%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL003-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 01:01:32 PM UTC 2026
% Result : Unsatisfiable 8.85s 7.04s
% Output : Proof 8.85s
% Verified :
% Comments :
%------------------------------------------------------------------------------
cnf(t4,axiom,
sFlat0 = apply(w,w),
introduced(definition) ).
cnf(t41,plain,
apply(w,w) = sFlat0,
inference(orient,[status(thm)],[t4]) ).
cnf(t5,axiom,
sFlat1 = apply(b,apply(w,w)),
introduced(definition) ).
cnf(t33,plain,
apply(b,apply(w,w)) = sFlat1,
inference(orient,[status(thm)],[t5]) ).
cnf(t789,plain,
apply(b,sFlat0) = sFlat1,
inference(step,[status(thm)],[t33,t41]) ).
cnf(t43,plain,
apply(b,sFlat0) = sFlat1,
inference(rw,[status(thm)],[t789]) ).
cnf(t54,plain,
apply(b,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t43]) ).
cnf(t6,axiom,
sFlat2 = apply(b,w),
introduced(definition) ).
cnf(t37,plain,
apply(b,w) = sFlat2,
inference(orient,[status(thm)],[t6]) ).
cnf(t7,axiom,
sFlat3 = apply(apply(b,w),b),
introduced(definition) ).
cnf(t26,plain,
apply(apply(b,w),b) = sFlat3,
inference(orient,[status(thm)],[t7]) ).
cnf(t788,plain,
apply(sFlat2,b) = sFlat3,
inference(step,[status(thm)],[t26,t37]) ).
cnf(t40,plain,
apply(sFlat2,b) = sFlat3,
inference(rw,[status(thm)],[t788]) ).
cnf(t52,plain,
apply(sFlat2,b) = sFlat3,
inference(orient,[status(thm)],[t40]) ).
cnf(t8,axiom,
sFlat4 = apply(b,apply(apply(b,w),b)),
introduced(definition) ).
cnf(t786,plain,
sFlat4 = apply(b,sFlat3),
inference(step,[status(thm)],[t8,t26]) ).
cnf(t30,plain,
apply(b,sFlat3) = sFlat4,
inference(orient,[status(thm)],[t786]) ).
cnf(t9,axiom,
sFlat5 = apply(apply(b,apply(apply(b,w),b)),b),
introduced(definition) ).
cnf(t20,plain,
apply(apply(b,apply(apply(b,w),b)),b) = sFlat5,
inference(orient,[status(thm)],[t9]) ).
cnf(t785,plain,
apply(apply(b,sFlat3),b) = sFlat5,
inference(step,[status(thm)],[t20,t26]) ).
cnf(t29,plain,
apply(apply(b,sFlat3),b) = sFlat5,
inference(rw,[status(thm)],[t785]) ).
cnf(t794,plain,
apply(sFlat4,b) = sFlat5,
inference(step,[status(thm)],[t29,t30]) ).
cnf(t57,plain,
apply(sFlat4,b) = sFlat5,
inference(orient,[status(thm)],[t794]) ).
cnf(t10,axiom,
sFlat6 = apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b)),
introduced(definition) ).
cnf(t784,plain,
sFlat6 = apply(apply(b,apply(w,w)),sFlat5),
inference(step,[status(thm)],[t10,t20]) ).
cnf(t23,plain,
apply(apply(b,apply(w,w)),sFlat5) = sFlat6,
inference(orient,[status(thm)],[t784]) ).
cnf(t787,plain,
apply(sFlat1,sFlat5) = sFlat6,
inference(step,[status(thm)],[t23,t33]) ).
cnf(t36,plain,
apply(sFlat1,sFlat5) = sFlat6,
inference(rw,[status(thm)],[t787]) ).
cnf(t51,plain,
apply(sFlat1,sFlat5) = sFlat6,
inference(orient,[status(thm)],[t36]) ).
cnf(t11,axiom,
sFlat7 = fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b))),
introduced(definition) ).
cnf(t790,plain,
sFlat7 = fixed_point(apply(apply(b,sFlat0),apply(apply(b,apply(apply(b,w),b)),b))),
inference(step,[status(thm)],[t11,t41]) ).
cnf(t791,plain,
sFlat7 = fixed_point(apply(apply(b,sFlat0),apply(apply(b,apply(sFlat2,b)),b))),
inference(step,[status(thm)],[t790,t37]) ).
cnf(t49,plain,
fixed_point(apply(apply(b,sFlat0),apply(apply(b,apply(sFlat2,b)),b))) = sFlat7,
inference(orient,[status(thm)],[t791]) ).
cnf(t792,plain,
fixed_point(apply(apply(b,sFlat0),apply(apply(b,sFlat3),b))) = sFlat7,
inference(step,[status(thm)],[t49,t52]) ).
cnf(t793,plain,
fixed_point(apply(apply(b,sFlat0),apply(sFlat4,b))) = sFlat7,
inference(step,[status(thm)],[t792,t30]) ).
cnf(t53,plain,
fixed_point(apply(apply(b,sFlat0),apply(sFlat4,b))) = sFlat7,
inference(rw,[status(thm)],[t793]) ).
