%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN566-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 03:35:13 PM UTC 2026
% Result : Unsatisfiable 6.33s 1.89s
% Output : Proof 6.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 42 unt; 0 def)
% Number of atoms : 98 ( 21 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 78 ( 42 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 77 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f9,negated_conjecture,
( ~ p2(X7,X8)
| p2(f5(X7),f5(X8)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_10) ).
fof(f9_nnf,plain,
! [X7,X8] :
( ~ p2(X7,X8)
| p2(f5(X7),f5(X8)) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X7,X8] :
( ~ p2(X7,X8)
| p2(f5(X7),f5(X8)) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ p2(X0,X1)
| p2(f5(X0),f5(X1)) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,negated_conjecture,
ifeq(p2(X0,X1),true,p2(f5(X0),f5(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(f1,negated_conjecture,
p2(X4,X4),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_2) ).
fof(f1_nnf,plain,
! [X4] : p2(X4,X4),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [X4] : p2(X4,X4),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
p2(X0,X0),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,negated_conjecture,
p2(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h1,plain,
p2(f5(V0),f5(V0)) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi1]) ).
cnf(f8,negated_conjecture,
( ~ p2(X14,X15)
| p3(f4(X14),f4(X15)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_9) ).
fof(f8_nnf,plain,
! [X14,X15] :
( ~ p2(X14,X15)
| p3(f4(X14),f4(X15)) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X14,X15] :
( ~ p2(X14,X15)
| p3(f4(X14),f4(X15)) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ p2(X0,X1)
| p3(f4(X0),f4(X1)) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(p2(X0,X1),true,p3(f4(X0),f4(X1)),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h20,plain,
p3(f4(f5(V0)),f4(f5(V0))) = true,
inference(hyper_resolution,[status(thm)],[hi8,h1]) ).
cnf(f6,negated_conjecture,
p2(c14,f6(c15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_7) ).
fof(f6_nnf,plain,
p2(c14,f6(c15)),
inference(nnf_transformation,[status(thm)],[f6]) ).
cnf(c6,plain,
p2(c14,f6(c15)),
inference(cnf_transformation,[status(esa)],[f6_nnf]) ).
cnf(hi6,negated_conjecture,
p2(c14,f6(c15)) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h7,plain,
p3(f4(c14),f4(f6(c15))) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi6]) ).
cnf(f17,negated_conjecture,
( ~ p3(X23,X22)
| ~ p8(X24,X23)
| ~ p7(X24,X21)
| p8(X21,X22) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_18) ).
fof(f17_nnf,plain,
! [X21,X22,X24,X23] :
( ~ p3(X23,X22)
| ~ p8(X24,X23)
| ~ p7(X24,X21)
| p8(X21,X22) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [X21,X22,X24,X23] :
( ~ p3(X23,X22)
| ~ p8(X24,X23)
| ~ p7(X24,X21)
| p8(X21,X22) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( ~ p3(X3,X1)
| ~ p8(X2,X3)
| ~ p7(X2,X0)
| p8(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,negated_conjecture,
ifeq(p7(X0,X1),true,ifeq(p8(X0,X2),true,ifeq(p3(X2,X3),true,p8(X1,X3),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(f3,negated_conjecture,
p7(X16,X16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p7_4) ).
fof(f3_nnf,plain,
! [X16] : p7(X16,X16),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [X16] : p7(X16,X16),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
p7(X0,X0),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,negated_conjecture,
p7(X0,X0) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(f5,negated_conjecture,
p8(c12,c13),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_6) ).
fof(f5_nnf,plain,
p8(c12,c13),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
p8(c12,c13),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi5,negated_conjecture,
p8(c12,c13) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f7,negated_conjecture,
p3(c13,f4(c14)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p3_8) ).
fof(f7_nnf,plain,
p3(c13,f4(c14)),
inference(nnf_transformation,[status(thm)],[f7]) ).
cnf(c7,plain,
p3(c13,f4(c14)),
inference(cnf_transformation,[status(esa)],[f7_nnf]) ).
cnf(hi7,negated_conjecture,
p3(c13,f4(c14)) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h8,plain,
p8(c12,f4(c14)) = true,
inference(hyper_resolution,[status(thm)],[hi17,hi3,hi5,hi7]) ).
cnf(h32,plain,
p8(c12,f4(f6(c15))) = true,
inference(hyper_resolution,[status(thm)],[hi17,hi3,h8,h7]) ).
cnf(f15,negated_conjecture,
( ~ p8(X19,f4(f6(X20)))
| p8(X19,f4(f5(X20))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_16) ).
fof(f15_nnf,plain,
! [X19,X20] :
( ~ p8(X19,f4(f6(X20)))
| p8(X19,f4(f5(X20))) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X19,X20] :
( ~ p8(X19,f4(f6(X20)))
| p8(X19,f4(f5(X20))) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( ~ p8(X0,f4(f6(X1)))
| p8(X0,f4(f5(X1))) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,negated_conjecture,
ifeq(p8(X0,f4(f6(X1))),true,p8(X0,f4(f5(X1))),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(h60,plain,
p8(c12,f4(f5(c15))) = true,
inference(hyper_resolution,[status(thm)],[hi15,h32]) ).
cnf(f18,negated_conjecture,
( ~ p2(X29,f5(X28))
| ~ p3(X30,f4(X29))
| ~ p8(c12,X30)
| ~ p10(X28,c11) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p10_19) ).
fof(f18_nnf,plain,
! [X28,X30,X29] :
( ~ p2(X29,f5(X28))
| ~ p3(X30,f4(X29))
| ~ p8(c12,X30)
| ~ p10(X28,c11) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X28,X30,X29] :
( ~ p2(X29,f5(X28))
| ~ p3(X30,f4(X29))
| ~ p8(c12,X30)
| ~ p10(X28,c11) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( ~ p2(X2,f5(X0))
| ~ p3(X1,f4(X2))
| ~ p8(c12,X1)
| ~ p10(X0,c11) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,negated_conjecture,
ifeq(p10(X0,c11),true,ifeq(p8(c12,X1),true,ifeq(p3(X1,f4(X2)),true,ifeq(p2(X2,f5(X0)),true,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(f4,negated_conjecture,
p10(c15,c11),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_5) ).
fof(f4_nnf,plain,
p10(c15,c11),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
p10(c15,c11),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
p10(c15,c11) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi18,hi4,h60,h20,h1]) ).
cnf(t393,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t393]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN566-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.95 % Computer : n017.cluster.edu
% 0.09/0.95 % Model : x86_64 x86_64
% 0.09/0.95 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.95 % Memory : 8046.5625MB
% 0.09/0.95 % OS : Linux 6.8.0-71-generic
% 0.09/0.95 % CPULimit : 300
% 0.09/0.95 % WCLimit : 300
% 0.09/0.95 % DateTime : Fri Sep 25 01:40:18 UTC 2026
% 0.09/0.95 % CPUTime :
% 0.09/0.95 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 6.33/1.89 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.33/1.89 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------