%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SYN102-1.007.007 : TPTP v9.3.1. Bugfixed v1.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n011.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 03:33:49 PM UTC 2026
% Result : Unsatisfiable 14.59s 2.39s
% Output : Proof 14.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 35
% Syntax : Number of formulae : 200 ( 88 unt; 0 def)
% Number of atoms : 500 ( 66 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 606 ( 306 ~; 300 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 8 ( 1 avg)
% Number of predicates : 36 ( 34 usr; 1 prp; 0-7 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-4 aty)
% Number of variables : 945 ( 0 sgn 378 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f53,axiom,
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_t3_1) ).
fof(f53_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f53]) ).
fof(f53_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f53_nnf]) ).
cnf(c53,plain,
( ~ nq_7(X6)
| ~ nq_6(X5)
| ~ nq_5(X4)
| ~ nq_4(X3)
| ~ nq_3(X2)
| ~ nq_2(X1)
| ~ nq_1(X0)
| p_12(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f53_sk]) ).
cnf(hi52,axiom,
ifeq(nq_1(X0),true,ifeq(nq_2(X1),true,ifeq(nq_3(X2),true,ifeq(nq_4(X3),true,ifeq(nq_5(X4),true,ifeq(nq_6(X5),true,ifeq(nq_7(X6),true,p_12(X0,X1,X2,X3,X4,X5,X6),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(f57,axiom,
nq_1(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_1) ).
fof(f57_nnf,plain,
nq_1(a),
inference(nnf_transformation,[status(thm)],[f57]) ).
cnf(c57,plain,
nq_1(a),
inference(cnf_transformation,[status(esa)],[f57_nnf]) ).
cnf(hi56,axiom,
nq_1(a) = true,
inference(equality_encoding,[status(esa)],[c57]) ).
cnf(f59,axiom,
nq_2(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_3) ).
fof(f59_nnf,plain,
nq_2(a),
inference(nnf_transformation,[status(thm)],[f59]) ).
cnf(c59,plain,
nq_2(a),
inference(cnf_transformation,[status(esa)],[f59_nnf]) ).
cnf(hi58,axiom,
nq_2(a) = true,
inference(equality_encoding,[status(esa)],[c59]) ).
cnf(f61,axiom,
nq_3(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_5) ).
fof(f61_nnf,plain,
nq_3(a),
inference(nnf_transformation,[status(thm)],[f61]) ).
cnf(c61,plain,
nq_3(a),
inference(cnf_transformation,[status(esa)],[f61_nnf]) ).
cnf(hi60,axiom,
nq_3(a) = true,
inference(equality_encoding,[status(esa)],[c61]) ).
cnf(f63,axiom,
nq_4(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_7) ).
fof(f63_nnf,plain,
nq_4(a),
inference(nnf_transformation,[status(thm)],[f63]) ).
cnf(c63,plain,
nq_4(a),
inference(cnf_transformation,[status(esa)],[f63_nnf]) ).
cnf(hi62,axiom,
nq_4(a) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
cnf(f65,axiom,
nq_5(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_9) ).
fof(f65_nnf,plain,
nq_5(a),
inference(nnf_transformation,[status(thm)],[f65]) ).
cnf(c65,plain,
nq_5(a),
inference(cnf_transformation,[status(esa)],[f65_nnf]) ).
cnf(hi64,axiom,
nq_5(a) = true,
inference(equality_encoding,[status(esa)],[c65]) ).
cnf(f67,axiom,
nq_6(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_11) ).
fof(f67_nnf,plain,
nq_6(a),
inference(nnf_transformation,[status(thm)],[f67]) ).
cnf(c67,plain,
nq_6(a),
inference(cnf_transformation,[status(esa)],[f67_nnf]) ).
cnf(hi66,axiom,
nq_6(a) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(f69,axiom,
nq_7(a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_13) ).
fof(f69_nnf,plain,
nq_7(a),
inference(nnf_transformation,[status(thm)],[f69]) ).
cnf(c69,plain,
nq_7(a),
inference(cnf_transformation,[status(esa)],[f69_nnf]) ).
cnf(hi68,axiom,
nq_7(a) = true,
inference(equality_encoding,[status(esa)],[c69]) ).
cnf(h255,plain,
p_12(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi52,hi56,hi58,hi60,hi62,hi64,hi66,hi68]) ).