cnf(t802,plain,
fixed_point(apply(sFlat1,apply(sFlat4,b))) = sFlat7,
inference(step,[status(thm)],[t53,t54]) ).
cnf(t803,plain,
fixed_point(apply(sFlat1,sFlat5)) = sFlat7,
inference(step,[status(thm)],[t802,t57]) ).
cnf(t804,plain,
fixed_point(sFlat6) = sFlat7,
inference(step,[status(thm)],[t803,t51]) ).
cnf(t245,plain,
fixed_point(sFlat6) = sFlat7,
inference(orient,[status(thm)],[t804]) ).
cnf(f2,axiom,
( fixed_point(Strong_fixed_point)
| apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',strong_fixed_point) ).
fof(f2_nnf,plain,
! [Strong_fixed_point] :
( fixed_point(Strong_fixed_point)
| apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [Strong_fixed_point] :
( fixed_point(Strong_fixed_point)
| apply(Strong_fixed_point,fixed_pt) != apply(fixed_pt,apply(Strong_fixed_point,fixed_pt)) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( fixed_point(X0)
| apply(X0,fixed_pt) != apply(fixed_pt,apply(X0,fixed_pt)) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t3,plain,
ifeq(apply(X1,fixed_pt),apply(fixed_pt,apply(X1,fixed_pt)),fixed_point(X1),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t44,plain,
ifeq(apply(X1,fixed_pt),apply(fixed_pt,apply(X1,fixed_pt)),fixed_point(X1),true) = true,
inference(orient,[status(thm)],[t3]) ).
cnf(f0,axiom,
apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_definition) ).
fof(f0_nnf,plain,
! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,Z] : apply(apply(apply(b,X),Y),Z) = apply(X,apply(Y,Z)),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
apply(apply(apply(b,X0),X1),X2) = apply(X0,apply(X1,X2)),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t2,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t13,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t2]) ).
cnf(f1,axiom,
apply(apply(w,X),Y) = apply(apply(X,Y),Y),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_definition) ).
fof(f1_nnf,plain,
! [X,Y] : apply(apply(w,X),Y) = apply(apply(X,Y),Y),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,Y] : apply(apply(w,X),Y) = apply(apply(X,Y),Y),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
apply(apply(w,X0),X1) = apply(apply(X0,X1),X1),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t1,plain,
apply(apply(w,X1),X2) = apply(apply(X1,X2),X2),
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t14,plain,
apply(apply(X1,X2),X2) = apply(apply(w,X1),X2),
inference(orient,[status(thm)],[t1]) ).
cnf(t15,plain,
apply(apply(w,apply(b,X1)),X2) = apply(X1,apply(X2,X2)),
inference(cp,[status(thm)],[t14,t13]) ).
cnf(t27,plain,
apply(w,apply(b,X1)) = apply(sFlat3,X1),
inference(cp,[status(thm)],[t13,t26]) ).
cnf(t63,plain,
apply(w,apply(b,X1)) = apply(sFlat3,X1),
inference(orient,[status(thm)],[t27]) ).
cnf(t800,plain,
apply(apply(sFlat3,X1),X2) = apply(X1,apply(X2,X2)),
inference(step,[status(thm)],[t15,t63]) ).
cnf(t178,plain,
apply(apply(sFlat3,X1),X2) = apply(X1,apply(X2,X2)),
inference(orient,[status(thm)],[t800]) ).
cnf(t190,plain,
apply(X1,apply(apply(X2,X2),X3)) = apply(apply(apply(sFlat3,apply(b,X1)),X2),X3),
inference(cp,[status(thm)],[t13,t178]) ).
cnf(t31,plain,
apply(sFlat3,apply(X1,X2)) = apply(apply(sFlat4,X1),X2),
inference(cp,[status(thm)],[t13,t30]) ).
cnf(t89,plain,
apply(apply(sFlat4,X1),X2) = apply(sFlat3,apply(X1,X2)),
inference(orient,[status(thm)],[t31]) ).
cnf(t92,plain,
apply(sFlat3,apply(b,X1)) = apply(sFlat5,X1),
inference(cp,[status(thm)],[t89,t57]) ).
cnf(t104,plain,
apply(sFlat3,apply(b,X1)) = apply(sFlat5,X1),
inference(orient,[status(thm)],[t92]) ).
cnf(t812,plain,
apply(X1,apply(apply(X2,X2),X3)) = apply(apply(apply(sFlat5,X1),X2),X3),
inference(step,[status(thm)],[t190,t104]) ).
cnf(t355,plain,
apply(X1,apply(apply(X2,X2),X3)) = apply(apply(apply(sFlat5,X1),X2),X3),
inference(orient,[status(thm)],[t812]) ).
cnf(t369,plain,
apply(X1,apply(apply(X2,X2),X2)) = apply(apply(w,apply(sFlat5,X1)),X2),
inference(cp,[status(thm)],[t355,t14]) ).
cnf(t42,plain,
apply(apply(w,X1),X1) = apply(sFlat0,X1),
inference(cp,[status(thm)],[t14,t41]) ).
