%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PLA022-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n019.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 02:30:41 PM UTC 2026
% Result : Unsatisfiable 9.15s 1.79s
% Output : Proof 9.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 16
% Syntax : Number of formulae : 81 ( 53 unt; 0 def)
% Number of atoms : 133 ( 30 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 110 ( 58 ~; 52 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 18 ( 18 usr; 9 con; 0-4 aty)
% Number of variables : 120 ( 12 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f30,negated_conjecture,
~ holds(and(on(c,d),on(a,c)),State),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_ACD) ).
fof(f30_nnf,plain,
! [State] : ~ holds(and(on(c,d),on(a,c)),State),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [State] : ~ holds(and(on(c,d),on(a,c)),State),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
~ holds(and(on(c,d),on(a,c)),X0),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(t44,plain,
eq(holds(and(on(c,d),on(a,c)),X1),true) = efalse,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t1486,plain,
eq(holds(and(on(c,d),on(a,c)),X1),true) = efalse,
inference(orient,[status(thm)],[t44]) ).
cnf(f10,axiom,
( ~ differ(Y,X)
| differ(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symmetry_of_differ) ).
fof(f10_nnf,plain,
! [X,Y] :
( ~ differ(Y,X)
| differ(X,Y) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X,Y] :
( ~ differ(Y,X)
| differ(X,Y) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ differ(X1,X0)
| differ(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(differ(X0,X1),true,differ(X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f12,axiom,
differ(a,c),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_a_c) ).
fof(f12_nnf,plain,
differ(a,c),
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
differ(a,c),
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,axiom,
differ(a,c) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h1,plain,
differ(c,a) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi12]) ).
cnf(f4,axiom,
( ~ differ(X,Z)
| ~ holds(clear(X),State)
| holds(clear(X),do(pickup(Z),State)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pickup_4) ).
fof(f4_nnf,plain,
! [X,Z,State] :
( ~ differ(X,Z)
| ~ holds(clear(X),State)
| holds(clear(X),do(pickup(Z),State)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,Z,State] :
( ~ differ(X,Z)
| ~ holds(clear(X),State)
| holds(clear(X),do(pickup(Z),State)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ differ(X0,X1)
| ~ holds(clear(X0),X2)
| holds(clear(X0),do(pickup(X1),X2)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,axiom,
ifeq(holds(clear(X0),X1),true,ifeq(differ(X0,X2),true,holds(clear(X0),do(pickup(X2),X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f27,axiom,
holds(clear(c),s0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state7) ).
fof(f27_nnf,plain,
holds(clear(c),s0),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
holds(clear(c),s0),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(hi27,axiom,
holds(clear(c),s0) = true,
inference(equality_encoding,[status(esa)],[c27]) ).
cnf(h42,plain,
holds(clear(c),do(pickup(a),s0)) = true,
inference(hyper_resolution,[status(thm)],[hi4,hi27,h1]) ).
cnf(f1,axiom,
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pickup_1) ).
fof(f1_nnf,plain,
! [X,State] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X,State] :
( ~ differ(X,table)
| ~ holds(clear(X),State)
| ~ holds(empty,State)
| holds(holding(X),do(pickup(X),State)) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ differ(X0,table)
| ~ holds(clear(X0),X1)
| ~ holds(empty,X1)
| holds(holding(X0),do(pickup(X0),X1)) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,axiom,
ifeq(holds(empty,X0),true,ifeq(holds(clear(X1),X0),true,ifeq(differ(X1,table),true,holds(holding(X1),do(pickup(X1),X0)),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f28,axiom,
holds(empty,s0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state8) ).
fof(f28_nnf,plain,
holds(empty,s0),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
holds(empty,s0),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(hi28,axiom,
holds(empty,s0) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(f25,axiom,
holds(clear(a),s0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state5) ).
fof(f25_nnf,plain,
holds(clear(a),s0),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
holds(clear(a),s0),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(hi25,axiom,
holds(clear(a),s0) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(f14,axiom,
differ(a,table),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',differ_a_table) ).
fof(f14_nnf,plain,
differ(a,table),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
differ(a,table),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(hi14,axiom,
differ(a,table) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h19,plain,
holds(holding(a),do(pickup(a),s0)) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi28,hi25,hi14]) ).
cnf(f6,axiom,
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',putdown_2) ).
