%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : LCL226-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.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 02:01:27 PM UTC 2026
% Result : Unsatisfiable 5.92s 1.20s
% Output : Proof 5.92s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t8,axiom,
sF0 = or(q,r),
introduced(definition) ).
cnf(t18,plain,
or(q,r) = sF0,
inference(orient,[status(thm)],[t8]) ).
cnf(t9,axiom,
sF1 = not(or(q,r)),
introduced(definition) ).
cnf(t738,plain,
sF1 = not(sF0),
inference(step,[status(thm)],[t9,t18]) ).
cnf(t20,plain,
not(sF0) = sF1,
inference(orient,[status(thm)],[t738]) ).
cnf(t10,axiom,
sF2 = not(r),
introduced(definition) ).
cnf(t17,plain,
not(r) = sF2,
inference(orient,[status(thm)],[t10]) ).
cnf(t11,axiom,
sF3 = or(not(r),s),
introduced(definition) ).
cnf(t739,plain,
sF3 = or(sF2,s),
inference(step,[status(thm)],[t11,t17]) ).
cnf(t21,plain,
or(sF2,s) = sF3,
inference(orient,[status(thm)],[t739]) ).
cnf(t12,axiom,
sF4 = not(or(not(r),s)),
introduced(definition) ).
cnf(t740,plain,
sF4 = not(or(sF2,s)),
inference(step,[status(thm)],[t12,t17]) ).
cnf(t741,plain,
sF4 = not(sF3),
inference(step,[status(thm)],[t740,t21]) ).
cnf(t23,plain,
not(sF3) = sF4,
inference(orient,[status(thm)],[t741]) ).
cnf(t13,axiom,
sF5 = or(q,s),
introduced(definition) ).
cnf(t19,plain,
or(q,s) = sF5,
inference(orient,[status(thm)],[t13]) ).
cnf(t14,axiom,
sF6 = or(not(or(not(r),s)),or(q,s)),
introduced(definition) ).
cnf(t759,plain,
sF6 = or(not(or(sF2,s)),or(q,s)),
inference(step,[status(thm)],[t14,t17]) ).
cnf(t760,plain,
sF6 = or(not(sF3),or(q,s)),
inference(step,[status(thm)],[t759,t21]) ).
cnf(t761,plain,
sF6 = or(sF4,or(q,s)),
inference(step,[status(thm)],[t760,t23]) ).
cnf(t762,plain,
sF6 = or(sF4,sF5),
inference(step,[status(thm)],[t761,t19]) ).
cnf(t89,plain,
or(sF4,sF5) = sF6,
inference(orient,[status(thm)],[t762]) ).
cnf(t15,axiom,
sF7 = or(not(or(q,r)),or(not(or(not(r),s)),or(q,s))),
introduced(definition) ).
cnf(t774,plain,
sF7 = or(not(sF0),or(not(or(not(r),s)),or(q,s))),
inference(step,[status(thm)],[t15,t18]) ).
cnf(t775,plain,
sF7 = or(sF1,or(not(or(not(r),s)),or(q,s))),
inference(step,[status(thm)],[t774,t20]) ).
cnf(t776,plain,
sF7 = or(sF1,or(not(or(sF2,s)),or(q,s))),
inference(step,[status(thm)],[t775,t17]) ).
cnf(t777,plain,
sF7 = or(sF1,or(not(sF3),or(q,s))),
inference(step,[status(thm)],[t776,t21]) ).
cnf(t778,plain,
sF7 = or(sF1,or(sF4,or(q,s))),
inference(step,[status(thm)],[t777,t23]) ).
cnf(t779,plain,
sF7 = or(sF1,or(sF4,sF5)),
inference(step,[status(thm)],[t778,t19]) ).
cnf(t780,plain,
sF7 = or(sF1,sF6),
inference(step,[status(thm)],[t779,t89]) ).
cnf(t243,plain,
or(sF1,sF6) = sF7,
inference(orient,[status(thm)],[t780]) ).
cnf(t16,axiom,
sF8 = theorem(or(not(or(q,r)),or(not(or(not(r),s)),or(q,s)))),
introduced(definition) ).
cnf(t786,plain,
sF8 = theorem(or(not(sF0),or(not(or(not(r),s)),or(q,s)))),
inference(step,[status(thm)],[t16,t18]) ).
cnf(t787,plain,
sF8 = theorem(or(sF1,or(not(or(not(r),s)),or(q,s)))),
inference(step,[status(thm)],[t786,t20]) ).
cnf(t788,plain,
sF8 = theorem(or(sF1,or(not(or(sF2,s)),or(q,s)))),
inference(step,[status(thm)],[t787,t17]) ).
cnf(t789,plain,
sF8 = theorem(or(sF1,or(not(sF3),or(q,s)))),
inference(step,[status(thm)],[t788,t21]) ).
cnf(t790,plain,
sF8 = theorem(or(sF1,or(sF4,or(q,s)))),
inference(step,[status(thm)],[t789,t23]) ).
cnf(t791,plain,
sF8 = theorem(or(sF1,or(sF4,sF5))),
inference(step,[status(thm)],[t790,t19]) ).
