%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN564-1 : TPTP v9.3.1. Released v2.5.0.
% 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 03:35:12 PM UTC 2026
% Result : Unsatisfiable 3.17s 0.88s
% Output : Proof 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 46 unt; 0 def)
% Number of atoms : 102 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 115 ( 0 sgn 46 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f12,negated_conjecture,
( ~ p10(X4,f3(X5,X6))
| p10(f9(X4,X6),X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_13) ).
fof(f12_nnf,plain,
! [X4,X6,X5] :
( ~ p10(X4,f3(X5,X6))
| p10(f9(X4,X6),X5) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X4,X6,X5] :
( ~ p10(X4,f3(X5,X6))
| p10(f9(X4,X6),X5) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( ~ p10(X0,f3(X2,X1))
| p10(f9(X0,X1),X2) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi11,negated_conjecture,
ifeq(p10(X0,f3(X1,X2)),true,p10(f9(X0,X2),X1),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f9,negated_conjecture,
p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_10) ).
fof(f9_nnf,plain,
! [X7,X8] : p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8))),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X7,X8] : p10(f5(X7),f3(f5(f6(X7,X8)),f5(X8))),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
p10(f5(X0),f3(f5(f6(X0,X1)),f5(X1))),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,negated_conjecture,
p10(f5(X0),f3(f5(f6(X0,X1)),f5(X1))) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h5,plain,
p10(f9(f5(c11),f5(f7(c12))),f5(f6(c11,f7(c12)))) = true,
inference(hyper_resolution,[status(thm)],[hi11,hi9]) ).
cnf(f2,negated_conjecture,
p2(f5(f7(X18)),f5(X18)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_3) ).
fof(f2_nnf,plain,
! [X18] : p2(f5(f7(X18)),f5(X18)),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X18] : p2(f5(f7(X18)),f5(X18)),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
p2(f5(f7(X0)),f5(X0)),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,negated_conjecture,
p2(f5(f7(X0)),f5(X0)) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h1,plain,
p2(f5(f7(c12)),f5(c12)) = true,
inference(hyper_resolution,[status(thm)],[hi2]) ).
cnf(f0,negated_conjecture,
p2(X9,X9),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_1) ).
fof(f0_nnf,plain,
! [X9] : p2(X9,X9),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X9] : p2(X9,X9),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
p2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h0,plain,
p2(f5(c11),f5(c11)) = true,
inference(hyper_resolution,[status(thm)],[hi0]) ).
cnf(f16,negated_conjecture,
( ~ p2(X20,X22)
| ~ p2(X19,X21)
| p2(f9(X19,X20),f9(X21,X22)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_17) ).
fof(f16_nnf,plain,
! [X19,X20,X21,X22] :
( ~ p2(X20,X22)
| ~ p2(X19,X21)
| p2(f9(X19,X20),f9(X21,X22)) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X19,X20,X21,X22] :
( ~ p2(X20,X22)
| ~ p2(X19,X21)
| p2(f9(X19,X20),f9(X21,X22)) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ p2(X1,X3)
| ~ p2(X0,X2)
| p2(f9(X0,X1),f9(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi15,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X2,X3),true,p2(f9(X0,X2),f9(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h4,plain,
p2(f9(f5(c11),f5(f7(c12))),f9(f5(c11),f5(c12))) = true,
inference(hyper_resolution,[status(thm)],[hi15,h0,h1]) ).
cnf(f13,negated_conjecture,
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_14) ).
fof(f13_nnf,plain,
! [X0,X1,X2,X3] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [X0,X1,X2,X3] :
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( ~ p10(X2,X3)
| ~ p2(X3,X1)
| ~ p2(X2,X0)
| p10(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(hi12,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X2,X3),true,ifeq(p10(X0,X2),true,p10(X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h6,plain,
p10(f9(f5(c11),f5(c12)),f5(f6(c11,f7(c12)))) = true,
inference(hyper_resolution,[status(thm)],[hi12,h4,hi0,h5]) ).
cnf(f8,negated_conjecture,
( ~ p4(X23,X25)
| ~ p4(X23,X24)
| p4(X24,X25) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_9) ).
fof(f8_nnf,plain,
! [X24,X25,X23] :
( ~ p4(X23,X25)
| ~ p4(X23,X24)
| p4(X24,X25) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X24,X25,X23] :
( ~ p4(X23,X25)
| ~ p4(X23,X24)
| p4(X24,X25) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ p4(X2,X1)
| ~ p4(X2,X0)
| p4(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(p4(X0,X1),true,ifeq(p4(X0,X2),true,p4(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f3,negated_conjecture,
p4(f8(X38,X39),f6(X38,f7(X39))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_4) ).
fof(f3_nnf,plain,
! [X38,X39] : p4(f8(X38,X39),f6(X38,f7(X39))),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X38,X39] : p4(f8(X38,X39),f6(X38,f7(X39))),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
p4(f8(X0,X1),f6(X0,f7(X1))),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,negated_conjecture,
p4(f8(X0,X1),f6(X0,f7(X1))) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f1,negated_conjecture,
p4(X23,X23),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p4_2) ).
fof(f1_nnf,plain,
! [X23] : p4(X23,X23),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X23] : p4(X23,X23),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
p4(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,negated_conjecture,
p4(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h2,plain,
p4(f6(c11,f7(c12)),f8(c11,c12)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi3,hi1]) ).
cnf(f5,negated_conjecture,
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_6) ).
fof(f5_nnf,plain,
! [X16,X17] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [X16,X17] :
( ~ p4(X16,X17)
| p2(f5(X16),f5(X17)) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( ~ p4(X0,X1)
| p2(f5(X0),f5(X1)) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,negated_conjecture,
ifeq(p4(X0,X1),true,p2(f5(X0),f5(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h3,plain,
p2(f5(f6(c11,f7(c12))),f5(f8(c11,c12))) = true,
inference(hyper_resolution,[status(thm)],[hi5,h2]) ).
cnf(t7,plain,
p10(f9(f5(c11),f5(c12)),f5(f8(c11,c12))) = true,
inference(hyper_resolution,[status(thm)],[hi12,hi0,h3,h6]) ).
cnf(t88,plain,
p10(f9(f5(c11),f5(c12)),f5(f8(c11,c12))) = true,
inference(orient,[status(thm)],[t7]) ).
cnf(f10,negated_conjecture,
~ p10(f9(f5(c11),f5(c12)),f5(f8(c11,c12))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p10_11) ).
fof(f10_nnf,plain,
~ p10(f9(f5(c11),f5(c12)),f5(f8(c11,c12))),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
~ p10(f9(f5(c11),f5(c12)),f5(f8(c11,c12))),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
~ p10(f9(f5(c11),f5(c12)),f5(f8(c11,c12))),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(goal_0,negated_conjecture,
p10(f9(f5(c11),f5(c12)),f5(f8(c11,c12))) != true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t88]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN564-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n015.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Fri Sep 25 01:48:26 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.17/0.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.17/0.88 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------