%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : HWC002-1 : TPTP v9.3.1. Released v1.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n018.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 01:37:33 PM UTC 2026
% Result : Unsatisfiable 22.65s 8.36s
% Output : Proof 22.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 12
% Syntax : Number of formulae : 126 ( 126 unt; 0 def)
% Number of atoms : 126 ( 117 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 11 ( 11 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 1 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-4 aty)
% Number of variables : 162 ( 4 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f30,axiom,
not(table(X1,X2,X3,X4)) = table(not(X1),not(X2),not(X3),not(X4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_table_definition) ).
fof(f30_nnf,plain,
! [X1,X2,X3,X4] : not(table(X1,X2,X3,X4)) = table(not(X1),not(X2),not(X3),not(X4)),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X1,X2,X3,X4] : not(table(X1,X2,X3,X4)) = table(not(X1),not(X2),not(X3),not(X4)),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
not(table(X0,X1,X2,X3)) = table(not(X0),not(X1),not(X2),not(X3)),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(t19,plain,
table(not(X1),not(X2),not(X3),not(X4)) = not(table(X1,X2,X3,X4)),
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(t272,plain,
table(not(X1),not(X2),not(X3),not(X4)) = not(table(X1,X2,X3,X4)),
inference(orient,[status(thm)],[t19]) ).
cnf(f8,axiom,
not(n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition1) ).
fof(f8_nnf,plain,
not(n0) = n1,
inference(nnf_transformation,[status(thm)],[f8]) ).
cnf(c8,plain,
not(n0) = n1,
inference(cnf_transformation,[status(esa)],[f8_nnf]) ).
cnf(t0,plain,
not(n0) = n1,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t265,plain,
not(n0) = n1,
inference(orient,[status(thm)],[t0]) ).
cnf(t276,plain,
not(table(X1,n0,X2,X3)) = table(not(X1),n1,not(X2),not(X3)),
inference(cp,[status(thm)],[t272,t265]) ).
cnf(t5088,plain,
table(not(X1),n1,not(X2),not(X3)) = not(table(X1,n0,X2,X3)),
inference(orient,[status(thm)],[t276]) ).
cnf(f9,axiom,
not(n1) = n0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition2) ).
fof(f9_nnf,plain,
not(n1) = n0,
inference(nnf_transformation,[status(thm)],[f9]) ).
cnf(c9,plain,
not(n1) = n0,
inference(cnf_transformation,[status(esa)],[f9_nnf]) ).
cnf(t1,plain,
not(n1) = n0,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t260,plain,
not(n1) = n0,
inference(orient,[status(thm)],[t1]) ).
cnf(t5209,plain,
not(table(X1,n0,n1,X2)) = table(not(X1),n1,n0,not(X2)),
inference(cp,[status(thm)],[t5088,t260]) ).
cnf(t7687,plain,
table(not(X1),n1,n0,not(X2)) = not(table(X1,n0,n1,X2)),
inference(orient,[status(thm)],[t5209]) ).
cnf(t7846,plain,
not(table(X1,n0,n1,n0)) = table(not(X1),n1,n0,n1),
inference(cp,[status(thm)],[t7687,t265]) ).
cnf(t8003,plain,
not(table(X1,n0,n1,n0)) = table(not(X1),n1,n0,n1),
inference(orient,[status(thm)],[t7846]) ).
cnf(t5210,plain,
not(table(X1,n0,n0,X2)) = table(not(X1),n1,n1,not(X2)),
inference(cp,[status(thm)],[t5088,t265]) ).
cnf(t8081,plain,
table(not(X1),n1,n1,not(X2)) = not(table(X1,n0,n0,X2)),
inference(orient,[status(thm)],[t5210]) ).
cnf(t8245,plain,
not(table(X1,n0,n0,n1)) = table(not(X1),n1,n1,n0),
inference(cp,[status(thm)],[t8081,t260]) ).
cnf(t8327,plain,
not(table(X1,n0,n0,n1)) = table(not(X1),n1,n1,n0),
inference(orient,[status(thm)],[t8245]) ).
cnf(f28,axiom,
or(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(or(X1,Y1),or(X2,Y2),or(X3,Y3),or(X4,Y4)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_table_definition) ).