cnf(t792,plain,
sF8 = theorem(or(sF1,sF6)),
inference(step,[status(thm)],[t791,t89]) ).
cnf(t793,plain,
sF8 = theorem(sF7),
inference(step,[status(thm)],[t792,t243]) ).
cnf(t274,plain,
theorem(sF7) = sF8,
inference(orient,[status(thm)],[t793]) ).
cnf(f7,axiom,
( ~ theorem(Y)
| ~ theorem(implies(Y,X))
| theorem(X) ),
file('/export/starexec/sandbox/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/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(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(t135,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/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(t38,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/sandbox/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(t95,plain,
true = axiom(or(not(or(sF4,or(X1,sF5))),or(X1,sF6))),
inference(cp,[status(thm)],[t75,t89]) ).
cnf(t456,plain,
axiom(or(not(or(sF4,or(X1,sF5))),or(X1,sF6))) = true,
inference(orient,[status(thm)],[t95]) ).
cnf(t457,plain,
true = axiom(or(not(or(sF4,or(sF1,sF5))),sF7)),
inference(cp,[status(thm)],[t456,t243]) ).
cnf(t458,plain,
axiom(or(not(or(sF4,or(sF1,sF5))),sF7)) = true,
inference(orient,[status(thm)],[t457]) ).
cnf(t459,plain,
true = ifeq(true,true,theorem(or(not(or(sF4,or(sF1,sF5))),sF7)),true),
inference(cp,[status(thm)],[t38,t458]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t22,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t837,plain,
true = theorem(or(not(or(sF4,or(sF1,sF5))),sF7)),
inference(step,[status(thm)],[t459,t22]) ).
cnf(t460,plain,
theorem(or(not(or(sF4,or(sF1,sF5))),sF7)) = true,
inference(orient,[status(thm)],[t837]) ).
cnf(t461,plain,
true = ifeq(true,true,ifeq(theorem(or(sF4,or(sF1,sF5))),true,theorem(sF7),true),true),
inference(cp,[status(thm)],[t135,t460]) ).
cnf(t844,plain,
true = ifeq(theorem(or(sF4,or(sF1,sF5))),true,theorem(sF7),true),
inference(step,[status(thm)],[t461,t22]) ).
cnf(t845,plain,
true = ifeq(theorem(or(sF4,or(sF1,sF5))),true,sF8,true),
inference(step,[status(thm)],[t844,t274]) ).
cnf(t481,plain,
ifeq(theorem(or(sF4,or(sF1,sF5))),true,sF8,true) = true,
inference(orient,[status(thm)],[t845]) ).
cnf(t495,plain,
ifeq(true,true,sF8,true) = true,
inference(rw,[status(thm)],[t481]) ).
cnf(t851,plain,
sF8 = true,
inference(step,[status(thm)],[t495,t22]) ).
cnf(t498,plain,
true = sF8,
inference(orient,[status(thm)],[t851]) ).
cnf(f8,negated_conjecture,
~ theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
fof(f8_nnf,plain,
~ theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
~ theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
~ theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(u6,negated_conjecture,
theorem(implies(or(q,r),implies(or(not(r),s),or(q,s)))) != true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(goal_0,negated_conjecture,
theorem(or(not(or(q,r)),or(not(or(not(r),s)),or(q,s)))) != true,
inference(definition_unfolding,[status(thm)],[u6,d0]) ).
cnf(g0_0,plain,
theorem(or(not(sF0),or(not(or(not(r),s)),or(q,s)))) != true,
inference(rw,[status(thm)],[goal_0,t18]) ).
cnf(g0_1,plain,
theorem(or(sF1,or(not(or(not(r),s)),or(q,s)))) != true,
inference(rw,[status(thm)],[g0_0,t20]) ).
cnf(g0_2,plain,
theorem(or(sF1,or(not(or(sF2,s)),or(q,s)))) != true,
inference(rw,[status(thm)],[g0_1,t17]) ).
cnf(g0_3,plain,
theorem(or(sF1,or(not(sF3),or(q,s)))) != true,
inference(rw,[status(thm)],[g0_2,t21]) ).
cnf(g0_4,plain,
theorem(or(sF1,or(sF4,or(q,s)))) != true,
inference(rw,[status(thm)],[g0_3,t23]) ).
cnf(g0_5,plain,
theorem(or(sF1,or(sF4,sF5))) != true,
inference(rw,[status(thm)],[g0_4,t19]) ).
cnf(g0_6,plain,
theorem(or(sF1,sF6)) != true,
inference(rw,[status(thm)],[g0_5,t89]) ).
cnf(g0_7,plain,
theorem(sF7) != true,
inference(rw,[status(thm)],[g0_6,t243]) ).
cnf(g0_8,plain,
sF8 != true,
inference(rw,[status(thm)],[g0_7,t274]) ).
cnf(g0_9,plain,
sF8 != sF8,
inference(rw,[status(thm)],[g0_8,t498]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL226-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n020.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Wed Sep 23 22:28:48 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.92/1.20 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.92/1.20 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------