%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO553+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n012.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 01:18:08 PM UTC 2026
% Result : Theorem 33.16s 5.15s
% Output : Proof 33.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 21
% Syntax : Number of formulae : 156 ( 58 unt; 0 def)
% Number of atoms : 318 ( 0 equ)
% Maximal formula atoms : 11 ( 2 avg)
% Number of connectives : 261 ( 99 ~; 95 |; 45 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 8 ( 8 usr; 8 con; 0-0 aty)
% Number of variables : 523 ( 21 sgn 322 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f74,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( perp(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> perp(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD74) ).
fof(f74_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f74]) ).
fof(f74_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( perp(A,B,C,D)
| ~ perp(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f74_nnf]) ).
cnf(c74,plain,
( perp(X0,X1,X2,X3)
| ~ perp(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f74_sk]) ).
fof(f42,axiom,
! [A,B,P,Q] :
( ( coll(P,Q,B)
& eqangle(P,A,P,B,Q,A,Q,B) )
=> cyclic(A,B,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD42b) ).
fof(f42_nnf,plain,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(nnf_transformation,[status(thm)],[f42]) ).
fof(f42_sk,plain,
! [P,A,B,Q] :
( cyclic(A,B,P,Q)
| ~ coll(P,Q,B)
| ~ eqangle(P,A,P,B,Q,A,Q,B) ),
inference(skolemisation,[status(esa)],[f42_nnf]) ).
cnf(c42,plain,
( cyclic(X0,X1,X2,X3)
| ~ coll(X2,X3,X1)
| ~ eqangle(X2,X0,X2,X1,X3,X0,X3,X1) ),
inference(cnf_transformation,[status(esa)],[f42_sk]) ).
fof(f18,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(C,D,A,B,U,V,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD19) ).
fof(f18_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(C,D,A,B,U,V,P,Q)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( eqangle(X2,X3,X0,X1,X6,X7,X4,X5)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
fof(f5,axiom,
! [A,B,C,D,E,F] :
( ( para(C,D,E,F)
& para(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD6) ).
fof(f5_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ para(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( para(X0,X1,X4,X5)
| ~ para(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,H] :
( ( coll(H,B,D)
& perp(H,C,B,D)
& coll(G,A,C)
& perp(G,D,A,C)
& coll(F,B,D)
& perp(F,A,B,D)
& coll(E,A,C)
& perp(E,B,A,C)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL012013) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H] :
( ( coll(H,B,D)
& perp(H,C,B,D)
& coll(G,A,C)
& perp(G,D,A,C)
& coll(F,B,D)
& perp(F,A,B,D)
& coll(E,A,C)
& perp(E,B,A,C)
& para(A,C,B,D)
& para(A,B,C,D) )
=> para(E,F,G,H) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,H] :
( ~ para(E,F,G,H)
& coll(H,B,D)
& perp(H,C,B,D)
& coll(G,A,C)
& perp(G,D,A,C)
& coll(F,B,D)
& perp(F,A,B,D)
& coll(E,A,C)
& perp(E,B,A,C)
& para(A,C,B,D)
& para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk24,sk25,sk26,sk27)
& coll(sk27,sk21,sk23)
& perp(sk27,sk22,sk21,sk23)
& coll(sk26,sk20,sk22)
& perp(sk26,sk23,sk20,sk22)
& coll(sk25,sk21,sk23)
& perp(sk25,sk20,sk21,sk23)
& coll(sk24,sk20,sk22)
& perp(sk24,sk21,sk20,sk22)
& para(sk20,sk22,sk21,sk23)
& para(sk20,sk21,sk22,sk23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27])],[f94_nnf]) ).
cnf(c113,plain,
para(sk20,sk21,sk22,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p429,plain,
( para(sk20,sk21,X0,X1)
| ~ para(sk22,sk23,X0,X1) ),
inference(resolution,[status(thm)],[c5,c113]) ).
fof(f4,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD5) ).
fof(f4_nnf,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A,B,C,D] :
( para(C,D,A,B)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( para(X2,X3,X0,X1)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p146,plain,
para(sk22,sk23,sk20,sk21),
inference(resolution,[status(thm)],[c4,c113]) ).
cnf(p445,plain,
para(sk20,sk21,sk20,sk21),
inference(resolution,[status(thm)],[p429,p146]) ).
fof(f39,axiom,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
=> eqangle(A,B,P,Q,C,D,P,Q) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD40) ).
fof(f39_nnf,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f39]) ).
fof(f39_sk,plain,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f39_nnf]) ).
cnf(c39,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f39_sk]) ).