fof(f28_nnf,plain,
! [X1,X2,X3,X4,Y1,Y2,Y3,Y4] : or(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(or(X1,Y1),or(X2,Y2),or(X3,Y3),or(X4,Y4)),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X1,X2,X3,X4,Y1,Y2,Y3,Y4] : or(table(X1,X2,X3,X4),table(Y1,Y2,Y3,Y4)) = table(or(X1,Y1),or(X2,Y2),or(X3,Y3),or(X4,Y4)),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
or(table(X0,X1,X2,X3),table(X4,X5,X6,X7)) = table(or(X0,X4),or(X1,X5),or(X2,X6),or(X3,X7)),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t59,plain,
table(or(X1,X2),or(X3,X4),or(X5,X6),or(X7,X8)) = or(table(X1,X3,X5,X7),table(X2,X4,X6,X8)),
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(t281,plain,
table(or(X1,X2),or(X3,X4),or(X5,X6),or(X7,X8)) = or(table(X1,X3,X5,X7),table(X2,X4,X6,X8)),
inference(orient,[status(thm)],[t59]) ).
cnf(f6,axiom,
or(n1,n0) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition3) ).
fof(f6_nnf,plain,
or(n1,n0) = n1,
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
or(n1,n0) = n1,
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(t11,plain,
or(n1,n0) = n1,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(t267,plain,
or(n1,n0) = n1,
inference(orient,[status(thm)],[t11]) ).
cnf(t282,plain,
or(table(n1,X1,X2,X3),table(n0,X4,X5,X6)) = table(n1,or(X1,X4),or(X2,X5),or(X3,X6)),
inference(cp,[status(thm)],[t281,t267]) ).
cnf(t19557,plain,
or(table(n1,X1,X2,X3),table(n0,X4,X5,X6)) = table(n1,or(X1,X4),or(X2,X5),or(X3,X6)),
inference(orient,[status(thm)],[t282]) ).
cnf(f33,axiom,
table(n1,n1,n1,n1) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',full_table) ).
fof(f33_nnf,plain,
table(n1,n1,n1,n1) = nil,
inference(nnf_transformation,[status(thm)],[f33]) ).
cnf(c33,plain,
table(n1,n1,n1,n1) = nil,
inference(cnf_transformation,[status(esa)],[f33_nnf]) ).
cnf(t16,plain,
table(n1,n1,n1,n1) = nil,
inference(equality_encoding,[status(esa)],[c33]) ).
cnf(t271,plain,
table(n1,n1,n1,n1) = nil,
inference(orient,[status(thm)],[t16]) ).
cnf(t19560,plain,
table(n1,or(n1,X1),or(n1,X2),or(n1,X3)) = or(nil,table(n0,X1,X2,X3)),
inference(cp,[status(thm)],[t19557,t271]) ).
cnf(f29,axiom,
or(nil,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition5) ).
fof(f29_nnf,plain,
! [X] : or(nil,X) = X,
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
! [X] : or(nil,X) = X,
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
or(nil,X0) = X0,
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(t13,plain,
or(nil,X1) = X1,
inference(equality_encoding,[status(esa)],[c29]) ).
cnf(t256,plain,
or(nil,X1) = X1,
inference(orient,[status(thm)],[t13]) ).
cnf(t20318,plain,
table(n1,or(n1,X1),or(n1,X2),or(n1,X3)) = table(n0,X1,X2,X3),
inference(step,[status(thm)],[t19560,t256]) ).
cnf(t19596,plain,
table(n1,or(n1,X1),or(n1,X2),or(n1,X3)) = table(n0,X1,X2,X3),
inference(orient,[status(thm)],[t20318]) ).
cnf(f7,axiom,
or(n1,n1) = n1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',or_definition4) ).
fof(f7_nnf,plain,
or(n1,n1) = n1,
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
or(n1,n1) = n1,
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(t12,plain,
or(n1,n1) = n1,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t268,plain,
or(n1,n1) = n1,
inference(orient,[status(thm)],[t12]) ).
cnf(t19598,plain,
table(n0,n1,X1,X2) = table(n1,n1,or(n1,X1),or(n1,X2)),
inference(cp,[status(thm)],[t19596,t268]) ).
cnf(t19597,plain,
table(n0,n0,X1,X2) = table(n1,n1,or(n1,X1),or(n1,X2)),
inference(cp,[status(thm)],[t19596,t267]) ).
cnf(t19604,plain,
table(n1,n1,or(n1,X1),or(n1,X2)) = table(n0,n0,X1,X2),
inference(orient,[status(thm)],[t19597]) ).
cnf(t20644,plain,
table(n0,n1,X1,X2) = table(n0,n0,X1,X2),
inference(step,[status(thm)],[t19598,t19604]) ).
cnf(t19974,plain,
table(n0,n0,X1,X2) = table(n0,n1,X1,X2),
inference(orient,[status(thm)],[t20644]) ).
