%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN561-1 : TPTP v9.3.1. Released v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n007.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 7.75s 1.57s
% Output : Proof 7.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 35 unt; 0 def)
% Number of atoms : 63 ( 15 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 46 ( 26 ~; 20 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-4 aty)
% Number of variables : 30 ( 0 sgn 12 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f8,negated_conjecture,
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_9) ).
fof(f8_nnf,plain,
! [X1,X2,X0] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X1,X2,X0] :
( ~ p2(X0,X2)
| ~ p2(X0,X1)
| p2(X1,X2) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ p2(X2,X1)
| ~ p2(X2,X0)
| p2(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(p2(X0,X1),true,ifeq(p2(X0,X2),true,p2(X1,X2),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(f5,negated_conjecture,
p2(f3(f4(f5(c12)),c13),c16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_6) ).
fof(f5_nnf,plain,
p2(f3(f4(f5(c12)),c13),c16),
inference(nnf_transformation,[status(thm)],[f5]) ).
cnf(c5,plain,
p2(f3(f4(f5(c12)),c13),c16),
inference(cnf_transformation,[status(esa)],[f5_nnf]) ).
cnf(hi5,negated_conjecture,
p2(f3(f4(f5(c12)),c13),c16) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(f0,negated_conjecture,
p2(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_1) ).
fof(f0_nnf,plain,
! [X0] : p2(X0,X0),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [X0] : p2(X0,X0),
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(h34,plain,
p2(c16,f3(f4(f5(c12)),c13)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi5,hi0]) ).
cnf(f4,negated_conjecture,
p2(f6(c15,c11),c16),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_5) ).
fof(f4_nnf,plain,
p2(f6(c15,c11),c16),
inference(nnf_transformation,[status(thm)],[f4]) ).
cnf(c4,plain,
p2(f6(c15,c11),c16),
inference(cnf_transformation,[status(esa)],[f4_nnf]) ).
cnf(hi4,negated_conjecture,
p2(f6(c15,c11),c16) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h15,plain,
p2(c16,f6(c15,c11)) = true,
inference(hyper_resolution,[status(thm)],[hi8,hi4,hi0]) ).
cnf(h53,plain,
p2(f6(c15,c11),f3(f4(f5(c12)),c13)) = true,
inference(hyper_resolution,[status(thm)],[hi8,h15,h34]) ).
cnf(f14,negated_conjecture,
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',not_p9_15) ).
fof(f14_nnf,plain,
! [X28,X27] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X28,X27] :
( ~ p2(f6(X27,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X28),X27)
| ~ p8(c11,X28)
| ~ p9(X28,c10) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ p2(f6(X1,c11),f3(f4(f5(c12)),c13))
| ~ p2(f7(c10,X0),X1)
| ~ p8(c11,X0)
| ~ p9(X0,c10) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,negated_conjecture,
ifeq(p9(X0,c10),true,ifeq(p8(c11,X0),true,ifeq(p2(f7(c10,X0),X1),true,ifeq(p2(f6(X1,c11),f3(f4(f5(c12)),c13)),true,false,true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(f1,negated_conjecture,
p9(c14,c10),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p9_2) ).
fof(f1_nnf,plain,
p9(c14,c10),
inference(nnf_transformation,[status(thm)],[f1]) ).
cnf(c1,plain,
p9(c14,c10),
inference(cnf_transformation,[status(esa)],[f1_nnf]) ).
cnf(hi1,negated_conjecture,
p9(c14,c10) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(f2,negated_conjecture,
p8(c11,c14),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p8_3) ).
fof(f2_nnf,plain,
p8(c11,c14),
inference(nnf_transformation,[status(thm)],[f2]) ).
cnf(c2,plain,
p8(c11,c14),
inference(cnf_transformation,[status(esa)],[f2_nnf]) ).
cnf(hi2,negated_conjecture,
p8(c11,c14) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(f3,negated_conjecture,
p2(f7(c10,c14),c15),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',p2_4) ).
fof(f3_nnf,plain,
p2(f7(c10,c14),c15),
inference(nnf_transformation,[status(thm)],[f3]) ).
cnf(c3,plain,
p2(f7(c10,c14),c15),
inference(cnf_transformation,[status(esa)],[f3_nnf]) ).
cnf(hi3,negated_conjecture,
p2(f7(c10,c14),c15) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi14,hi1,hi2,hi3,h53]) ).
cnf(t1143,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1143]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN561-1 : TPTP v9.3.1. Released v2.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.38 % Computer : n007.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Fri Sep 25 01:43:37 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 7.75/1.57 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.75/1.57 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------