64s 31.96s
% Output : Proof 237.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 79 ( 71 unt; 0 def)
% Number of atoms : 91 ( 50 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 30 ( 18 ~; 12 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 69 ( 3 sgn 26 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f4,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
fof(f4_nnf,plain,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C] : axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi5,axiom,
axiom(implies(implies(X0,X1),implies(or(X2,X0),or(X2,X1)))) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f5,axiom,
implies(X,Y) = or(not(X),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',implies_definition) ).
fof(f5_nnf,plain,
! [X,Y] : implies(X,Y) = or(not(X),Y),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X,Y] : implies(X,Y) = or(not(X),Y),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
implies(X0,X1) = or(not(X0),X1),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi1,axiom,
implies(X0,X1) = or(not(X0),X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h0,plain,
axiom(or(not(or(not(q),r)),or(not(or(p,q)),or(p,r)))) = true,
inference(hyper_resolution,[status(thm)],[hi5,hi1]) ).
cnf(f6,axiom,
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
fof(f6_nnf,plain,
! [X] :
( ~ axiom(X)
| theorem(X) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X] :
( ~ axiom(X)
| theorem(X) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ axiom(X0)
| theorem(X0) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(axiom(X0),true,theorem(X0),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h1,plain,
theorem(or(not(or(not(q),r)),or(not(or(p,q)),or(p,r)))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h0]) ).
cnf(h66,plain,
theorem(or(not(or(not(or(not(q),r)),or(not(or(p,q)),or(p,r)))),or(not(or(p,or(not(q),r))),or(p,or(not(or(p,q)),or(p,r)))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi5,hi1]) ).
cnf(f7,axiom,
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
fof(f7_nnf,plain,
! [X,Y] :
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [X,Y] :
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( ~ theorem(X1)
| ~ theorem(implies(X1,X0))
| theorem(X0) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,axiom,
ifeq(theorem(implies(X0,X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h67,plain,
theorem(or(not(or(p,or(not(q),r))),or(p,or(not(or(p,q)),or(p,r))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h66,h1,hi1]) ).
cnf(f2,axiom,
axiom(implies(or(A,B),or(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
fof(f2_nnf,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B] : axiom(implies(or(A,B),or(B,A))),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
axiom(implies(or(X0,X1),or(X1,X0))),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi3,axiom,
axiom(implies(or(X0,X1),or(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h64,plain,
theorem(or(not(or(p,or(not(or(p,q)),or(p,r)))),or(or(not(or(p,q)),or(p,r)),p))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3,hi1]) ).
cnf(h63,plain,
theorem(or(not(or(not(or(p,or(not(or(p,q)),or(p,r)))),or(or(not(or(p,q)),or(p,r)),p))),or(not(or(not(or(p,or(not(q),r))),or(p,or(not(or(p,q)),or(p,r))))),or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),p))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi5,hi1]) ).
cnf(h65,plain,
theorem(or(not(or(not(or(p,or(not(q),r))),or(p,or(not(or(p,q)),or(p,r))))),or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),p)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h63,h64,hi1]) ).
cnf(h68,plain,
theorem(or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),p))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h65,h67,hi1]) ).
cnf(f1,axiom,
axiom(implies(A,or(B,A))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
fof(f1_nnf,plain,
! [A,B] : axiom(implies(A,or(B,A))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] : axiom(implies(A,or(B,A))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
axiom(implies(X0,or(X1,X0))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi2,axiom,
axiom(implies(X0,or(X1,X0))) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h42,plain,
axiom(or(not(p),or(r,p))) = true,
inference(hyper_resolution,[status(thm)],[hi2,hi1]) ).
cnf(h43,plain,
theorem(or(not(p),or(r,p))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h42]) ).
cnf(h45,plain,
theorem(or(not(or(r,p)),or(p,r))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi3,hi1]) ).
cnf(h44,plain,
theorem(or(not(or(not(or(r,p)),or(p,r))),or(not(or(not(p),or(r,p))),or(not(p),or(p,r))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi5,hi1]) ).
cnf(h46,plain,
theorem(or(not(or(not(p),or(r,p))),or(not(p),or(p,r)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h44,h45,hi1]) ).
cnf(h47,plain,
theorem(or(not(p),or(p,r))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h46,h43,hi1]) ).
cnf(h60,plain,
theorem(or(not(or(not(p),or(p,r))),or(not(or(or(not(or(p,q)),or(p,r)),p)),or(or(not(or(p,q)),or(p,r)),or(p,r))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi5,hi1]) ).
cnf(h61,plain,
theorem(or(not(or(or(not(or(p,q)),or(p,r)),p)),or(or(not(or(p,q)),or(p,r)),or(p,r)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h60,h47,hi1]) ).
cnf(h59,plain,
theorem(or(not(or(not(or(or(not(or(p,q)),or(p,r)),p)),or(or(not(or(p,q)),or(p,r)),or(p,r)))),or(not(or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),p))),or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),or(p,r)))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi5,hi1]) ).
cnf(h62,plain,
theorem(or(not(or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),p))),or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),or(p,r))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h59,h61,hi1]) ).
cnf(h69,plain,
theorem(or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),or(p,r)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h62,h68,hi1]) ).
cnf(h56,plain,
theorem(or(not(or(p,r)),or(not(or(p,q)),or(p,r)))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi2,hi1]) ).
