%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL173-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n010.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 5.01s 1.11s
% Output : Proof 5.01s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
sF0 = not(q),
introduced(definition) ).
cnf(t18,plain,
not(q) = sF0,
inference(orient,[status(thm)],[t8]) ).
cnf(t9,axiom,
sF1 = or(not(q),r),
introduced(definition) ).
cnf(t752,plain,
sF1 = or(sF0,r),
inference(step,[status(thm)],[t9,t18]) ).
cnf(t20,plain,
or(sF0,r) = sF1,
inference(orient,[status(thm)],[t752]) ).
cnf(t10,axiom,
sF2 = not(or(not(q),r)),
introduced(definition) ).
cnf(t755,plain,
sF2 = not(or(sF0,r)),
inference(step,[status(thm)],[t10,t18]) ).
cnf(t756,plain,
sF2 = not(sF1),
inference(step,[status(thm)],[t755,t20]) ).
cnf(t24,plain,
not(sF1) = sF2,
inference(orient,[status(thm)],[t756]) ).
cnf(t11,axiom,
sF3 = not(p),
introduced(definition) ).
cnf(t19,plain,
not(p) = sF3,
inference(orient,[status(thm)],[t11]) ).
cnf(t12,axiom,
sF4 = or(not(p),q),
introduced(definition) ).
cnf(t753,plain,
sF4 = or(sF3,q),
inference(step,[status(thm)],[t12,t19]) ).
cnf(t21,plain,
or(sF3,q) = sF4,
inference(orient,[status(thm)],[t753]) ).
cnf(t13,axiom,
sF5 = not(or(not(p),q)),
introduced(definition) ).
cnf(t757,plain,
sF5 = not(or(sF3,q)),
inference(step,[status(thm)],[t13,t19]) ).
cnf(t758,plain,
sF5 = not(sF4),
inference(step,[status(thm)],[t757,t21]) ).
cnf(t25,plain,
not(sF4) = sF5,
inference(orient,[status(thm)],[t758]) ).
cnf(t14,axiom,
sF6 = or(not(p),r),
introduced(definition) ).
cnf(t754,plain,
sF6 = or(sF3,r),
inference(step,[status(thm)],[t14,t19]) ).
cnf(t22,plain,
or(sF3,r) = sF6,
inference(orient,[status(thm)],[t754]) ).
cnf(t15,axiom,
sF7 = or(not(or(not(p),q)),or(not(p),r)),
introduced(definition) ).
cnf(t778,plain,
sF7 = or(not(or(sF3,q)),or(not(p),r)),
inference(step,[status(thm)],[t15,t19]) ).
cnf(t779,plain,
sF7 = or(not(sF4),or(not(p),r)),
inference(step,[status(thm)],[t778,t21]) ).
cnf(t780,plain,
sF7 = or(sF5,or(not(p),r)),
inference(step,[status(thm)],[t779,t25]) ).
cnf(t781,plain,
sF7 = or(sF5,or(sF3,r)),
inference(step,[status(thm)],[t780,t19]) ).
cnf(t782,plain,
sF7 = or(sF5,sF6),
inference(step,[status(thm)],[t781,t22]) ).
cnf(t96,plain,
or(sF5,sF6) = sF7,
inference(orient,[status(thm)],[t782]) ).
cnf(t16,axiom,
sF8 = or(not(or(not(q),r)),or(not(or(not(p),q)),or(not(p),r))),
introduced(definition) ).
cnf(t793,plain,
sF8 = or(not(or(sF0,r)),or(not(or(not(p),q)),or(not(p),r))),
inference(step,[status(thm)],[t16,t18]) ).
cnf(t794,plain,
sF8 = or(not(sF1),or(not(or(not(p),q)),or(not(p),r))),
inference(step,[status(thm)],[t793,t20]) ).
cnf(t795,plain,
sF8 = or(sF2,or(not(or(not(p),q)),or(not(p),r))),
inference(step,[status(thm)],[t794,t24]) ).
cnf(t796,plain,
sF8 = or(sF2,or(not(or(sF3,q)),or(not(p),r))),
inference(step,[status(thm)],[t795,t19]) ).
cnf(t797,plain,
sF8 = or(sF2,or(not(sF4),or(not(p),r))),
inference(step,[status(thm)],[t796,t21]) ).
cnf(t798,plain,
sF8 = or(sF2,or(sF5,or(not(p),r))),
inference(step,[status(thm)],[t797,t25]) ).
cnf(t799,plain,
sF8 = or(sF2,or(sF5,or(sF3,r))),
inference(step,[status(thm)],[t798,t19]) ).
cnf(t800,plain,
sF8 = or(sF2,or(sF5,sF6)),
inference(step,[status(thm)],[t799,t22]) ).
cnf(t801,plain,
sF8 = or(sF2,sF7),
inference(step,[status(thm)],[t800,t96]) ).
cnf(t245,plain,
or(sF2,sF7) = sF8,
inference(orient,[status(thm)],[t801]) ).
cnf(t17,axiom,
sF9 = theorem(or(not(or(not(q),r)),or(not(or(not(p),q)),or(not(p),r)))),
introduced(definition) ).
cnf(t805,plain,
sF9 = theorem(or(not(or(sF0,r)),or(not(or(not(p),q)),or(not(p),r)))),
inference(step,[status(thm)],[t17,t18]) ).
cnf(t806,plain,
sF9 = theorem(or(not(sF1),or(not(or(not(p),q)),or(not(p),r)))),
inference(step,[status(thm)],[t805,t20]) ).