cnf(t19997,plain,
table(not(n0),n1,n1,n0) = not(table(n0,n1,n0,n1)),
inference(cp,[status(thm)],[t8327,t19974]) ).
cnf(t20686,plain,
table(n1,n1,n1,n0) = not(table(n0,n1,n0,n1)),
inference(step,[status(thm)],[t19997,t265]) ).
cnf(t19605,plain,
table(n0,n0,n0,X1) = table(n1,n1,n1,or(n1,X1)),
inference(cp,[status(thm)],[t19604,t267]) ).
cnf(t19610,plain,
table(n1,n1,n1,or(n1,X1)) = table(n0,n0,n0,X1),
inference(orient,[status(thm)],[t19605]) ).
cnf(t19611,plain,
table(n0,n0,n0,n1) = table(n1,n1,n1,n1),
inference(cp,[status(thm)],[t19610,t268]) ).
cnf(t20319,plain,
table(n0,n0,n0,n1) = nil,
inference(step,[status(thm)],[t19611,t271]) ).
cnf(t19614,plain,
table(n0,n0,n0,n1) = nil,
inference(orient,[status(thm)],[t20319]) ).
cnf(t19616,plain,
table(not(n0),n1,n1,n0) = not(nil),
inference(cp,[status(thm)],[t8327,t19614]) ).
cnf(t20320,plain,
table(n1,n1,n1,n0) = not(nil),
inference(step,[status(thm)],[t19616,t265]) ).
cnf(f31,axiom,
not(nil) = nil,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_definition3) ).
fof(f31_nnf,plain,
not(nil) = nil,
inference(nnf_transformation,[status(thm)],[f31]) ).
cnf(c31,plain,
not(nil) = nil,
inference(cnf_transformation,[status(esa)],[f31_nnf]) ).
cnf(t2,plain,
not(nil) = nil,
inference(equality_encoding,[status(esa)],[c31]) ).
cnf(t323,plain,
not(nil) = nil,
inference(orient,[status(thm)],[t2]) ).
cnf(t20321,plain,
table(n1,n1,n1,n0) = nil,
inference(step,[status(thm)],[t20320,t323]) ).
cnf(t19620,plain,
table(n1,n1,n1,n0) = nil,
inference(orient,[status(thm)],[t20321]) ).
cnf(t20687,plain,
nil = not(table(n0,n1,n0,n1)),
inference(step,[status(thm)],[t20686,t19620]) ).
cnf(t274,plain,
not(table(n0,X1,X2,X3)) = table(n1,not(X1),not(X2),not(X3)),
inference(cp,[status(thm)],[t272,t265]) ).
cnf(t2138,plain,
table(n1,not(X1),not(X2),not(X3)) = not(table(n0,X1,X2,X3)),
inference(orient,[status(thm)],[t274]) ).
cnf(t2164,plain,
not(table(n0,n1,X1,X2)) = table(n1,n0,not(X1),not(X2)),
inference(cp,[status(thm)],[t2138,t260]) ).
cnf(t2798,plain,
table(n1,n0,not(X1),not(X2)) = not(table(n0,n1,X1,X2)),
inference(orient,[status(thm)],[t2164]) ).
cnf(t2834,plain,
not(table(n0,n1,n0,X1)) = table(n1,n0,n1,not(X1)),
inference(cp,[status(thm)],[t2798,t265]) ).
cnf(t2947,plain,
not(table(n0,n1,n0,X1)) = table(n1,n0,n1,not(X1)),
inference(orient,[status(thm)],[t2834]) ).
cnf(t20688,plain,
nil = table(n1,n0,n1,not(n1)),
inference(step,[status(thm)],[t20687,t2947]) ).
cnf(t20689,plain,
nil = table(n1,n0,n1,n0),
inference(step,[status(thm)],[t20688,t260]) ).
cnf(t20030,plain,
table(n1,n0,n1,n0) = nil,
inference(orient,[status(thm)],[t20689]) ).
cnf(t20032,plain,
table(not(n1),n1,n0,n1) = not(nil),
inference(cp,[status(thm)],[t8003,t20030]) ).
cnf(t20700,plain,
table(n0,n1,n0,n1) = not(nil),
inference(step,[status(thm)],[t20032,t260]) ).
cnf(t20701,plain,
table(n0,n1,n0,n1) = nil,
inference(step,[status(thm)],[t20700,t323]) ).
cnf(t20052,plain,
table(n0,n1,n0,n1) = nil,
inference(orient,[status(thm)],[t20701]) ).
cnf(f34,axiom,
connect(nil,X) = X,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connect_definition1) ).
