%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL172-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 02:01:08 PM UTC 2026
% Result : Unsatisfiable 3.08s 0.85s
% Output : Proof 3.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 28 unt; 0 def)
% Number of atoms : 36 ( 19 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 10 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 6 ( 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 : 34 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f3,axiom,
axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
fof(f3_nnf,plain,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C] : axiom(implies(or(A,or(B,C)),or(B,or(A,C)))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi4,axiom,
axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
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(p),or(not(q),r))),or(not(q),or(not(p),r)))) = true,
inference(hyper_resolution,[status(thm)],[hi4,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(t9,plain,
theorem(or(not(or(not(p),or(not(q),r))),or(not(q),or(not(p),r)))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h0]) ).
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(not(p),or(not(q),r)),or(not(q),or(not(p),r)))) = true,
inference(step,[status(thm)],[t9,t11]) ).
cnf(t29,plain,
theorem(implies(implies(p,or(not(q),r)),or(not(q),or(not(p),r)))) = true,
inference(step,[status(thm)],[t28,t11]) ).
cnf(t30,plain,
theorem(implies(implies(p,implies(q,r)),or(not(q),or(not(p),r)))) = true,
inference(step,[status(thm)],[t29,t11]) ).
cnf(t31,plain,
theorem(implies(implies(p,implies(q,r)),implies(q,or(not(p),r)))) = true,
inference(step,[status(thm)],[t30,t11]) ).
cnf(t32,plain,
theorem(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))) = true,
inference(step,[status(thm)],[t31,t11]) ).
cnf(t27,plain,
theorem(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))) = true,
inference(orient,[status(thm)],[t32]) ).
cnf(f8,negated_conjecture,
~ theorem(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f8_nnf,plain,
~ theorem(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ theorem(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ theorem(implies(implies(p,implies(q,r)),implies(q,implies(p,r)))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(goal_0,negated_conjecture,
theorem(implies(implies(p,implies(q,r)),implies(q,implies(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 : LCL172-3 : 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 : n002.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 22:12:33 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 3.08/0.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 3.08/0.85 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------