%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : COL003-9 : TPTP v9.3.1. Released v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 01:01:40 PM UTC 2026
% Result : Unsatisfiable 2.98s 7.20s
% Output : Proof 2.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 93 ( 89 unt; 0 def)
% Number of atoms : 97 ( 88 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 15 ( 11 ~; 4 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 1 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 11 con; 0-4 aty)
% Number of variables : 92 ( 2 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
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(t49,plain,
ifeq(apply(X1,fixed_pt),apply(fixed_pt,apply(X1,fixed_pt)),fixed_point(X1),true) = true,
inference(orient,[status(thm)],[t3]) ).
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(t15,plain,
apply(apply(X1,X2),X2) = apply(apply(w,X1),X2),
inference(orient,[status(thm)],[t1]) ).
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(t14,plain,
apply(apply(apply(b,X1),X2),X3) = apply(X1,apply(X2,X3)),
inference(orient,[status(thm)],[t2]) ).
cnf(t17,plain,
apply(apply(w,apply(apply(b,X1),X2)),X3) = apply(apply(X1,apply(X2,X3)),X3),
inference(cp,[status(thm)],[t15,t14]) ).
cnf(t346,plain,
apply(apply(w,apply(apply(b,X1),X2)),X3) = apply(apply(X1,apply(X2,X3)),X3),
inference(orient,[status(thm)],[t17]) ).
cnf(t362,plain,
apply(apply(X1,apply(X2,X2)),X2) = apply(apply(w,apply(apply(b,w),apply(b,X1))),X2),
inference(cp,[status(thm)],[t346,t346]) ).
cnf(t6,axiom,
sFlat2 = apply(b,w),
introduced(definition) ).
cnf(t42,plain,
apply(b,w) = sFlat2,
inference(orient,[status(thm)],[t6]) ).
cnf(t1652,plain,
apply(apply(X1,apply(X2,X2)),X2) = apply(apply(w,apply(sFlat2,apply(b,X1))),X2),
inference(step,[status(thm)],[t362,t42]) ).
cnf(t7,axiom,
sFlat3 = apply(b,apply(b,w)),
introduced(definition) ).
cnf(t34,plain,
apply(b,apply(b,w)) = sFlat3,
inference(orient,[status(thm)],[t7]) ).
cnf(t1636,plain,
apply(b,sFlat2) = sFlat3,
inference(step,[status(thm)],[t34,t42]) ).
cnf(t45,plain,
apply(b,sFlat2) = sFlat3,
inference(rw,[status(thm)],[t1636]) ).
cnf(t58,plain,
apply(b,sFlat2) = sFlat3,
inference(orient,[status(thm)],[t45]) ).
cnf(t59,plain,
apply(sFlat2,apply(X1,X2)) = apply(apply(sFlat3,X1),X2),
inference(cp,[status(thm)],[t14,t58]) ).
cnf(t97,plain,
apply(apply(sFlat3,X1),X2) = apply(sFlat2,apply(X1,X2)),
inference(orient,[status(thm)],[t59]) ).
cnf(t8,axiom,
sFlat4 = apply(apply(b,apply(b,w)),b),
introduced(definition) ).
cnf(t24,plain,
apply(apply(b,apply(b,w)),b) = sFlat4,
inference(orient,[status(thm)],[t8]) ).
cnf(t1634,plain,
apply(sFlat3,b) = sFlat4,
inference(step,[status(thm)],[t24,t34]) ).
cnf(t37,plain,
apply(sFlat3,b) = sFlat4,
inference(rw,[status(thm)],[t1634]) ).
cnf(t56,plain,
apply(sFlat3,b) = sFlat4,
inference(orient,[status(thm)],[t37]) ).
cnf(t99,plain,
apply(sFlat2,apply(b,X1)) = apply(sFlat4,X1),
inference(cp,[status(thm)],[t97,t56]) ).
cnf(t111,plain,
apply(sFlat2,apply(b,X1)) = apply(sFlat4,X1),
inference(orient,[status(thm)],[t99]) ).
cnf(t1653,plain,
apply(apply(X1,apply(X2,X2)),X2) = apply(apply(w,apply(sFlat4,X1)),X2),
inference(step,[status(thm)],[t1652,t111]) ).