cnf(p448,plain,
eqangle(sk20,sk21,X0,X1,sk20,sk21,X0,X1),
inference(resolution,[status(thm)],[p445,c39]) ).
cnf(p1641,plain,
eqangle(X0,X1,sk20,sk21,X0,X1,sk20,sk21),
inference(resolution,[status(thm)],[c18,p448]) ).
fof(f38,axiom,
! [A,B,C,D,P,Q] :
( eqangle(A,B,P,Q,C,D,P,Q)
=> para(A,B,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD39) ).
fof(f38_nnf,plain,
! [A,B,C,D,P,Q] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B,P,Q,C,D] :
( para(A,B,C,D)
| ~ eqangle(A,B,P,Q,C,D,P,Q) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c38,plain,
( para(X0,X1,X2,X3)
| ~ eqangle(X0,X1,X4,X5,X2,X3,X4,X5) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(p1737,plain,
para(X0,X1,X0,X1),
inference(resolution,[status(thm)],[p1641,c38]) ).
cnf(p1741,plain,
eqangle(X0,X1,X2,X3,X0,X1,X2,X3),
inference(resolution,[status(thm)],[p1737,c39]) ).
cnf(p2157,plain,
( cyclic(X2,X1,X0,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[c42,p1741]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD66) ).
fof(f66_nnf,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f66]) ).
fof(f66_sk,plain,
! [A,B,C] :
( coll(A,B,C)
| ~ para(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f66_nnf]) ).
cnf(c66,plain,
( coll(X0,X1,X2)
| ~ para(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f66_sk]) ).
cnf(p1739,plain,
coll(X0,X1,X1),
inference(resolution,[status(thm)],[p1737,c66]) ).
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD3) ).
fof(f2_nnf,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A,B,C,D] :
( coll(C,D,A)
| ~ coll(A,B,D)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( coll(X2,X3,X0)
| ~ coll(X0,X1,X3)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p186,plain,
( coll(X2,X2,X0)
| ~ coll(X0,X1,X2) ),
inference(factoring,[status(thm)],[c2]) ).
cnf(p1744,plain,
coll(X0,X0,X1),
inference(resolution,[status(thm)],[p1739,p186]) ).
cnf(p1745,plain,
( coll(X2,X1,X0)
| ~ coll(X0,X0,X1) ),
inference(resolution,[status(thm)],[p1744,c2]) ).
cnf(p1829,plain,
coll(X0,X1,X2),
inference(resolution,[status(thm)],[p1745,p1744]) ).
cnf(p2159,plain,
cyclic(X0,X1,X2,X2),
inference(resolution,[status(thm)],[p2157,p1829]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD15) ).
fof(f14_nnf,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
fof(f14_sk,plain,
! [A,B,C,D] :
( cyclic(A,C,B,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f14_nnf]) ).
cnf(c14,plain,
( cyclic(X0,X2,X1,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f14_sk]) ).
cnf(p2160,plain,
cyclic(X0,X1,X2,X1),
inference(resolution,[status(thm)],[p2159,c14]) ).
fof(f13,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD14) ).
fof(f13_nnf,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B,C,D] :
( cyclic(A,B,D,C)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( cyclic(X0,X1,X3,X2)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p2162,plain,
cyclic(X0,X1,X1,X2),
inference(resolution,[status(thm)],[p2160,c13]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD16) ).
fof(f15_nnf,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B,C,D] :
( cyclic(B,A,C,D)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( cyclic(X1,X0,X2,X3)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p2166,plain,
cyclic(X0,X1,X0,X2),
inference(resolution,[status(thm)],[p2162,c15]) ).
fof(f16,axiom,
! [A,B,C,D,E] :
( ( cyclic(A,B,C,E)
& cyclic(A,B,C,D) )
=> cyclic(B,C,D,E) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD17) ).
fof(f16_nnf,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B,C,D,E] :
( cyclic(B,C,D,E)
| ~ cyclic(A,B,C,E)
| ~ cyclic(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( cyclic(X1,X2,X3,X4)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p2173,plain,
( cyclic(X1,X0,X3,X2)
| ~ cyclic(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[p2166,c16]) ).
cnf(p2203,plain,
cyclic(X0,X1,X2,X3),
inference(resolution,[status(thm)],[p2173,p2166]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD41) ).
fof(f40_nnf,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(nnf_transformation,[status(thm)],[f40]) ).
fof(f40_sk,plain,
! [A,B,P,Q] :
( eqangle(P,A,P,B,Q,A,Q,B)
| ~ cyclic(A,B,P,Q) ),
inference(skolemisation,[status(esa)],[f40_nnf]) ).