cnf(f56,axiom,
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| q_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_t3_4) ).
fof(f56_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| q_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| q_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( ~ nq_7(X6)
| ~ nq_6(X5)
| ~ nq_5(X4)
| ~ nq_4(X3)
| ~ nq_3(X2)
| ~ nq_2(X1)
| ~ nq_1(X0)
| q_13(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(hi55,axiom,
ifeq(nq_1(X0),true,ifeq(nq_2(X1),true,ifeq(nq_3(X2),true,ifeq(nq_4(X3),true,ifeq(nq_5(X4),true,ifeq(nq_6(X5),true,ifeq(nq_7(X6),true,q_13(X0,X1,X2,X3,X4,X5,X6),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(h63,plain,
q_13(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi55,hi56,hi58,hi60,hi62,hi64,hi66,hi68]) ).
cnf(f55,axiom,
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_t3_3) ).
fof(f55_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f55]) ).
fof(f55_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f55_nnf]) ).
cnf(c55,plain,
( ~ nq_7(X6)
| ~ nq_6(X5)
| ~ nq_5(X4)
| ~ nq_4(X3)
| ~ nq_3(X2)
| ~ nq_2(X1)
| ~ nq_1(X0)
| q_12(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f55_sk]) ).
cnf(hi54,axiom,
ifeq(nq_1(X0),true,ifeq(nq_2(X1),true,ifeq(nq_3(X2),true,ifeq(nq_4(X3),true,ifeq(nq_5(X4),true,ifeq(nq_6(X5),true,ifeq(nq_7(X6),true,q_12(X0,X1,X2,X3,X4,X5,X6),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(h127,plain,
q_12(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi54,hi56,hi58,hi60,hi62,hi64,hi66,hi68]) ).
cnf(f24,axiom,
( ~ q_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type11_24) ).
fof(f24_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( ~ q_13(X0,X1,X2,X3,X4,X5,X6)
| ~ q_12(X0,X1,X2,X3,X4,X5,X6)
| p_11(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(hi23,axiom,
ifeq(q_12(X0,X1,X2,X3,X4,X5,X6),true,ifeq(q_13(X0,X1,X2,X3,X4,X5,X6),true,p_11(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c24]) ).
cnf(h575,plain,
p_11(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi23,h127,h63]) ).
cnf(f21,axiom,
( ~ p_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type11_21) ).
fof(f21_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( ~ p_12(X0,X1,X2,X3,X4,X5,X6)
| ~ p_11(X0,X1,X2,X3,X4,X5,X6)
| p_10(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi20,axiom,
ifeq(p_11(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_12(X0,X1,X2,X3,X4,X5,X6),true,p_10(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(h895,plain,
p_10(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi20,h575,h255]) ).
cnf(f45,axiom,
( ~ q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_21) ).
fof(f45_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f45]) ).
fof(f45_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f45_nnf]) ).
cnf(c45,plain,
( ~ q_12(X0,X1,X2,X3,X4,X5,X6)
| ~ p_11(X0,X1,X2,X3,X4,X5,X6)
| q_10(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f45_sk]) ).
cnf(hi44,axiom,
ifeq(p_11(X0,X1,X2,X3,X4,X5,X6),true,ifeq(q_12(X0,X1,X2,X3,X4,X5,X6),true,q_10(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c45]) ).
cnf(h894,plain,
q_10(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi44,h575,h127]) ).
cnf(f44,axiom,
( ~ p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_20) ).
fof(f44_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f44]) ).
fof(f44_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f44_nnf]) ).
cnf(c44,plain,
( ~ p_11(X0,X1,X2,X3,X4,X5,X6)
| ~ q_10(X0,X1,X2,X3,X4,X5,X6)
| q_9(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f44_sk]) ).
cnf(hi43,axiom,
ifeq(q_10(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_11(X0,X1,X2,X3,X4,X5,X6),true,q_9(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c44]) ).
cnf(h1150,plain,
q_9(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi43,h894,h575]) ).
cnf(f42,axiom,
( ~ p_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_18) ).
fof(f42_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( ~ p_10(X0,X1,X2,X3,X4,X5,X6)
| ~ q_9(X0,X1,X2,X3,X4,X5,X6)
| q_8(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
cnf(hi41,axiom,
ifeq(q_9(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_10(X0,X1,X2,X3,X4,X5,X6),true,q_8(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(h1406,plain,
q_8(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi41,h1150,h895]) ).