cnf(t443,plain,
apply(apply(X1,apply(X2,X2)),X2) = apply(apply(w,apply(sFlat4,X1)),X2),
inference(orient,[status(thm)],[t1653]) ).
cnf(t445,plain,
apply(apply(w,apply(sFlat4,apply(b,X1))),X2) = apply(X1,apply(apply(X2,X2),X2)),
inference(cp,[status(thm)],[t443,t14]) ).
cnf(t4,axiom,
sFlat0 = apply(w,w),
introduced(definition) ).
cnf(t46,plain,
apply(w,w) = sFlat0,
inference(orient,[status(thm)],[t4]) ).
cnf(t47,plain,
apply(apply(w,X1),X1) = apply(sFlat0,X1),
inference(cp,[status(thm)],[t15,t46]) ).
cnf(t65,plain,
apply(apply(w,X1),X1) = apply(sFlat0,X1),
inference(orient,[status(thm)],[t47]) ).
cnf(t66,plain,
apply(sFlat0,X1) = apply(apply(X1,X1),X1),
inference(cp,[status(thm)],[t65,t15]) ).
cnf(t74,plain,
apply(apply(X1,X1),X1) = apply(sFlat0,X1),
inference(orient,[status(thm)],[t66]) ).
cnf(t1698,plain,
apply(apply(w,apply(sFlat4,apply(b,X1))),X2) = apply(X1,apply(sFlat0,X2)),
inference(step,[status(thm)],[t445,t74]) ).
cnf(t1532,plain,
apply(apply(w,apply(sFlat4,apply(b,X1))),X2) = apply(X1,apply(sFlat0,X2)),
inference(orient,[status(thm)],[t1698]) ).
cnf(t1533,plain,
apply(X1,apply(sFlat0,apply(sFlat4,apply(b,X1)))) = apply(sFlat0,apply(sFlat4,apply(b,X1))),
inference(cp,[status(thm)],[t1532,t65]) ).
cnf(t5,axiom,
sFlat1 = apply(b,apply(w,w)),
introduced(definition) ).
cnf(t38,plain,
apply(b,apply(w,w)) = sFlat1,
inference(orient,[status(thm)],[t5]) ).
cnf(t1637,plain,
apply(b,sFlat0) = sFlat1,
inference(step,[status(thm)],[t38,t46]) ).
cnf(t48,plain,
apply(b,sFlat0) = sFlat1,
inference(rw,[status(thm)],[t1637]) ).
cnf(t62,plain,
apply(b,sFlat0) = sFlat1,
inference(orient,[status(thm)],[t48]) ).
cnf(t63,plain,
apply(sFlat0,apply(X1,X2)) = apply(apply(sFlat1,X1),X2),
inference(cp,[status(thm)],[t14,t62]) ).
cnf(t104,plain,
apply(apply(sFlat1,X1),X2) = apply(sFlat0,apply(X1,X2)),
inference(orient,[status(thm)],[t63]) ).
cnf(t9,axiom,
sFlat5 = apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),
introduced(definition) ).
cnf(t1631,plain,
sFlat5 = apply(apply(b,apply(w,w)),sFlat4),
inference(step,[status(thm)],[t9,t24]) ).
cnf(t28,plain,
apply(apply(b,apply(w,w)),sFlat4) = sFlat5,
inference(orient,[status(thm)],[t1631]) ).
cnf(t1635,plain,
apply(sFlat1,sFlat4) = sFlat5,
inference(step,[status(thm)],[t28,t38]) ).
cnf(t41,plain,
apply(sFlat1,sFlat4) = sFlat5,
inference(rw,[status(thm)],[t1635]) ).
cnf(t57,plain,
apply(sFlat1,sFlat4) = sFlat5,
inference(orient,[status(thm)],[t41]) ).
cnf(t106,plain,
apply(sFlat0,apply(sFlat4,X1)) = apply(sFlat5,X1),
inference(cp,[status(thm)],[t104,t57]) ).
cnf(t122,plain,
apply(sFlat0,apply(sFlat4,X1)) = apply(sFlat5,X1),
inference(orient,[status(thm)],[t106]) ).
cnf(t1699,plain,
apply(X1,apply(sFlat5,apply(b,X1))) = apply(sFlat0,apply(sFlat4,apply(b,X1))),
inference(step,[status(thm)],[t1533,t122]) ).