cnf(h55,plain,
theorem(or(not(or(not(or(p,r)),or(not(or(p,q)),or(p,r)))),or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(or(not(or(p,q)),or(p,r)),or(not(or(p,q)),or(p,r)))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi5,hi1]) ).
cnf(h57,plain,
theorem(or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(or(not(or(p,q)),or(p,r)),or(not(or(p,q)),or(p,r))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h55,h56,hi1]) ).
cnf(f0,axiom,
axiom(implies(or(A,A),A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
fof(f0_nnf,plain,
! [A] : axiom(implies(or(A,A),A)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A] : axiom(implies(or(A,A),A)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
axiom(implies(or(X0,X0),X0)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
axiom(implies(or(X0,X0),X0)) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h52,plain,
theorem(or(not(or(or(not(or(p,q)),or(p,r)),or(not(or(p,q)),or(p,r)))),or(not(or(p,q)),or(p,r)))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi0,hi1]) ).
cnf(h51,plain,
theorem(or(not(or(not(or(or(not(or(p,q)),or(p,r)),or(not(or(p,q)),or(p,r)))),or(not(or(p,q)),or(p,r)))),or(not(or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(or(not(or(p,q)),or(p,r)),or(not(or(p,q)),or(p,r))))),or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(not(or(p,q)),or(p,r)))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi5,hi1]) ).
cnf(h53,plain,
theorem(or(not(or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(or(not(or(p,q)),or(p,r)),or(not(or(p,q)),or(p,r))))),or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(not(or(p,q)),or(p,r))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h51,h52,hi1]) ).
cnf(h49,plain,
theorem(or(not(or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(not(or(p,q)),or(p,r)))),or(not(or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),or(p,r)))),or(not(or(p,or(not(q),r))),or(not(or(p,q)),or(p,r)))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi5,hi1]) ).
cnf(h48,plain,
theorem(or(not(or(not(or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(not(or(p,q)),or(p,r)))),or(not(or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),or(p,r)))),or(not(or(p,or(not(q),r))),or(not(or(p,q)),or(p,r)))))),or(not(or(not(or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(or(not(or(p,q)),or(p,r)),or(not(or(p,q)),or(p,r))))),or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(not(or(p,q)),or(p,r))))),or(not(or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(or(not(or(p,q)),or(p,r)),or(not(or(p,q)),or(p,r))))),or(not(or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),or(p,r)))),or(not(or(p,or(not(q),r))),or(not(or(p,q)),or(p,r)))))))) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi5,hi1]) ).
cnf(h50,plain,
theorem(or(not(or(not(or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(or(not(or(p,q)),or(p,r)),or(not(or(p,q)),or(p,r))))),or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(not(or(p,q)),or(p,r))))),or(not(or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(or(not(or(p,q)),or(p,r)),or(not(or(p,q)),or(p,r))))),or(not(or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),or(p,r)))),or(not(or(p,or(not(q),r))),or(not(or(p,q)),or(p,r))))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h48,h49,hi1]) ).
cnf(h54,plain,
theorem(or(not(or(not(or(or(not(or(p,q)),or(p,r)),or(p,r))),or(or(not(or(p,q)),or(p,r)),or(not(or(p,q)),or(p,r))))),or(not(or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),or(p,r)))),or(not(or(p,or(not(q),r))),or(not(or(p,q)),or(p,r)))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h50,h53,hi1]) ).
cnf(h58,plain,
theorem(or(not(or(not(or(p,or(not(q),r))),or(or(not(or(p,q)),or(p,r)),or(p,r)))),or(not(or(p,or(not(q),r))),or(not(or(p,q)),or(p,r))))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h54,h57,hi1]) ).
cnf(t9,plain,
theorem(or(not(or(p,or(not(q),r))),or(not(or(p,q)),or(p,r)))) = true,
inference(hyper_resolution,[status(thm)],[hi7,h58,h69,hi1]) ).
cnf(t3,plain,
or(not(X1),X2) = implies(X1,X2),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t11,plain,
or(not(X1),X2) = implies(X1,X2),
inference(orient,[status(thm)],[t3]) ).
cnf(t28,plain,
theorem(implies(or(p,or(not(q),r)),or(not(or(p,q)),or(p,r)))) = true,
inference(step,[status(thm)],[t9,t11]) ).
cnf(t29,plain,
theorem(implies(or(p,implies(q,r)),or(not(or(p,q)),or(p,r)))) = true,
inference(step,[status(thm)],[t28,t11]) ).
cnf(t30,plain,
theorem(implies(or(p,implies(q,r)),implies(or(p,q),or(p,r)))) = true,
inference(step,[status(thm)],[t29,t11]) ).
cnf(t27,plain,
theorem(implies(or(p,implies(q,r)),implies(or(p,q),or(p,r)))) = true,
inference(orient,[status(thm)],[t30]) ).
cnf(f8,negated_conjecture,
~ theorem(implies(or(p,implies(q,r)),implies(or(p,q),or(p,r)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f8_nnf,plain,
~ theorem(implies(or(p,implies(q,r)),implies(or(p,q),or(p,r)))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ theorem(implies(or(p,implies(q,r)),implies(or(p,q),or(p,r)))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ theorem(implies(or(p,implies(q,r)),implies(or(p,q),or(p,r)))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
theorem(implies(or(p,implies(q,r)),implies(or(p,q),or(p,r)))) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t27]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL224-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n013.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Wed Sep 23 22:26:35 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 237.64/31.96 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 237.64/31.96 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------