%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN004-1.007 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n005.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 4.47s 1.08s
% Output : Proof 4.47s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 90 ( 38 unt; 0 def)
% Number of atoms : 190 ( 31 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 206 ( 106 ~; 100 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 16 ( 14 usr; 15 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-4 aty)
% Number of variables : 0 ( 0 sgn 0 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f6,negated_conjecture,
( q_2
| ~ q_1
| ~ p_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqq_1) ).
fof(f6_nnf,plain,
( q_2
| ~ q_1
| ~ p_1 ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
( q_2
| ~ q_1
| ~ p_1 ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( q_2
| ~ q_1
| ~ p_1 ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi6,negated_conjecture,
ifeq(p_1,true,ifeq(q_1,true,q_2,true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(f12,negated_conjecture,
p_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_1) ).
fof(f12_nnf,plain,
p_1,
inference(nnf_transformation,[status(thm)],[f12]) ).
cnf(c12,plain,
p_1,
inference(cnf_transformation,[status(esa)],[f12_nnf]) ).
cnf(hi12,negated_conjecture,
p_1 = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(f13,negated_conjecture,
q_1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_2) ).
fof(f13_nnf,plain,
q_1,
inference(nnf_transformation,[status(thm)],[f13]) ).
cnf(c13,plain,
q_1,
inference(cnf_transformation,[status(esa)],[f13_nnf]) ).
cnf(hi13,negated_conjecture,
q_1 = true,
inference(equality_encoding,[status(esa)],[c13]) ).
cnf(h0,plain,
q_2 = true,
inference(hyper_resolution,[status(thm)],[hi6,hi12,hi13]) ).
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(h1,plain,
p_2 = true,
inference(hyper_resolution,[status(thm)],[hi0,hi12,hi13]) ).
cnf(f7,negated_conjecture,
( q_3
| ~ q_2
| ~ p_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqq_2) ).
fof(f7_nnf,plain,
( q_3
| ~ q_2
| ~ p_2 ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
( q_3
| ~ q_2
| ~ p_2 ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( q_3
| ~ q_2
| ~ p_2 ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(hi7,negated_conjecture,
ifeq(p_2,true,ifeq(q_2,true,q_3,true),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h2,plain,
q_3 = true,
inference(hyper_resolution,[status(thm)],[hi7,h1,h0]) ).
cnf(f1,negated_conjecture,
( p_3
| ~ q_2
| ~ p_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqp_2) ).
fof(f1_nnf,plain,
( p_3
| ~ q_2
| ~ p_2 ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
( p_3
| ~ q_2
| ~ p_2 ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( p_3
| ~ q_2
| ~ p_2 ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(hi1,negated_conjecture,
ifeq(p_2,true,ifeq(q_2,true,p_3,true),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(h3,plain,
p_3 = true,
inference(hyper_resolution,[status(thm)],[hi1,h1,h0]) ).
cnf(f8,negated_conjecture,
( q_4
| ~ q_3
| ~ p_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqq_3) ).
fof(f8_nnf,plain,
( q_4
| ~ q_3
| ~ p_3 ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
( q_4
| ~ q_3
| ~ p_3 ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( q_4
| ~ q_3
| ~ p_3 ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi8,negated_conjecture,
ifeq(p_3,true,ifeq(q_3,true,q_4,true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h4,plain,
q_4 = true,
inference(hyper_resolution,[status(thm)],[hi8,h3,h2]) ).
cnf(f2,negated_conjecture,
( p_4
| ~ q_3
| ~ p_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqp_3) ).
fof(f2_nnf,plain,
( p_4
| ~ q_3
| ~ p_3 ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
( p_4
| ~ q_3
| ~ p_3 ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( p_4
| ~ q_3
| ~ p_3 ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi2,negated_conjecture,
ifeq(p_3,true,ifeq(q_3,true,p_4,true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h5,plain,
p_4 = true,
inference(hyper_resolution,[status(thm)],[hi2,h3,h2]) ).
cnf(f9,negated_conjecture,
( q_5
| ~ q_4
| ~ p_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqq_4) ).
