%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL174-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n004.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 02:01:10 PM UTC 2026
% Result : Unsatisfiable 5.64s 1.18s
% Output : Proof 5.64s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
sF0 = not(p),
introduced(definition) ).
cnf(t18,plain,
not(p) = sF0,
inference(orient,[status(thm)],[t8]) ).
cnf(t9,axiom,
sF1 = or(not(p),q),
introduced(definition) ).
cnf(t756,plain,
sF1 = or(sF0,q),
inference(step,[status(thm)],[t9,t18]) ).
cnf(t20,plain,
or(sF0,q) = sF1,
inference(orient,[status(thm)],[t756]) ).
cnf(t10,axiom,
sF2 = not(or(not(p),q)),
introduced(definition) ).
cnf(t759,plain,
sF2 = not(or(sF0,q)),
inference(step,[status(thm)],[t10,t18]) ).
cnf(t760,plain,
sF2 = not(sF1),
inference(step,[status(thm)],[t759,t20]) ).
cnf(t24,plain,
not(sF1) = sF2,
inference(orient,[status(thm)],[t760]) ).
cnf(t11,axiom,
sF3 = not(q),
introduced(definition) ).
cnf(t19,plain,
not(q) = sF3,
inference(orient,[status(thm)],[t11]) ).
cnf(t12,axiom,
sF4 = or(not(q),r),
introduced(definition) ).
cnf(t757,plain,
sF4 = or(sF3,r),
inference(step,[status(thm)],[t12,t19]) ).
cnf(t21,plain,
or(sF3,r) = sF4,
inference(orient,[status(thm)],[t757]) ).
cnf(t13,axiom,
sF5 = not(or(not(q),r)),
introduced(definition) ).
cnf(t761,plain,
sF5 = not(or(sF3,r)),
inference(step,[status(thm)],[t13,t19]) ).
cnf(t762,plain,
sF5 = not(sF4),
inference(step,[status(thm)],[t761,t21]) ).
cnf(t25,plain,
not(sF4) = sF5,
inference(orient,[status(thm)],[t762]) ).
cnf(t14,axiom,
sF6 = or(not(p),r),
introduced(definition) ).
cnf(t758,plain,
sF6 = or(sF0,r),
inference(step,[status(thm)],[t14,t18]) ).
cnf(t22,plain,
or(sF0,r) = sF6,
inference(orient,[status(thm)],[t758]) ).
cnf(t15,axiom,
sF7 = or(not(or(not(q),r)),or(not(p),r)),
introduced(definition) ).
cnf(t782,plain,
sF7 = or(not(or(sF3,r)),or(not(p),r)),
inference(step,[status(thm)],[t15,t19]) ).
cnf(t783,plain,
sF7 = or(not(sF4),or(not(p),r)),
inference(step,[status(thm)],[t782,t21]) ).
cnf(t784,plain,
sF7 = or(sF5,or(not(p),r)),
inference(step,[status(thm)],[t783,t25]) ).
cnf(t785,plain,
sF7 = or(sF5,or(sF0,r)),
inference(step,[status(thm)],[t784,t18]) ).
cnf(t786,plain,
sF7 = or(sF5,sF6),
inference(step,[status(thm)],[t785,t22]) ).
cnf(t96,plain,
or(sF5,sF6) = sF7,
inference(orient,[status(thm)],[t786]) ).
cnf(t16,axiom,
sF8 = or(not(or(not(p),q)),or(not(or(not(q),r)),or(not(p),r))),
introduced(definition) ).
cnf(t796,plain,
sF8 = or(not(or(sF0,q)),or(not(or(not(q),r)),or(not(p),r))),
inference(step,[status(thm)],[t16,t18]) ).
cnf(t797,plain,
sF8 = or(not(sF1),or(not(or(not(q),r)),or(not(p),r))),
inference(step,[status(thm)],[t796,t20]) ).
cnf(t798,plain,
sF8 = or(sF2,or(not(or(not(q),r)),or(not(p),r))),
inference(step,[status(thm)],[t797,t24]) ).
cnf(t799,plain,
sF8 = or(sF2,or(not(or(sF3,r)),or(not(p),r))),
inference(step,[status(thm)],[t798,t19]) ).
cnf(t800,plain,
sF8 = or(sF2,or(not(sF4),or(not(p),r))),
inference(step,[status(thm)],[t799,t21]) ).