cnf(t58,plain,
apply(apply(w,X1),X1) = apply(sFlat0,X1),
inference(orient,[status(thm)],[t42]) ).
cnf(t59,plain,
apply(sFlat0,X1) = apply(apply(X1,X1),X1),
inference(cp,[status(thm)],[t58,t14]) ).
cnf(t82,plain,
apply(apply(X1,X1),X1) = apply(sFlat0,X1),
inference(orient,[status(thm)],[t59]) ).
cnf(t830,plain,
apply(X1,apply(sFlat0,X2)) = apply(apply(w,apply(sFlat5,X1)),X2),
inference(step,[status(thm)],[t369,t82]) ).
cnf(t715,plain,
apply(apply(w,apply(sFlat5,X1)),X2) = apply(X1,apply(sFlat0,X2)),
inference(orient,[status(thm)],[t830]) ).
cnf(t717,plain,
apply(X1,apply(sFlat0,apply(sFlat5,X1))) = apply(sFlat0,apply(sFlat5,X1)),
inference(cp,[status(thm)],[t715,t58]) ).
cnf(t55,plain,
apply(sFlat0,apply(X1,X2)) = apply(apply(sFlat1,X1),X2),
inference(cp,[status(thm)],[t13,t54]) ).
cnf(t114,plain,
apply(apply(sFlat1,X1),X2) = apply(sFlat0,apply(X1,X2)),
inference(orient,[status(thm)],[t55]) ).
cnf(t117,plain,
apply(sFlat0,apply(sFlat5,X1)) = apply(sFlat6,X1),
inference(cp,[status(thm)],[t114,t51]) ).
cnf(t139,plain,
apply(sFlat0,apply(sFlat5,X1)) = apply(sFlat6,X1),
inference(orient,[status(thm)],[t117]) ).
cnf(t831,plain,
apply(X1,apply(sFlat6,X1)) = apply(sFlat0,apply(sFlat5,X1)),
inference(step,[status(thm)],[t717,t139]) ).
cnf(t832,plain,
apply(X1,apply(sFlat6,X1)) = apply(sFlat6,X1),
inference(step,[status(thm)],[t831,t139]) ).
cnf(t739,plain,
apply(X1,apply(sFlat6,X1)) = apply(sFlat6,X1),
inference(orient,[status(thm)],[t832]) ).
cnf(t767,plain,
true = ifeq(apply(sFlat6,fixed_pt),apply(sFlat6,fixed_pt),fixed_point(sFlat6),true),
inference(cp,[status(thm)],[t44,t739]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t12,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t833,plain,
true = fixed_point(sFlat6),
inference(step,[status(thm)],[t767,t12]) ).
cnf(t834,plain,
true = sFlat7,
inference(step,[status(thm)],[t833,t245]) ).
cnf(t782,plain,
true = sFlat7,
inference(orient,[status(thm)],[t834]) ).
cnf(f3,negated_conjecture,
~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_strong_fixed_point) ).
fof(f3_nnf,plain,
~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
fixed_point(apply(apply(b,apply(w,w)),apply(apply(b,apply(apply(b,w),b)),b))) != true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
fixed_point(apply(apply(b,sFlat0),apply(apply(b,apply(apply(b,w),b)),b))) != true,
inference(rw,[status(thm)],[goal_0,t41]) ).
cnf(g0_1,plain,
fixed_point(apply(sFlat1,apply(apply(b,apply(apply(b,w),b)),b))) != true,
inference(rw,[status(thm)],[g0_0,t54]) ).
cnf(g0_2,plain,
fixed_point(apply(sFlat1,apply(apply(b,apply(sFlat2,b)),b))) != true,
inference(rw,[status(thm)],[g0_1,t37]) ).
cnf(g0_3,plain,
fixed_point(apply(sFlat1,apply(apply(b,sFlat3),b))) != true,
inference(rw,[status(thm)],[g0_2,t52]) ).
cnf(g0_4,plain,
fixed_point(apply(sFlat1,apply(sFlat4,b))) != true,
inference(rw,[status(thm)],[g0_3,t30]) ).
cnf(g0_5,plain,
fixed_point(apply(sFlat1,sFlat5)) != true,
inference(rw,[status(thm)],[g0_4,t57]) ).
cnf(g0_6,plain,
fixed_point(sFlat6) != true,
inference(rw,[status(thm)],[g0_5,t51]) ).
cnf(g0_7,plain,
sFlat7 != true,
inference(rw,[status(thm)],[g0_6,t245]) ).
cnf(g0_8,plain,
sFlat7 != sFlat7,
inference(rw,[status(thm)],[g0_7,t782]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : COL003-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/5.38 % Computer : n026.cluster.edu
% 0.11/5.38 % Model : x86_64 x86_64
% 0.11/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.38 % Memory : 8046.5625MB
% 0.11/5.38 % OS : Linux 6.8.0-71-generic
% 0.11/5.38 % CPULimit : 300
% 0.11/5.38 % WCLimit : 300
% 0.11/5.38 % DateTime : Fri Sep 25 07:12:02 UTC 2026
% 0.11/5.39 % CPUTime :
% 0.11/5.39 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 8.85/7.04 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 8.85/7.04 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------