cnf(t807,plain,
sF9 = theorem(or(sF2,or(not(or(not(p),q)),or(not(p),r)))),
inference(step,[status(thm)],[t806,t24]) ).
cnf(t808,plain,
sF9 = theorem(or(sF2,or(not(or(sF3,q)),or(not(p),r)))),
inference(step,[status(thm)],[t807,t19]) ).
cnf(t809,plain,
sF9 = theorem(or(sF2,or(not(sF4),or(not(p),r)))),
inference(step,[status(thm)],[t808,t21]) ).
cnf(t810,plain,
sF9 = theorem(or(sF2,or(sF5,or(not(p),r)))),
inference(step,[status(thm)],[t809,t25]) ).
cnf(t811,plain,
sF9 = theorem(or(sF2,or(sF5,or(sF3,r)))),
inference(step,[status(thm)],[t810,t19]) ).
cnf(t812,plain,
sF9 = theorem(or(sF2,or(sF5,sF6))),
inference(step,[status(thm)],[t811,t22]) ).
cnf(t813,plain,
sF9 = theorem(or(sF2,sF7)),
inference(step,[status(thm)],[t812,t96]) ).
cnf(t814,plain,
sF9 = theorem(sF8),
inference(step,[status(thm)],[t813,t245]) ).
cnf(t275,plain,
theorem(sF8) = sF9,
inference(orient,[status(thm)],[t814]) ).
cnf(f6,axiom,
( ~ axiom(X)
| theorem(X) ),
file('/export/starexec/sandbox/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(f4,axiom,
axiom(implies(implies(A,B),implies(or(C,A),or(C,B)))),
file('/export/starexec/sandbox/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(u4,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/sandbox/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(t6,plain,
axiom(or(not(or(not(X1),X2)),or(not(or(X3,X1)),or(X3,X2)))) = true,
inference(definition_unfolding,[status(thm)],[u4,d0]) ).
cnf(t105,plain,
axiom(or(not(or(not(X1),X2)),or(not(or(X3,X1)),or(X3,X2)))) = true,
inference(orient,[status(thm)],[t6]) ).
cnf(t110,plain,
true = axiom(or(not(or(not(q),X1)),or(not(sF4),or(sF3,X1)))),
inference(cp,[status(thm)],[t105,t21]) ).
cnf(t869,plain,
true = axiom(or(not(or(sF0,X1)),or(not(sF4),or(sF3,X1)))),
inference(step,[status(thm)],[t110,t18]) ).
cnf(t870,plain,
true = axiom(or(not(or(sF0,X1)),or(sF5,or(sF3,X1)))),
inference(step,[status(thm)],[t869,t25]) ).
cnf(t500,plain,
axiom(or(not(or(sF0,X1)),or(sF5,or(sF3,X1)))) = true,
inference(orient,[status(thm)],[t870]) ).
cnf(t501,plain,
true = axiom(or(not(sF1),or(sF5,or(sF3,r)))),
inference(cp,[status(thm)],[t500,t20]) ).
cnf(t871,plain,
true = axiom(or(sF2,or(sF5,or(sF3,r)))),
inference(step,[status(thm)],[t501,t24]) ).
cnf(t872,plain,
true = axiom(or(sF2,or(sF5,sF6))),
inference(step,[status(thm)],[t871,t22]) ).
cnf(t873,plain,
true = axiom(or(sF2,sF7)),
inference(step,[status(thm)],[t872,t96]) ).
cnf(t874,plain,
true = axiom(sF8),
inference(step,[status(thm)],[t873,t245]) ).
cnf(t504,plain,
axiom(sF8) = true,
inference(orient,[status(thm)],[t874]) ).
cnf(t506,plain,
true = ifeq(true,true,theorem(sF8),true),
inference(cp,[status(thm)],[t42,t504]) ).
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(t875,plain,
true = theorem(sF8),
inference(step,[status(thm)],[t506,t23]) ).
cnf(t876,plain,
true = sF9,
inference(step,[status(thm)],[t875,t275]) ).
cnf(t507,plain,
true = sF9,
inference(orient,[status(thm)],[t876]) ).
cnf(f8,negated_conjecture,
~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f8_nnf,plain,
~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(u6,negated_conjecture,
theorem(implies(implies(q,r),implies(implies(p,q),implies(p,r)))) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(goal_0,negated_conjecture,
theorem(or(not(or(not(q),r)),or(not(or(not(p),q)),or(not(p),r)))) != true,
inference(definition_unfolding,[status(thm)],[u6,d0]) ).
cnf(g0_0,plain,
theorem(or(not(or(sF0,r)),or(not(or(not(p),q)),or(not(p),r)))) != true,
inference(rw,[status(thm)],[goal_0,t18]) ).
cnf(g0_1,plain,
theorem(or(not(sF1),or(not(or(not(p),q)),or(not(p),r)))) != true,
inference(rw,[status(thm)],[g0_0,t20]) ).
cnf(g0_2,plain,
theorem(or(sF2,or(not(or(not(p),q)),or(not(p),r)))) != true,
inference(rw,[status(thm)],[g0_1,t24]) ).
cnf(g0_3,plain,
theorem(or(sF2,or(not(or(sF3,q)),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(sF3,r)))) != true,
inference(rw,[status(thm)],[g0_5,t19]) ).
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,t245]) ).
cnf(g0_10,plain,
sF9 != true,
inference(rw,[status(thm)],[g0_9,t275]) ).
cnf(g0_11,plain,
sF9 != sF9,
inference(rw,[status(thm)],[g0_10,t507]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_11]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL173-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n010.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Wed Sep 23 22:10:12 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.01/1.11 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.01/1.11 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------