%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : PUZ056-1 : TPTP v9.3.1. Released v2.7.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n015.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 02:31:59 PM UTC 2026
% Result : Unsatisfiable 5.39s 1.28s
% Output : Proof 5.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 10
% Syntax : Number of formulae : 88 ( 84 unt; 0 def)
% Number of atoms : 96 ( 59 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 42 ( 34 ~; 8 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 105 ( 18 sgn 28 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f2,axiom,
nextto(X,Y) = nextto(Y,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nextto_commutative) ).
fof(f2_nnf,plain,
! [X,Y] : nextto(X,Y) = nextto(Y,X),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X,Y] : nextto(X,Y) = nextto(Y,X),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
nextto(X0,X1) = nextto(X1,X0),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(t7,plain,
nextto(X1,X2) = nextto(X2,X1),
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t26,plain,
nextto(X1,X2) = nextto(X2,X1),
inference(orient,[status(thm)],[t7]) ).
cnf(f4,axiom,
( ~ fits(X,A)
| ~ fits(X,B)
| nextto(on(X,A),B) = nextto(A,on(X,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_move) ).
fof(f4_nnf,plain,
! [X,A,B] :
( ~ fits(X,A)
| ~ fits(X,B)
| nextto(on(X,A),B) = nextto(A,on(X,B)) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [X,A,B] :
( ~ fits(X,A)
| ~ fits(X,B)
| nextto(on(X,A),B) = nextto(A,on(X,B)) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( ~ fits(X0,X1)
| ~ fits(X0,X2)
| nextto(on(X0,X1),X2) = nextto(X1,on(X0,X2)) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi3,axiom,
ifeq(fits(X0,X1),true,ifeq(fits(X0,X2),true,nextto(on(X0,X2),X1),nextto(X2,on(X0,X1))),nextto(X2,on(X0,X1))) = nextto(X2,on(X0,X1)),
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(f5,axiom,
fits(small,pin(N)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fits_1) ).
fof(f5_nnf,plain,
! [N] : fits(small,pin(N)),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [N] : fits(small,pin(N)),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
fits(small,pin(X0)),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi4,axiom,
fits(small,pin(X0)) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f8,axiom,
fits(small,on(medium,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fits_4) ).
fof(f8_nnf,plain,
! [A] : fits(small,on(medium,A)),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] : fits(small,on(medium,A)),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
fits(small,on(medium,X0)),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi7,axiom,
fits(small,on(medium,X0)) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t14,plain,
nextto(on(small,on(medium,X1)),pin(X2)) = nextto(on(medium,X1),on(small,pin(X2))),
inference(hyper_resolution,[status(thm)],[hi3,hi4,hi7]) ).
cnf(t78,plain,
nextto(on(small,on(medium,X1)),pin(X2)) = nextto(on(medium,X1),on(small,pin(X2))),
inference(orient,[status(thm)],[t14]) ).
cnf(f3,axiom,
nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nextto_associative) ).
fof(f3_nnf,plain,
! [X,Y,Z] : nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X,Y,Z] : nextto(X,nextto(Y,Z)) = nextto(nextto(X,Y),Z),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
nextto(X0,nextto(X1,X2)) = nextto(nextto(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(t8,plain,
nextto(nextto(X1,X2),X3) = nextto(X1,nextto(X2,X3)),
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t31,plain,
nextto(nextto(X1,X2),X3) = nextto(X1,nextto(X2,X3)),
inference(orient,[status(thm)],[t8]) ).
cnf(t32,plain,
nextto(X1,nextto(X2,X3)) = nextto(X3,nextto(X1,X2)),
inference(cp,[status(thm)],[t31,t26]) ).
cnf(t127,plain,
nextto(X1,nextto(X2,X3)) = nextto(X3,nextto(X1,X2)),
inference(orient,[status(thm)],[t32]) ).
cnf(f6,axiom,
fits(medium,pin(N)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fits_2) ).
fof(f6_nnf,plain,
! [N] : fits(medium,pin(N)),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [N] : fits(medium,pin(N)),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
fits(medium,pin(X0)),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
fits(medium,pin(X0)) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f9,axiom,
fits(medium,on(large,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fits_5) ).
fof(f9_nnf,plain,
! [A] : fits(medium,on(large,A)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] : fits(medium,on(large,A)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
fits(medium,on(large,X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi8,axiom,
fits(medium,on(large,X0)) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t12,plain,
nextto(on(medium,on(large,X1)),pin(X2)) = nextto(on(large,X1),on(medium,pin(X2))),
inference(hyper_resolution,[status(thm)],[hi3,hi5,hi8]) ).
cnf(t42,plain,
nextto(on(medium,on(large,X1)),pin(X2)) = nextto(on(large,X1),on(medium,pin(X2))),
inference(orient,[status(thm)],[t12]) ).
cnf(f10,axiom,
fits(small,on(large,A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fits_6) ).
fof(f10_nnf,plain,
! [A] : fits(small,on(large,A)),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A] : fits(small,on(large,A)),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
fits(small,on(large,X0)),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi9,axiom,
fits(small,on(large,X0)) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(t16,plain,
nextto(pin(X1),on(small,on(large,X2))) = nextto(on(small,pin(X1)),on(large,X2)),
inference(hyper_resolution,[status(thm)],[hi3,hi9,hi4]) ).
cnf(t92,plain,
nextto(on(small,pin(X1)),on(large,X2)) = nextto(pin(X1),on(small,on(large,X2))),
inference(orient,[status(thm)],[t16]) ).
cnf(t21,plain,
nextto(on(small,on(large,X1)),on(medium,X2)) = nextto(on(large,X1),on(small,on(medium,X2))),
inference(hyper_resolution,[status(thm)],[hi3,hi7,hi9]) ).