cnf(f54,axiom,
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_t3_2) ).
fof(f54_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f54]) ).
fof(f54_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ nq_7(X_7)
| ~ nq_6(X_6)
| ~ nq_5(X_5)
| ~ nq_4(X_4)
| ~ nq_3(X_3)
| ~ nq_2(X_2)
| ~ nq_1(X_1)
| p_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f54_nnf]) ).
cnf(c54,plain,
( ~ nq_7(X6)
| ~ nq_6(X5)
| ~ nq_5(X4)
| ~ nq_4(X3)
| ~ nq_3(X2)
| ~ nq_2(X1)
| ~ nq_1(X0)
| p_13(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f54_sk]) ).
cnf(hi53,axiom,
ifeq(nq_1(X0),true,ifeq(nq_2(X1),true,ifeq(nq_3(X2),true,ifeq(nq_4(X3),true,ifeq(nq_5(X4),true,ifeq(nq_6(X5),true,ifeq(nq_7(X6),true,p_13(X0,X1,X2,X3,X4,X5,X6),true),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c54]) ).
cnf(h191,plain,
p_13(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi53,hi56,hi58,hi60,hi62,hi64,hi66,hi68]) ).
cnf(f48,axiom,
( ~ p_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_24) ).
fof(f48_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f48]) ).
fof(f48_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_13(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_12(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f48_nnf]) ).
cnf(c48,plain,
( ~ p_13(X0,X1,X2,X3,X4,X5,X6)
| ~ q_12(X0,X1,X2,X3,X4,X5,X6)
| q_11(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f48_sk]) ).
cnf(hi47,axiom,
ifeq(q_12(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_13(X0,X1,X2,X3,X4,X5,X6),true,q_11(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c48]) ).
cnf(h639,plain,
q_11(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi47,h127,h191]) ).
cnf(f20,axiom,
( ~ q_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type11_20) ).
fof(f20_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_11(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( ~ q_11(X0,X1,X2,X3,X4,X5,X6)
| ~ q_10(X0,X1,X2,X3,X4,X5,X6)
| p_9(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(hi19,axiom,
ifeq(q_10(X0,X1,X2,X3,X4,X5,X6),true,ifeq(q_11(X0,X1,X2,X3,X4,X5,X6),true,p_9(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h1151,plain,
p_9(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi19,h894,h639]) ).
cnf(f40,axiom,
( ~ p_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_16) ).
fof(f40_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( ~ p_9(X0,X1,X2,X3,X4,X5,X6)
| ~ q_8(X0,X1,X2,X3,X4,X5,X6)
| q_7(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(hi39,axiom,
ifeq(q_8(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_9(X0,X1,X2,X3,X4,X5,X6),true,q_7(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(h1662,plain,
q_7(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi39,h1406,h1151]) ).
cnf(f14,axiom,
( ~ q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type11_14) ).
fof(f14_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( ~ q_8(X0,X1,X2,X3,X4,X5,X6)
| ~ q_7(X0,X1,X2,X3,X4,X5,X6)
| p_6(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(hi13,axiom,
ifeq(q_7(X0,X1,X2,X3,X4,X5,X6),true,ifeq(q_8(X0,X1,X2,X3,X4,X5,X6),true,p_6(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(h2046,plain,
p_6(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi13,h1662,h1406]) ).
cnf(f16,axiom,
( ~ q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type11_16) ).
fof(f16_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( ~ q_9(X0,X1,X2,X3,X4,X5,X6)
| ~ q_8(X0,X1,X2,X3,X4,X5,X6)
| p_7(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(hi15,axiom,
ifeq(q_8(X0,X1,X2,X3,X4,X5,X6),true,ifeq(q_9(X0,X1,X2,X3,X4,X5,X6),true,p_7(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c16]) ).
cnf(h1663,plain,
p_7(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi15,h1406,h1150]) ).
cnf(f18,axiom,
( ~ q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type11_18) ).
fof(f18_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_10(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_9(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( ~ q_10(X0,X1,X2,X3,X4,X5,X6)
| ~ q_9(X0,X1,X2,X3,X4,X5,X6)
| p_8(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(hi17,axiom,
ifeq(q_9(X0,X1,X2,X3,X4,X5,X6),true,ifeq(q_10(X0,X1,X2,X3,X4,X5,X6),true,p_8(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(h1407,plain,
p_8(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi17,h1150,h894]) ).