cnf(c40,plain,
( eqangle(X2,X0,X2,X1,X3,X0,X3,X1)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f40_sk]) ).
cnf(p2204,plain,
eqangle(X0,X1,X0,X2,X3,X1,X3,X2),
inference(resolution,[status(thm)],[p2203,c40]) ).
cnf(p6981,plain,
( perp(X3,X1,X3,X2)
| ~ perp(X0,X1,X0,X2) ),
inference(resolution,[status(thm)],[c74,p2204]) ).
fof(f9,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& para(A,B,C,D) )
=> perp(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD10) ).
fof(f9_nnf,plain,
! [A,B,C,D,E,F] :
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A,B,C,D,E,F] :
( perp(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c9,plain,
( perp(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
cnf(c114,plain,
para(sk20,sk22,sk21,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p1375,plain,
( perp(sk20,sk22,X0,X1)
| ~ perp(sk21,sk23,X0,X1) ),
inference(resolution,[status(thm)],[c9,c114]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD8) ).
fof(f7_nnf,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
fof(f7_sk,plain,
! [A,B,C,D] :
( perp(C,D,A,B)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f7_nnf]) ).
cnf(c7,plain,
( perp(X2,X3,X0,X1)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f7_sk]) ).
cnf(c117,plain,
perp(sk25,sk20,sk21,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p163,plain,
perp(sk21,sk23,sk25,sk20),
inference(resolution,[status(thm)],[c7,c117]) ).
fof(f6,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD7) ).
fof(f6_nnf,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A,B,C,D] :
( perp(A,B,D,C)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( perp(X0,X1,X3,X2)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p171,plain,
perp(sk21,sk23,sk20,sk25),
inference(resolution,[status(thm)],[p163,c6]) ).
cnf(p1424,plain,
perp(sk20,sk22,sk20,sk25),
inference(resolution,[status(thm)],[p1375,p171]) ).
cnf(p8917,plain,
perp(X0,sk22,X0,sk25),
inference(resolution,[status(thm)],[p6981,p1424]) ).
fof(f8,axiom,
! [A,B,C,D,E,F] :
( ( perp(C,D,E,F)
& perp(A,B,C,D) )
=> para(A,B,E,F) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD9) ).
fof(f8_nnf,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A,B,C,D,E,F] :
( para(A,B,E,F)
| ~ perp(C,D,E,F)
| ~ perp(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( para(X0,X1,X4,X5)
| ~ perp(X2,X3,X4,X5)
| ~ perp(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p8927,plain,
( para(X0,sk22,X1,X2)
| ~ perp(X0,sk25,X1,X2) ),
inference(resolution,[status(thm)],[p8917,c8]) ).
cnf(p147,plain,
para(sk21,sk23,sk20,sk22),
inference(resolution,[status(thm)],[c4,c114]) ).
cnf(p1379,plain,
( perp(sk21,sk23,X0,X1)
| ~ perp(sk20,sk22,X0,X1) ),
inference(resolution,[status(thm)],[c9,p147]) ).
cnf(c115,plain,
perp(sk24,sk21,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p162,plain,
perp(sk20,sk22,sk24,sk21),
inference(resolution,[status(thm)],[c7,c115]) ).
cnf(p170,plain,
perp(sk20,sk22,sk21,sk24),
inference(resolution,[status(thm)],[p162,c6]) ).
cnf(p1588,plain,
perp(sk21,sk23,sk21,sk24),
inference(resolution,[status(thm)],[p1379,p170]) ).
cnf(p8921,plain,
perp(X0,sk23,X0,sk24),
inference(resolution,[status(thm)],[p6981,p1588]) ).
fof(f3,axiom,
! [A,B,C,D] :
( para(A,B,C,D)
=> para(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD4) ).
fof(f3_nnf,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A,B,C,D] :
( para(A,B,D,C)
| ~ para(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( para(X0,X1,X3,X2)
| ~ para(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p1740,plain,
para(X0,X1,X1,X0),
inference(resolution,[status(thm)],[p1737,c3]) ).
cnf(p1748,plain,
( perp(X1,X0,X2,X3)
| ~ perp(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[p1740,c9]) ).
cnf(p9006,plain,
perp(sk23,X0,X0,sk24),
inference(resolution,[status(thm)],[p8921,p1748]) ).
cnf(p12626,plain,
para(sk23,sk22,sk25,sk24),
inference(resolution,[status(thm)],[p8927,p9006]) ).
cnf(p12639,plain,
para(sk25,sk24,sk23,sk22),
inference(resolution,[status(thm)],[p12626,c4]) ).