cnf(t801,plain,
sF8 = or(sF2,or(sF5,or(not(p),r))),
inference(step,[status(thm)],[t800,t25]) ).
cnf(t802,plain,
sF8 = or(sF2,or(sF5,or(sF0,r))),
inference(step,[status(thm)],[t801,t18]) ).
cnf(t803,plain,
sF8 = or(sF2,or(sF5,sF6)),
inference(step,[status(thm)],[t802,t22]) ).
cnf(t804,plain,
sF8 = or(sF2,sF7),
inference(step,[status(thm)],[t803,t96]) ).
cnf(t239,plain,
or(sF2,sF7) = sF8,
inference(orient,[status(thm)],[t804]) ).
cnf(t17,axiom,
sF9 = theorem(or(not(or(not(p),q)),or(not(or(not(q),r)),or(not(p),r)))),
introduced(definition) ).
cnf(t808,plain,
sF9 = theorem(or(not(or(sF0,q)),or(not(or(not(q),r)),or(not(p),r)))),
inference(step,[status(thm)],[t17,t18]) ).
cnf(t809,plain,
sF9 = theorem(or(not(sF1),or(not(or(not(q),r)),or(not(p),r)))),
inference(step,[status(thm)],[t808,t20]) ).
cnf(t810,plain,
sF9 = theorem(or(sF2,or(not(or(not(q),r)),or(not(p),r)))),
inference(step,[status(thm)],[t809,t24]) ).
cnf(t811,plain,
sF9 = theorem(or(sF2,or(not(or(sF3,r)),or(not(p),r)))),
inference(step,[status(thm)],[t810,t19]) ).
cnf(t812,plain,
sF9 = theorem(or(sF2,or(not(sF4),or(not(p),r)))),
inference(step,[status(thm)],[t811,t21]) ).
cnf(t813,plain,
sF9 = theorem(or(sF2,or(sF5,or(not(p),r)))),
inference(step,[status(thm)],[t812,t25]) ).
cnf(t814,plain,
sF9 = theorem(or(sF2,or(sF5,or(sF0,r)))),
inference(step,[status(thm)],[t813,t18]) ).
cnf(t815,plain,
sF9 = theorem(or(sF2,or(sF5,sF6))),
inference(step,[status(thm)],[t814,t22]) ).
cnf(t816,plain,
sF9 = theorem(or(sF2,sF7)),
inference(step,[status(thm)],[t815,t96]) ).
cnf(t817,plain,
sF9 = theorem(sF8),
inference(step,[status(thm)],[t816,t239]) ).
cnf(t270,plain,
theorem(sF8) = sF9,
inference(orient,[status(thm)],[t817]) ).
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(u5,axiom,
ifeq(theorem(implies(X0,X1)),true,ifeq(theorem(X0),true,theorem(X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
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(d0,axiom,
implies(X0,X1) = or(not(X0),X1),
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(t7,plain,
ifeq(theorem(or(not(X1),X2)),true,ifeq(theorem(X1),true,theorem(X2),true),true) = true,
inference(definition_unfolding,[status(thm)],[u5,d0]) ).
cnf(t133,plain,
ifeq(theorem(or(not(X1),X2)),true,ifeq(theorem(X1),true,theorem(X2),true),true) = true,
inference(orient,[status(thm)],[t7]) ).
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(t3,plain,
ifeq(axiom(X1),true,theorem(X1),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t42,plain,
ifeq(axiom(X1),true,theorem(X1),true) = true,
inference(orient,[status(thm)],[t3]) ).
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(u3,axiom,
axiom(implies(or(X0,or(X1,X2)),or(X1,or(X0,X2)))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t5,plain,
axiom(or(not(or(X1,or(X2,X3))),or(X2,or(X1,X3)))) = true,
inference(definition_unfolding,[status(thm)],[u3,d0]) ).
cnf(t75,plain,
axiom(or(not(or(X1,or(X2,X3))),or(X2,or(X1,X3)))) = true,
inference(orient,[status(thm)],[t5]) ).
cnf(t102,plain,
true = axiom(or(not(or(sF5,or(X1,sF6))),or(X1,sF7))),
inference(cp,[status(thm)],[t75,t96]) ).
cnf(t490,plain,
axiom(or(not(or(sF5,or(X1,sF6))),or(X1,sF7))) = true,
inference(orient,[status(thm)],[t102]) ).
cnf(t491,plain,
true = axiom(or(not(or(sF5,or(sF2,sF6))),sF8)),
inference(cp,[status(thm)],[t490,t239]) ).