cnf(f38,axiom,
( ~ p_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_14) ).
fof(f38_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_8(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( ~ p_8(X0,X1,X2,X3,X4,X5,X6)
| ~ q_7(X0,X1,X2,X3,X4,X5,X6)
| q_6(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(hi37,axiom,
ifeq(q_7(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_8(X0,X1,X2,X3,X4,X5,X6),true,q_6(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(h2045,plain,
q_6(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi37,h1662,h1407]) ).
cnf(f36,axiom,
( ~ p_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_12) ).
fof(f36_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f36]) ).
fof(f36_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f36_nnf]) ).
cnf(c36,plain,
( ~ p_7(X0,X1,X2,X3,X4,X5,X6)
| ~ q_6(X0,X1,X2,X3,X4,X5,X6)
| q_5(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f36_sk]) ).
cnf(hi35,axiom,
ifeq(q_6(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_7(X0,X1,X2,X3,X4,X5,X6),true,q_5(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c36]) ).
cnf(h2430,plain,
q_5(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi35,h2045,h1663]) ).
cnf(f34,axiom,
( ~ p_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_10) ).
fof(f34_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f34]) ).
fof(f34_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f34_nnf]) ).
cnf(c34,plain,
( ~ p_6(X0,X1,X2,X3,X4,X5,X6)
| ~ q_5(X0,X1,X2,X3,X4,X5,X6)
| q_4(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(hi33,axiom,
ifeq(q_5(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_6(X0,X1,X2,X3,X4,X5,X6),true,q_4(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c34]) ).
cnf(h2686,plain,
q_4(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi33,h2430,h2046]) ).
cnf(f12,axiom,
( ~ q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type11_12) ).
fof(f12_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_7(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( ~ q_7(X0,X1,X2,X3,X4,X5,X6)
| ~ q_6(X0,X1,X2,X3,X4,X5,X6)
| p_5(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(hi11,axiom,
ifeq(q_6(X0,X1,X2,X3,X4,X5,X6),true,ifeq(q_7(X0,X1,X2,X3,X4,X5,X6),true,p_5(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(h2431,plain,
p_5(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi11,h2045,h1662]) ).
cnf(f32,axiom,
( ~ p_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_8) ).
fof(f32_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f32]) ).
fof(f32_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f32_nnf]) ).
cnf(c32,plain,
( ~ p_5(X0,X1,X2,X3,X4,X5,X6)
| ~ q_4(X0,X1,X2,X3,X4,X5,X6)
| q_3(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f32_sk]) ).
cnf(hi31,axiom,
ifeq(q_4(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_5(X0,X1,X2,X3,X4,X5,X6),true,q_3(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c32]) ).
cnf(h2942,plain,
q_3(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi31,h2686,h2431]) ).
cnf(f6,axiom,
( ~ q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type11_6) ).
fof(f6_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( ~ q_4(X0,X1,X2,X3,X4,X5,X6)
| ~ q_3(X0,X1,X2,X3,X4,X5,X6)
| p_2(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(hi5,axiom,
ifeq(q_3(X0,X1,X2,X3,X4,X5,X6),true,ifeq(q_4(X0,X1,X2,X3,X4,X5,X6),true,p_2(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(h3199,plain,
p_2(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi5,h2942,h2686]) ).
cnf(f8,axiom,
( ~ q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type11_8) ).
fof(f8_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( ~ q_5(X0,X1,X2,X3,X4,X5,X6)
| ~ q_4(X0,X1,X2,X3,X4,X5,X6)
| p_3(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(hi7,axiom,
ifeq(q_4(X0,X1,X2,X3,X4,X5,X6),true,ifeq(q_5(X0,X1,X2,X3,X4,X5,X6),true,p_3(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h2943,plain,
p_3(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi7,h2686,h2430]) ).
cnf(f10,axiom,
( ~ q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type11_10) ).