fof(f6_nnf,plain,
! [X,Y,State] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X,Y,State] :
( ~ holds(clear(Y),State)
| ~ holds(holding(X),State)
| holds(on(X,Y),do(putdown(X,Y),State)) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ holds(clear(X1),X2)
| ~ holds(holding(X0),X2)
| holds(on(X0,X1),do(putdown(X0,X1),X2)) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,axiom,
ifeq(holds(holding(X0),X1),true,ifeq(holds(clear(X2),X1),true,holds(on(X0,X2),do(putdown(X0,X2),X1)),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h288,plain,
holds(on(a,c),do(putdown(a,c),do(pickup(a),s0))) = true,
inference(hyper_resolution,[status(thm)],[hi6,h19,h42]) ).
cnf(f3,axiom,
( ~ differ(X,Z)
| ~ holds(on(X,Y),State)
| holds(on(X,Y),do(pickup(Z),State)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pickup_3) ).
fof(f3_nnf,plain,
! [X,Y,Z,State] :
( ~ differ(X,Z)
| ~ holds(on(X,Y),State)
| holds(on(X,Y),do(pickup(Z),State)) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z,State] :
( ~ differ(X,Z)
| ~ holds(on(X,Y),State)
| holds(on(X,Y),do(pickup(Z),State)) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( ~ differ(X0,X2)
| ~ holds(on(X0,X1),X3)
| holds(on(X0,X1),do(pickup(X2),X3)) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,axiom,
ifeq(holds(on(X0,X1),X2),true,ifeq(differ(X0,X3),true,holds(on(X0,X1),do(pickup(X3),X2)),true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f23,axiom,
holds(on(c,d),s0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',initial_state3) ).
fof(f23_nnf,plain,
holds(on(c,d),s0),
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
holds(on(c,d),s0),
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi23,axiom,
holds(on(c,d),s0) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h108,plain,
holds(on(c,d),do(pickup(a),s0)) = true,
inference(hyper_resolution,[status(thm)],[hi3,hi23,h1]) ).
cnf(f8,axiom,
( ~ holds(on(X,Y),State)
| holds(on(X,Y),do(putdown(Z,W),State)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',putdown_4) ).
fof(f8_nnf,plain,
! [X,Y,Z,W,State] :
( ~ holds(on(X,Y),State)
| holds(on(X,Y),do(putdown(Z,W),State)) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X,Y,Z,W,State] :
( ~ holds(on(X,Y),State)
| holds(on(X,Y),do(putdown(Z,W),State)) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ holds(on(X0,X1),X4)
| holds(on(X0,X1),do(putdown(X2,X3),X4)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,axiom,
ifeq(holds(on(X0,X1),X2),true,holds(on(X0,X1),do(putdown(X3,X4),X2)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h745,plain,
holds(on(c,d),do(putdown(V0,V1),do(pickup(a),s0))) = true,
inference(hyper_resolution,[status(thm)],[hi8,h108]) ).
cnf(f0,axiom,
( ~ holds(Y,State)
| ~ holds(X,State)
| holds(and(X,Y),State) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',and_definition) ).
fof(f0_nnf,plain,
! [X,Y,State] :
( ~ holds(Y,State)
| ~ holds(X,State)
| holds(and(X,Y),State) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X,Y,State] :
( ~ holds(Y,State)
| ~ holds(X,State)
| holds(and(X,Y),State) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ holds(X1,X2)
| ~ holds(X0,X2)
| holds(and(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,axiom,
ifeq(holds(X0,X1),true,ifeq(holds(X2,X1),true,holds(and(X0,X2),X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t245,plain,
holds(and(on(c,d),on(a,c)),do(putdown(a,c),do(pickup(a),s0))) = true,
inference(hyper_resolution,[status(thm)],[hi0,h745,h288]) ).
cnf(t475,plain,
holds(and(on(c,d),on(a,c)),do(putdown(a,c),do(pickup(a),s0))) = true,
inference(orient,[status(thm)],[t245]) ).
cnf(t1487,plain,
efalse = eq(true,true),
inference(cp,[status(thm)],[t1486,t475]) ).
cnf(t20,plain,
eq(X1,X1) = etrue,
introduced(definition) ).
cnf(t1485,plain,
eq(X1,X1) = etrue,
inference(orient,[status(thm)],[t20]) ).
cnf(t1491,plain,
efalse = etrue,
inference(step,[status(thm)],[t1487,t1485]) ).
cnf(t1488,plain,
efalse = etrue,
inference(orient,[status(thm)],[t1491]) ).
cnf(goal_0,negated_conjecture,
etrue != efalse,
introduced(definition) ).
cnf(g0_0,plain,
etrue != etrue,
inference(rw,[status(thm)],[goal_0,t1488]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PLA022-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.36 % Computer : n019.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 06:13:20 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 9.15/1.79 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 9.15/1.79 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------