cnf(t11,axiom,
sFlat7 = apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b),
introduced(definition) ).
cnf(t21,plain,
apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b) = sFlat7,
inference(orient,[status(thm)],[t11]) ).
cnf(t22,plain,
apply(apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b)),apply(b,X1)) = apply(sFlat7,X1),
inference(cp,[status(thm)],[t14,t21]) ).
cnf(t1681,plain,
apply(apply(w,w),apply(apply(apply(b,apply(b,w)),b),apply(b,X1))) = apply(sFlat7,X1),
inference(step,[status(thm)],[t22,t14]) ).
cnf(t1682,plain,
apply(sFlat0,apply(apply(apply(b,apply(b,w)),b),apply(b,X1))) = apply(sFlat7,X1),
inference(step,[status(thm)],[t1681,t46]) ).
cnf(t1683,plain,
apply(sFlat0,apply(apply(b,w),apply(b,apply(b,X1)))) = apply(sFlat7,X1),
inference(step,[status(thm)],[t1682,t14]) ).
cnf(t1684,plain,
apply(sFlat0,apply(sFlat2,apply(b,apply(b,X1)))) = apply(sFlat7,X1),
inference(step,[status(thm)],[t1683,t42]) ).
cnf(t1685,plain,
apply(sFlat0,apply(sFlat4,apply(b,X1))) = apply(sFlat7,X1),
inference(step,[status(thm)],[t1684,t111]) ).
cnf(t1686,plain,
apply(sFlat5,apply(b,X1)) = apply(sFlat7,X1),
inference(step,[status(thm)],[t1685,t122]) ).
cnf(t1242,plain,
apply(sFlat5,apply(b,X1)) = apply(sFlat7,X1),
inference(orient,[status(thm)],[t1686]) ).
cnf(t1700,plain,
apply(X1,apply(sFlat7,X1)) = apply(sFlat0,apply(sFlat4,apply(b,X1))),
inference(step,[status(thm)],[t1699,t1242]) ).
cnf(t1701,plain,
apply(X1,apply(sFlat7,X1)) = apply(sFlat5,apply(b,X1)),
inference(step,[status(thm)],[t1700,t122]) ).
cnf(t1702,plain,
apply(X1,apply(sFlat7,X1)) = apply(sFlat7,X1),
inference(step,[status(thm)],[t1701,t1242]) ).
cnf(t1566,plain,
apply(X1,apply(sFlat7,X1)) = apply(sFlat7,X1),
inference(orient,[status(thm)],[t1702]) ).
cnf(t1605,plain,
true = ifeq(apply(sFlat7,fixed_pt),apply(sFlat7,fixed_pt),fixed_point(sFlat7),true),
inference(cp,[status(thm)],[t49,t1566]) ).
cnf(t0,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t13,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t0]) ).
cnf(t1703,plain,
true = fixed_point(sFlat7),
inference(step,[status(thm)],[t1605,t13]) ).
cnf(t1629,plain,
fixed_point(sFlat7) = true,
inference(orient,[status(thm)],[t1703]) ).
cnf(f3,negated_conjecture,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,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(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
~ fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(goal_0,negated_conjecture,
fixed_point(apply(apply(b,apply(apply(b,apply(w,w)),apply(apply(b,apply(b,w)),b))),b)) != true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(g0_0,plain,
fixed_point(sFlat7) != true,
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
fixed_point(sFlat7) != fixed_point(sFlat7),
inference(rw,[status(thm)],[g0_0,t1629]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : COL003-9 : TPTP v9.3.1. Released v1.2.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.03/5.52 % Computer : n012.cluster.edu
% 0.03/5.52 % Model : x86_64 x86_64
% 0.03/5.52 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/5.52 % Memory : 8046.5625MB
% 0.03/5.52 % OS : Linux 6.8.0-71-generic
% 0.03/5.52 % CPULimit : 300
% 0.03/5.52 % WCLimit : 300
% 0.03/5.52 % DateTime : Fri Sep 25 07:09:44 UTC 2026
% 0.03/5.52 % CPUTime :
% 0.03/5.52 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 2.98/7.20 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 2.98/7.20 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------