fof(f34_nnf,plain,
! [X] : connect(nil,X) = X,
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X] : connect(nil,X) = X,
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
connect(nil,X0) = X0,
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(t8,plain,
connect(nil,X1) = X1,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(t258,plain,
connect(nil,X1) = X1,
inference(orient,[status(thm)],[t8]) ).
cnf(t19606,plain,
table(n0,n0,n1,X1) = table(n1,n1,n1,or(n1,X1)),
inference(cp,[status(thm)],[t19604,t268]) ).
cnf(t20322,plain,
table(n0,n0,n1,X1) = table(n0,n0,n0,X1),
inference(step,[status(thm)],[t19606,t19610]) ).
cnf(t19622,plain,
table(n0,n0,n0,X1) = table(n0,n0,n1,X1),
inference(orient,[status(thm)],[t20322]) ).
cnf(t20327,plain,
table(n0,n0,n1,n1) = nil,
inference(step,[status(thm)],[t19614,t19622]) ).
cnf(t19637,plain,
table(n0,n0,n1,n1) = nil,
inference(rw,[status(thm)],[t20327]) ).
cnf(t19652,plain,
table(n0,n0,n1,n1) = nil,
inference(orient,[status(thm)],[t19637]) ).
cnf(t20667,plain,
table(n0,n1,n1,n1) = nil,
inference(step,[status(thm)],[t19652,t19974]) ).
cnf(t20015,plain,
table(n0,n1,n1,n1) = nil,
inference(rw,[status(thm)],[t20667]) ).
cnf(t20048,plain,
table(n0,n1,n1,n1) = nil,
inference(orient,[status(thm)],[t20015]) ).
cnf(f25,axiom,
circuit(top(X),Y,bottom(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subsume_symmetric) ).
fof(f25_nnf,plain,
! [X,Y] : circuit(top(X),Y,bottom(X)),
inference(nnf_transformation,[status(thm)],[f25]) ).
fof(f25_sk,plain,
! [X,Y] : circuit(top(X),Y,bottom(X)),
inference(skolemisation,[status(esa)],[f25_nnf]) ).
cnf(c25,plain,
circuit(top(X0),X1,bottom(X0)),
inference(cnf_transformation,[status(esa)],[f25_sk]) ).
cnf(t17,plain,
circuit(top(X1),X2,bottom(X1)) = true,
inference(equality_encoding,[status(esa)],[c25]) ).
cnf(t329,plain,
circuit(top(X1),X2,bottom(X1)) = true,
inference(orient,[status(thm)],[t17]) ).
cnf(f37,negated_conjecture,
~ circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_output_configuration) ).
fof(f37_nnf,plain,
~ circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
~ circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c37,plain,
~ circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))),
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(goal_0,negated_conjecture,
circuit(top(connect(table(n0,n1,n0,n1),nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))) != true,
inference(equality_encoding,[status(esa)],[c37]) ).
cnf(g0_0,plain,
circuit(top(connect(nil,nil)),nil,bottom(connect(table(n0,n0,n1,n1),nil))) != true,
inference(rw,[status(thm)],[goal_0,t20052]) ).
cnf(g0_1,plain,
circuit(top(nil),nil,bottom(connect(table(n0,n0,n1,n1),nil))) != true,
inference(rw,[status(thm)],[g0_0,t258]) ).
cnf(g0_2,plain,
circuit(top(nil),nil,bottom(connect(table(n0,n1,n1,n1),nil))) != true,
inference(rw,[status(thm)],[g0_1,t19974]) ).
cnf(g0_3,plain,
circuit(top(nil),nil,bottom(connect(nil,nil))) != true,
inference(rw,[status(thm)],[g0_2,t20048]) ).
cnf(g0_4,plain,
circuit(top(nil),nil,bottom(nil)) != true,
inference(rw,[status(thm)],[g0_3,t258]) ).
cnf(g0_5,plain,
true != true,
inference(rw,[status(thm)],[g0_4,t329]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : HWC002-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/5.37 % Computer : n018.cluster.edu
% 0.09/5.37 % Model : x86_64 x86_64
% 0.09/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.37 % Memory : 8046.5625MB
% 0.09/5.37 % OS : Linux 6.8.0-71-generic
% 0.09/5.37 % CPULimit : 300
% 0.09/5.37 % WCLimit : 300
% 0.09/5.37 % DateTime : Wed Sep 23 16:21:08 UTC 2026
% 0.09/5.37 % CPUTime :
% 0.09/5.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 22.65/8.36 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 22.65/8.36 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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