cnf(p12697,plain,
( para(sk25,sk24,X0,X1)
| ~ para(sk23,sk22,X0,X1) ),
inference(resolution,[status(thm)],[p12639,c5]) ).
cnf(c121,plain,
perp(sk27,sk22,sk21,sk23),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p165,plain,
perp(sk21,sk23,sk27,sk22),
inference(resolution,[status(thm)],[c7,c121]) ).
cnf(p173,plain,
perp(sk21,sk23,sk22,sk27),
inference(resolution,[status(thm)],[p165,c6]) ).
cnf(p1425,plain,
perp(sk20,sk22,sk22,sk27),
inference(resolution,[status(thm)],[p1375,p173]) ).
cnf(p1444,plain,
perp(sk22,sk27,sk20,sk22),
inference(resolution,[status(thm)],[p1425,c7]) ).
cnf(p1506,plain,
perp(sk22,sk27,sk22,sk20),
inference(resolution,[status(thm)],[p1444,c6]) ).
cnf(p8919,plain,
perp(X0,sk27,X0,sk20),
inference(resolution,[status(thm)],[p6981,p1506]) ).
cnf(p8971,plain,
( para(X0,sk27,X1,X2)
| ~ perp(X0,sk20,X1,X2) ),
inference(resolution,[status(thm)],[p8919,c8]) ).
cnf(c119,plain,
perp(sk26,sk23,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p164,plain,
perp(sk20,sk22,sk26,sk23),
inference(resolution,[status(thm)],[c7,c119]) ).
cnf(p172,plain,
perp(sk20,sk22,sk23,sk26),
inference(resolution,[status(thm)],[p164,c6]) ).
cnf(p1589,plain,
perp(sk21,sk23,sk23,sk26),
inference(resolution,[status(thm)],[p1379,p172]) ).
cnf(p1596,plain,
perp(sk23,sk26,sk21,sk23),
inference(resolution,[status(thm)],[p1589,c7]) ).
cnf(p1606,plain,
perp(sk23,sk26,sk23,sk21),
inference(resolution,[status(thm)],[p1596,c6]) ).
cnf(p8923,plain,
perp(X0,sk26,X0,sk21),
inference(resolution,[status(thm)],[p6981,p1606]) ).
cnf(p144,plain,
para(sk20,sk21,sk23,sk22),
inference(resolution,[status(thm)],[c3,c113]) ).
cnf(p148,plain,
para(sk23,sk22,sk20,sk21),
inference(resolution,[status(thm)],[c4,p144]) ).
cnf(p417,plain,
eqangle(sk23,sk22,X0,X1,sk20,sk21,X0,X1),
inference(resolution,[status(thm)],[c39,p148]) ).
cnf(p1631,plain,
eqangle(X0,X1,sk23,sk22,X0,X1,sk20,sk21),
inference(resolution,[status(thm)],[c18,p417]) ).
fof(f17,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(B,A,C,D,P,Q,U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD18) ).
fof(f17_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(B,A,C,D,P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( eqangle(X1,X0,X2,X3,X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p1727,plain,
eqangle(X0,X1,sk23,sk22,X1,X0,sk20,sk21),
inference(resolution,[status(thm)],[p1631,c17]) ).
cnf(p6598,plain,
( perp(X1,X0,sk23,sk22)
| ~ perp(X0,X1,sk20,sk21) ),
inference(resolution,[status(thm)],[c74,p1727]) ).
cnf(p9042,plain,
perp(sk26,sk20,sk23,sk22),
inference(resolution,[status(thm)],[p8923,p6598]) ).
cnf(p19676,plain,
para(sk26,sk27,sk23,sk22),
inference(resolution,[status(thm)],[p8971,p9042]) ).
cnf(p19735,plain,
para(sk23,sk22,sk26,sk27),
inference(resolution,[status(thm)],[p19676,c4]) ).
cnf(p25905,plain,
para(sk25,sk24,sk26,sk27),
inference(resolution,[status(thm)],[p12697,p19735]) ).
cnf(p1747,plain,
( para(X1,X0,X2,X3)
| ~ para(X0,X1,X2,X3) ),
inference(resolution,[status(thm)],[p1740,c5]) ).
cnf(p25911,plain,
para(sk24,sk25,sk26,sk27),
inference(resolution,[status(thm)],[p25905,p1747]) ).
cnf(c123,plain,
~ para(sk24,sk25,sk26,sk27),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(p25925,plain,
$false,
inference(resolution,[status(thm)],[p25911,c123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO553+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.02 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Wed Sep 23 12:22:35 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 33.16/5.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 33.16/5.15 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------