fof(f9_nnf,plain,
( q_5
| ~ q_4
| ~ p_4 ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
( q_5
| ~ q_4
| ~ p_4 ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( q_5
| ~ q_4
| ~ p_4 ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(hi9,negated_conjecture,
ifeq(p_4,true,ifeq(q_4,true,q_5,true),true) = true,
inference(equality_encoding,[status(esa)],[c9]) ).
cnf(h6,plain,
q_5 = true,
inference(hyper_resolution,[status(thm)],[hi9,h5,h4]) ).
cnf(f3,negated_conjecture,
( p_5
| ~ q_4
| ~ p_4 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqp_4) ).
fof(f3_nnf,plain,
( p_5
| ~ q_4
| ~ p_4 ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
( p_5
| ~ q_4
| ~ p_4 ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( p_5
| ~ q_4
| ~ p_4 ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(hi3,negated_conjecture,
ifeq(p_4,true,ifeq(q_4,true,p_5,true),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(h7,plain,
p_5 = true,
inference(hyper_resolution,[status(thm)],[hi3,h5,h4]) ).
cnf(f10,negated_conjecture,
( q_6
| ~ q_5
| ~ p_5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqq_5) ).
fof(f10_nnf,plain,
( q_6
| ~ q_5
| ~ p_5 ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
( q_6
| ~ q_5
| ~ p_5 ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( q_6
| ~ q_5
| ~ p_5 ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,negated_conjecture,
ifeq(p_5,true,ifeq(q_5,true,q_6,true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h8,plain,
q_6 = true,
inference(hyper_resolution,[status(thm)],[hi10,h7,h6]) ).
cnf(f4,negated_conjecture,
( p_6
| ~ q_5
| ~ p_5 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqp_5) ).
fof(f4_nnf,plain,
( p_6
| ~ q_5
| ~ p_5 ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
( p_6
| ~ q_5
| ~ p_5 ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( p_6
| ~ q_5
| ~ p_5 ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(hi4,negated_conjecture,
ifeq(p_5,true,ifeq(q_5,true,p_6,true),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(h9,plain,
p_6 = true,
inference(hyper_resolution,[status(thm)],[hi4,h7,h6]) ).
cnf(f11,negated_conjecture,
( q_7
| ~ q_6
| ~ p_6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqq_6) ).
fof(f11_nnf,plain,
( q_7
| ~ q_6
| ~ p_6 ),
inference(nnf_transformation,[status(thm)],[f11]) ).
fof(f11_sk,plain,
( q_7
| ~ q_6
| ~ p_6 ),
inference(skolemisation,[status(esa)],[f11_nnf]) ).
cnf(c11,plain,
( q_7
| ~ q_6
| ~ p_6 ),
inference(cnf_transformation,[status(esa)],[f11_sk]) ).
cnf(hi11,negated_conjecture,
ifeq(p_6,true,ifeq(q_6,true,q_7,true),true) = true,
inference(equality_encoding,[status(esa)],[c11]) ).
cnf(h10,plain,
q_7 = true,
inference(hyper_resolution,[status(thm)],[hi11,h9,h8]) ).
cnf(f5,negated_conjecture,
( p_7
| ~ q_6
| ~ p_6 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',pqp_6) ).
fof(f5_nnf,plain,
( p_7
| ~ q_6
| ~ p_6 ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
( p_7
| ~ q_6
| ~ p_6 ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( p_7
| ~ q_6
| ~ p_6 ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(hi5,negated_conjecture,
ifeq(p_6,true,ifeq(q_6,true,p_7,true),true) = true,
inference(equality_encoding,[status(esa)],[c5]) ).
cnf(h11,plain,
p_7 = true,
inference(hyper_resolution,[status(thm)],[hi5,h9,h8]) ).
cnf(f14,negated_conjecture,
( ~ q_7
| ~ p_7 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',base_3) ).
fof(f14_nnf,plain,
( ~ q_7
| ~ p_7 ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
( ~ q_7
| ~ p_7 ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ q_7
| ~ p_7 ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi14,negated_conjecture,
ifeq(p_7,true,ifeq(q_7,true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi14,h11,h10]) ).
cnf(t70,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,t70]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYN004-1.007 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.09/0.35 % Computer : n005.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 : Thu Sep 24 23:50:03 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 4.47/1.08 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.47/1.08 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------