%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN569-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n004.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 34.46s 4.96s
% Output : Proof 34.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 11
% Syntax : Number of formulae : 63 ( 39 unt; 0 def)
% Number of atoms : 107 ( 22 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 94 ( 50 ~; 44 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-4 aty)
% Number of variables : 81 ( 0 sgn 32 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,negated_conjecture,
( ~ p8(X4,X5)
| p10(X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p10_7) ).
fof(f6_nnf,plain,
! [X4,X5] :
( ~ p8(X4,X5)
| p10(X4,X5) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X4,X5] :
( ~ p8(X4,X5)
| p10(X4,X5) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ p8(X0,X1)
| p10(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,negated_conjecture,
ifeq(p8(X0,X1),true,p10(X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f4,negated_conjecture,
p8(c11,c14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_5) ).
fof(f4_nnf,plain,
p8(c11,c14),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
p8(c11,c14),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
p8(c11,c14) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h2,plain,
p10(c11,c14) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi4]) ).
cnf(f2,negated_conjecture,
p8(c14,c12),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_3) ).
fof(f2_nnf,plain,
p8(c14,c12),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
p8(c14,c12),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi2,negated_conjecture,
p8(c14,c12) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h0,plain,
p10(c14,c12) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi2]) ).
cnf(f11,negated_conjecture,
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_12) ).
fof(f11_nnf,plain,
! [X40] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
! [X40] :
( ~ p10(c11,X40)
| ~ p10(X40,c12)
| p9(c13,f3(X40),X40) ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( ~ p10(c11,X0)
| ~ p10(X0,c12)
| p9(c13,f3(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,negated_conjecture,
ifeq(p10(X0,c12),true,ifeq(p10(c11,X0),true,p9(c13,f3(X0),X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h3,plain,
p9(c13,f3(c14),c14) = true,
inference(hyper_resolution,[status(thm)],[hi11,h0,h2]) ).
cnf(f10,negated_conjecture,
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_11) ).
fof(f10_nnf,plain,
! [X9,X10,X11,X12] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X9,X10,X11,X12] :
( ~ p9(X11,X10,X12)
| ~ p9(X11,X9,X12)
| p2(X9,X10) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ p9(X2,X1,X3)
| ~ p9(X2,X0,X3)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,negated_conjecture,
ifeq(p9(X0,X1,X2),true,ifeq(p9(X0,X3,X2),true,p2(X1,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f5,negated_conjecture,
p9(c13,c15,c14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_6) ).
fof(f5_nnf,plain,
p9(c13,c15,c14),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
p9(c13,c15,c14),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi5,negated_conjecture,
p9(c13,c15,c14) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h4,plain,
p2(c15,f3(c14)) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi5,h3]) ).
cnf(f15,negated_conjecture,
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_16) ).
fof(f15_nnf,plain,
! [X15,X16,X17,X18] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [X15,X16,X17,X18] :
( ~ p2(X16,X18)
| ~ p2(X15,X17)
| p2(f4(X15,X16),f4(X17,X18)) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( ~ p2(X1,X3)
| ~ p2(X0,X2)
| p2(f4(X0,X1),f4(X2,X3)) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(hi15,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X2,X3),true,p2(f4(X0,X2),f4(X1,X3)),true),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(f0,negated_conjecture,
p2(X6,X6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_1) ).
fof(f0_nnf,plain,
! [X6] : p2(X6,X6),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X6] : p2(X6,X6),
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(h11,plain,
p2(f4(V0,c15),f4(V0,f3(c14))) = true,
inference(hyper_resolution,[status(thm)],[hi15,hi0,h4]) ).
cnf(f9,negated_conjecture,
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_10) ).
fof(f9_nnf,plain,
! [X7,X8,X6] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [X7,X8,X6] :
( ~ p2(X6,X8)
| ~ p2(X6,X7)
| p2(X7,X8) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X0,X2),true,p2(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(f14,negated_conjecture,
p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_15) ).
fof(f14_nnf,plain,
p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15)),
inference(nnf_transformation,[status(thm)],[f14]) ).
cnf(c14,plain,
p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15)),
inference(cnf_transformation,[status(esa)],[f14_nnf]) ).
cnf(hi14,negated_conjecture,
p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),c15)) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h980,plain,
p2(f4(f5(c12,c11),c15),f5(f7(c13,c12),f7(c13,c11))) = true,
inference(hyper_resolution,[status(thm)],[hi9,hi14,hi0]) ).
cnf(h1143,plain,
p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(c14))) = true,
inference(hyper_resolution,[status(thm)],[hi9,h980,h11]) ).
cnf(f19,negated_conjecture,
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(c11,X41)
| ~ p8(X41,c12) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p8_20) ).
fof(f19_nnf,plain,
! [X41] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(c11,X41)
| ~ p8(X41,c12) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [X41] :
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X41)))
| ~ p8(c11,X41)
| ~ p8(X41,c12) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( ~ p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X0)))
| ~ p8(c11,X0)
| ~ p8(X0,c12) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,negated_conjecture,
ifeq(p8(X0,c12),true,ifeq(p8(c11,X0),true,ifeq(p2(f5(f7(c13,c12),f7(c13,c11)),f4(f5(c12,c11),f3(X0))),true,false,true),true),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi19,hi2,hi4,h1143]) ).
cnf(t4229,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t4229]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN569-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.35 % Computer : n004.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 01:44:23 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 34.46/4.96 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 34.46/4.96 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------