fof(f10_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_6(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_5(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( ~ q_6(X0,X1,X2,X3,X4,X5,X6)
| ~ q_5(X0,X1,X2,X3,X4,X5,X6)
| p_4(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi9,axiom,
ifeq(q_5(X0,X1,X2,X3,X4,X5,X6),true,ifeq(q_6(X0,X1,X2,X3,X4,X5,X6),true,p_4(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
cnf(h2687,plain,
p_4(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi9,h2430,h2045]) ).
cnf(f30,axiom,
( ~ p_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_6) ).
fof(f30_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f30]) ).
fof(f30_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_4(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f30_nnf]) ).
cnf(c30,plain,
( ~ p_4(X0,X1,X2,X3,X4,X5,X6)
| ~ q_3(X0,X1,X2,X3,X4,X5,X6)
| q_2(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f30_sk]) ).
cnf(hi29,axiom,
ifeq(q_3(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_4(X0,X1,X2,X3,X4,X5,X6),true,q_2(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c30]) ).
cnf(h3198,plain,
q_2(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi29,h2942,h2687]) ).
cnf(f28,axiom,
( ~ p_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_1(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_4) ).
fof(f28_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_1(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_3(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_1(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c28,plain,
( ~ p_3(X0,X1,X2,X3,X4,X5,X6)
| ~ q_2(X0,X1,X2,X3,X4,X5,X6)
| q_1(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(hi27,axiom,
ifeq(q_2(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_3(X0,X1,X2,X3,X4,X5,X6),true,q_1(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c28]) ).
cnf(h3454,plain,
q_1(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi27,h3198,h2943]) ).
cnf(f26,axiom,
( ~ p_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_1(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_0(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type12_2) ).
fof(f26_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_1(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_0(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
fof(f26_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ p_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_1(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| q_0(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f26_nnf]) ).
cnf(c26,plain,
( ~ p_2(X0,X1,X2,X3,X4,X5,X6)
| ~ q_1(X0,X1,X2,X3,X4,X5,X6)
| q_0(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f26_sk]) ).
cnf(hi25,axiom,
ifeq(q_1(X0,X1,X2,X3,X4,X5,X6),true,ifeq(p_2(X0,X1,X2,X3,X4,X5,X6),true,q_0(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c26]) ).
cnf(h3710,plain,
q_0(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi25,h3454,h3199]) ).
cnf(f2,axiom,
( ~ q_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_1(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_0(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_type11_2) ).
fof(f2_nnf,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_1(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_0(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [X_1,X_2,X_3,X_4,X_5,X_6,X_7] :
( ~ q_2(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| ~ q_1(X_1,X_2,X_3,X_4,X_5,X_6,X_7)
| p_0(X_1,X_2,X_3,X_4,X_5,X_6,X_7) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( ~ q_2(X0,X1,X2,X3,X4,X5,X6)
| ~ q_1(X0,X1,X2,X3,X4,X5,X6)
| p_0(X0,X1,X2,X3,X4,X5,X6) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(hi1,axiom,
ifeq(q_1(X0,X1,X2,X3,X4,X5,X6),true,ifeq(q_2(X0,X1,X2,X3,X4,X5,X6),true,p_0(X0,X1,X2,X3,X4,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h3711,plain,
p_0(a,a,a,a,a,a,a) = true,
inference(hyper_resolution,[status(thm)],[hi1,h3454,h3198]) ).
cnf(f0,negated_conjecture,
( ~ q_0(a,a,a,a,a,a,a)
| ~ p_0(a,a,a,a,a,a,a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',n_s3_goal_1) ).
fof(f0_nnf,plain,
( ~ q_0(a,a,a,a,a,a,a)
| ~ p_0(a,a,a,a,a,a,a) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
( ~ q_0(a,a,a,a,a,a,a)
| ~ p_0(a,a,a,a,a,a,a) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ q_0(a,a,a,a,a,a,a)
| ~ p_0(a,a,a,a,a,a,a) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(hi70,negated_conjecture,
ifeq(p_0(a,a,a,a,a,a,a),true,ifeq(q_0(a,a,a,a,a,a,a),true,false,true),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t0,plain,
true = false,
inference(hyper_resolution,[status(thm)],[hi70,h3711,h3710]) ).
cnf(t1209,plain,
false = true,
inference(orient,[status(thm)],[t0]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1209]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYN102-1.007.007 : TPTP v9.3.1. Bugfixed v1.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n011.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Fri Sep 25 00:10:43 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 14.59/2.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 14.59/2.39 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------