cnf(t52,plain,
nextto(on(small,on(large,X1)),on(medium,X2)) = nextto(on(large,X1),on(small,on(medium,X2))),
inference(orient,[status(thm)],[t21]) ).
cnf(t17,plain,
nextto(pin(X1),on(small,on(medium,X2))) = nextto(on(small,pin(X1)),on(medium,X2)),
inference(hyper_resolution,[status(thm)],[hi3,hi7,hi4]) ).
cnf(t98,plain,
nextto(on(small,pin(X1)),on(medium,X2)) = nextto(pin(X1),on(small,on(medium,X2))),
inference(orient,[status(thm)],[t17]) ).
cnf(f7,axiom,
fits(large,pin(N)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fits_3) ).
fof(f7_nnf,plain,
! [N] : fits(large,pin(N)),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [N] : fits(large,pin(N)),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
fits(large,pin(X0)),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi6,axiom,
fits(large,pin(X0)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t9,plain,
nextto(pin(X1),on(large,pin(X2))) = nextto(on(large,pin(X1)),pin(X2)),
inference(hyper_resolution,[status(thm)],[hi3,hi6,hi6]) ).
cnf(t62,plain,
nextto(on(large,pin(X1)),pin(X2)) = nextto(pin(X1),on(large,pin(X2))),
inference(orient,[status(thm)],[t9]) ).
cnf(f1,negated_conjecture,
~ state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',final_state) ).
fof(f1_nnf,plain,
~ state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
~ state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
~ state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(goal_0,negated_conjecture,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(g0_0,plain,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != state(nextto(pin(n2),nextto(pin(n3),on(small,on(medium,on(large,pin(n1))))))),
inference(rw,[status(thm)],[goal_0]) ).
cnf(g0_1,plain,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != state(nextto(pin(n2),nextto(on(small,on(medium,on(large,pin(n1)))),pin(n3)))),
inference(rw,[status(thm)],[g0_0,t26]) ).
cnf(g0_2,plain,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != state(nextto(pin(n2),nextto(on(medium,on(large,pin(n1))),on(small,pin(n3))))),
inference(rw,[status(thm)],[g0_1,t78]) ).
cnf(g0_3,plain,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != state(nextto(pin(n2),nextto(on(small,pin(n3)),on(medium,on(large,pin(n1)))))),
inference(rw,[status(thm)],[g0_2,t26]) ).
cnf(g0_4,plain,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != state(nextto(on(small,pin(n3)),nextto(on(medium,on(large,pin(n1))),pin(n2)))),
inference(rw,[status(thm)],[g0_3,t127]) ).
cnf(g0_5,plain,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != state(nextto(on(small,pin(n3)),nextto(on(large,pin(n1)),on(medium,pin(n2))))),
inference(rw,[status(thm)],[g0_4,t42]) ).
cnf(g0_6,plain,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != state(nextto(on(medium,pin(n2)),nextto(on(small,pin(n3)),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_5,t127]) ).
cnf(g0_7,plain,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != state(nextto(on(medium,pin(n2)),nextto(pin(n3),on(small,on(large,pin(n1)))))),
inference(rw,[status(thm)],[g0_6,t92]) ).
cnf(g0_8,plain,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != state(nextto(pin(n3),nextto(on(small,on(large,pin(n1))),on(medium,pin(n2))))),
inference(rw,[status(thm)],[g0_7,t127]) ).
cnf(g0_9,plain,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != state(nextto(pin(n3),nextto(on(large,pin(n1)),on(small,on(medium,pin(n2)))))),
inference(rw,[status(thm)],[g0_8,t52]) ).
cnf(g0_10,plain,
state(nextto(pin(n1),nextto(pin(n2),on(small,on(medium,on(large,pin(n3))))))) != state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_9,t127]) ).
cnf(g0_11,plain,
state(nextto(pin(n2),nextto(on(small,on(medium,on(large,pin(n3)))),pin(n1)))) != state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_10,t127]) ).
cnf(g0_12,plain,
state(nextto(pin(n2),nextto(on(medium,on(large,pin(n3))),on(small,pin(n1))))) != state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_11,t78]) ).
cnf(g0_13,plain,
state(nextto(pin(n2),nextto(on(small,pin(n1)),on(medium,on(large,pin(n3)))))) != state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_12,t26]) ).
cnf(g0_14,plain,
state(nextto(on(small,pin(n1)),nextto(on(medium,on(large,pin(n3))),pin(n2)))) != state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_13,t127]) ).
cnf(g0_15,plain,
state(nextto(on(small,pin(n1)),nextto(on(large,pin(n3)),on(medium,pin(n2))))) != state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_14,t42]) ).
cnf(g0_16,plain,
state(nextto(on(small,pin(n1)),nextto(on(medium,pin(n2)),on(large,pin(n3))))) != state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_15,t26]) ).
cnf(g0_17,plain,
state(nextto(on(large,pin(n3)),nextto(on(small,pin(n1)),on(medium,pin(n2))))) != state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_16,t127]) ).
cnf(g0_18,plain,
state(nextto(on(large,pin(n3)),nextto(pin(n1),on(small,on(medium,pin(n2)))))) != state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_17,t98]) ).
cnf(g0_19,plain,
state(nextto(on(small,on(medium,pin(n2))),nextto(on(large,pin(n3)),pin(n1)))) != state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_18,t127]) ).
cnf(g0_20,plain,
state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))) != state(nextto(on(small,on(medium,pin(n2))),nextto(pin(n3),on(large,pin(n1))))),
inference(rw,[status(thm)],[g0_19,t62]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_20]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : PUZ056-1 : TPTP v9.3.1. Released v2.7.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.34 % Computer : n015.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Thu Sep 24 06:52:55 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.09/0.34 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 5.39/1.28 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.39/1.28 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------