%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN003-1.006 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.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 03:33:17 PM UTC 2026
% Result : Unsatisfiable 3.27s 1.05s
% Output : Proof 3.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 80 ( 40 unt; 0 def)
% Number of atoms : 140 ( 26 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 126 ( 66 ~; 60 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 15 ( 13 usr; 14 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f19,negated_conjecture,
( r_5
| ~ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_5) ).
fof(f19_nnf,plain,
( r_5
| ~ r ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
( r_5
| ~ r ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( r_5
| ~ r ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(hi19,negated_conjecture,
ifeq(r,true,r_5,true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(f23,negated_conjecture,
r,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_4) ).
fof(f23_nnf,plain,
r,
inference(nnf_transformation,[status(thm)],[f23]) ).
cnf(c23,plain,
r,
inference(cnf_transformation,[status(esa)],[f23_nnf]) ).
cnf(hi22,negated_conjecture,
r = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(h5,plain,
r_5 = true,
inference(hyper_resolution,[status(thm)],[hi19,hi22]) ).
cnf(f18,negated_conjecture,
( r_4
| ~ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_4) ).
fof(f18_nnf,plain,
( r_4
| ~ r ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
( r_4
| ~ r ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( r_4
| ~ r ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi18,negated_conjecture,
ifeq(r,true,r_4,true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h6,plain,
r_4 = true,
inference(hyper_resolution,[status(thm)],[hi18,hi22]) ).
cnf(f17,negated_conjecture,
( r_3
| ~ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_3) ).
fof(f17_nnf,plain,
( r_3
| ~ r ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
( r_3
| ~ r ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( r_3
| ~ r ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(hi17,negated_conjecture,
ifeq(r,true,r_3,true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h7,plain,
r_3 = true,
inference(hyper_resolution,[status(thm)],[hi17,hi22]) ).
cnf(f16,negated_conjecture,
( r_2
| ~ r ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rr_2) ).
fof(f16_nnf,plain,
( r_2
| ~ r ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
( r_2
| ~ r ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( r_2
| ~ r ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi16,negated_conjecture,
ifeq(r,true,r_2,true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h8,plain,
r_2 = true,
inference(hyper_resolution,[status(thm)],[hi16,hi22]) ).
cnf(f10,negated_conjecture,
( q_1
| ~ q ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qq_1) ).
fof(f10_nnf,plain,
( q_1
| ~ q ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
( q_1
| ~ q ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( q_1
| ~ q ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,negated_conjecture,
ifeq(q,true,q_1,true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(f22,negated_conjecture,
q,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_3) ).
fof(f22_nnf,plain,
q,
inference(nnf_transformation,[status(thm)],[f22]) ).
cnf(c22,plain,
q,
inference(cnf_transformation,[status(esa)],[f22_nnf]) ).
cnf(hi21,negated_conjecture,
q = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(h4,plain,
q_1 = true,
inference(hyper_resolution,[status(thm)],[hi10,hi21]) ).
cnf(f0,negated_conjecture,
( p_2
| ~ q_1
| ~ p_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqp_1) ).
fof(f0_nnf,plain,
( p_2
| ~ q_1
| ~ p_1 ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
( p_2
| ~ q_1
| ~ p_1 ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( p_2
| ~ q_1
| ~ p_1 ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi0,negated_conjecture,
ifeq(p_1,true,ifeq(q_1,true,p_2,true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(f20,negated_conjecture,
p_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_1) ).
fof(f20_nnf,plain,
p_1,
inference(nnf_transformation,[status(thm)],[f20]) ).
cnf(c20,plain,
p_1,
inference(cnf_transformation,[status(esa)],[f20_nnf]) ).
cnf(hi20,negated_conjecture,
p_1 = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h10,plain,
p_2 = true,
inference(hyper_resolution,[status(thm)],[hi0,hi20,h4]) ).
cnf(f6,negated_conjecture,
( p_3
| ~ r_2
| ~ p_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prp_2) ).
fof(f6_nnf,plain,
( p_3
| ~ r_2
| ~ p_2 ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
( p_3
| ~ r_2
| ~ p_2 ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( p_3
| ~ r_2
| ~ p_2 ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,negated_conjecture,
ifeq(p_2,true,ifeq(r_2,true,p_3,true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h11,plain,
p_3 = true,
inference(hyper_resolution,[status(thm)],[hi6,h10,h8]) ).
cnf(f7,negated_conjecture,
( p_4
| ~ r_3
| ~ p_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prp_3) ).
fof(f7_nnf,plain,
( p_4
| ~ r_3
| ~ p_3 ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
( p_4
| ~ r_3
| ~ p_3 ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( p_4
| ~ r_3
| ~ p_3 ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,negated_conjecture,
ifeq(p_3,true,ifeq(r_3,true,p_4,true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h12,plain,
p_4 = true,
inference(hyper_resolution,[status(thm)],[hi7,h11,h7]) ).
cnf(f8,negated_conjecture,
( p_5
| ~ r_4
| ~ p_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prp_4) ).
fof(f8_nnf,plain,
( p_5
| ~ r_4
| ~ p_4 ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
( p_5
| ~ r_4
| ~ p_4 ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( p_5
| ~ r_4
| ~ p_4 ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(p_4,true,ifeq(r_4,true,p_5,true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h13,plain,
p_5 = true,
inference(hyper_resolution,[status(thm)],[hi8,h12,h6]) ).
cnf(f9,negated_conjecture,
( p_6
| ~ r_5
| ~ p_5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prp_5) ).
fof(f9_nnf,plain,
( p_6
| ~ r_5
| ~ p_5 ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
( p_6
| ~ r_5
| ~ p_5 ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( p_6
| ~ r_5
| ~ p_5 ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,negated_conjecture,
ifeq(p_5,true,ifeq(r_5,true,p_6,true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(t5,plain,
true = p_6,
inference(hyper_resolution,[status(thm)],[hi9,h13,h5]) ).
cnf(t97,plain,
p_6 = true,
inference(orient,[status(thm)],[t5]) ).
cnf(f21,negated_conjecture,
~ p_6,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_2) ).
fof(f21_nnf,plain,
~ p_6,
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
~ p_6,
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
~ p_6,
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(goal_0,negated_conjecture,
true != p_6,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t97]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN003-1.006 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.37 % Computer : n009.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Thu Sep 24 23:50:14 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 3.27/1.05 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.27/1.05 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------