cnf(t492,plain,
axiom(or(not(or(sF5,or(sF2,sF6))),sF8)) = true,
inference(orient,[status(thm)],[t491]) ).
cnf(t493,plain,
true = ifeq(true,true,theorem(or(not(or(sF5,or(sF2,sF6))),sF8)),true),
inference(cp,[status(thm)],[t42,t492]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t23,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t870,plain,
true = theorem(or(not(or(sF5,or(sF2,sF6))),sF8)),
inference(step,[status(thm)],[t493,t23]) ).
cnf(t494,plain,
theorem(or(not(or(sF5,or(sF2,sF6))),sF8)) = true,
inference(orient,[status(thm)],[t870]) ).
cnf(t495,plain,
true = ifeq(true,true,ifeq(theorem(or(sF5,or(sF2,sF6))),true,theorem(sF8),true),true),
inference(cp,[status(thm)],[t133,t494]) ).
cnf(t871,plain,
true = ifeq(theorem(or(sF5,or(sF2,sF6))),true,theorem(sF8),true),
inference(step,[status(thm)],[t495,t23]) ).
cnf(t872,plain,
true = ifeq(theorem(or(sF5,or(sF2,sF6))),true,sF9,true),
inference(step,[status(thm)],[t871,t270]) ).
cnf(t498,plain,
ifeq(theorem(or(sF5,or(sF2,sF6))),true,sF9,true) = true,
inference(orient,[status(thm)],[t872]) ).
cnf(t507,plain,
ifeq(true,true,sF9,true) = true,
inference(rw,[status(thm)],[t498]) ).
cnf(t878,plain,
sF9 = true,
inference(step,[status(thm)],[t507,t23]) ).
cnf(t510,plain,
true = sF9,
inference(orient,[status(thm)],[t878]) ).
cnf(f8,negated_conjecture,
~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
fof(f8_nnf,plain,
~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(u6,negated_conjecture,
theorem(implies(implies(p,q),implies(implies(q,r),implies(p,r)))) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(goal_0,negated_conjecture,
theorem(or(not(or(not(p),q)),or(not(or(not(q),r)),or(not(p),r)))) != true,
inference(definition_unfolding,[status(thm)],[u6,d0]) ).
cnf(g0_0,plain,
theorem(or(not(or(sF0,q)),or(not(or(not(q),r)),or(not(p),r)))) != true,
inference(rw,[status(thm)],[goal_0,t18]) ).
cnf(g0_1,plain,
theorem(or(not(sF1),or(not(or(not(q),r)),or(not(p),r)))) != true,
inference(rw,[status(thm)],[g0_0,t20]) ).
cnf(g0_2,plain,
theorem(or(sF2,or(not(or(not(q),r)),or(not(p),r)))) != true,
inference(rw,[status(thm)],[g0_1,t24]) ).
cnf(g0_3,plain,
theorem(or(sF2,or(not(or(sF3,r)),or(not(p),r)))) != true,
inference(rw,[status(thm)],[g0_2,t19]) ).
cnf(g0_4,plain,
theorem(or(sF2,or(not(sF4),or(not(p),r)))) != true,
inference(rw,[status(thm)],[g0_3,t21]) ).
cnf(g0_5,plain,
theorem(or(sF2,or(sF5,or(not(p),r)))) != true,
inference(rw,[status(thm)],[g0_4,t25]) ).
cnf(g0_6,plain,
theorem(or(sF2,or(sF5,or(sF0,r)))) != true,
inference(rw,[status(thm)],[g0_5,t18]) ).
cnf(g0_7,plain,
theorem(or(sF2,or(sF5,sF6))) != true,
inference(rw,[status(thm)],[g0_6,t22]) ).
cnf(g0_8,plain,
theorem(or(sF2,sF7)) != true,
inference(rw,[status(thm)],[g0_7,t96]) ).
cnf(g0_9,plain,
theorem(sF8) != true,
inference(rw,[status(thm)],[g0_8,t239]) ).
cnf(g0_10,plain,
sF9 != true,
inference(rw,[status(thm)],[g0_9,t270]) ).
cnf(g0_11,plain,
sF9 != sF9,
inference(rw,[status(thm)],[g0_10,t510]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL174-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.38 % Computer : n004.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Wed Sep 23 22:10:05 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 5.64/1.18 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 5.64/1.18 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------