%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO600+1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/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 01:18:15 PM UTC 2026
% Result : Theorem 70.09s 14.45s
% Output : Proof 70.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 11
% Syntax : Number of formulae : 91 ( 51 unt; 0 def)
% Number of atoms : 195 ( 48 equ)
% Maximal formula atoms : 15 ( 2 avg)
% Number of connectives : 146 ( 42 ~; 36 |; 57 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-8 aty)
% Number of functors : 25 ( 25 usr; 24 con; 0-4 aty)
% Number of variables : 399 ( 22 sgn 190 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B,C,D] :
( ( coll(A,B,D)
& coll(A,B,C) )
=> coll(C,D,A) ),
file('/export/starexec/sandbox2/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(t156,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(t260,plain,
ifeq(coll(X1,X2,X3),true,ifeq(coll(X1,X2,X4),true,coll(X3,X4,X1),true),true) = true,
inference(orient,[status(thm)],[t156]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD1) ).
fof(f0_nnf,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C] :
( coll(A,C,B)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( coll(X0,X2,X1)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(t106,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(t263,plain,
ifeq(coll(X1,X2,X3),true,coll(X1,X3,X2),true) = true,
inference(orient,[status(thm)],[t106]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD2) ).
fof(f1_nnf,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B,C] :
( coll(B,A,C)
| ~ coll(A,B,C) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( coll(X1,X0,X2)
| ~ coll(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(t107,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(t261,plain,
ifeq(coll(X1,X2,X3),true,coll(X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t107]) ).
fof(f66,axiom,
! [A,B,C] :
( para(A,B,A,C)
=> coll(A,B,C) ),
file('/export/starexec/sandbox2/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(t111,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t353,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t111]) ).
fof(f73,axiom,
! [A,B,C,D,P,Q,U,V] :
( ( para(P,Q,U,V)
& eqangle(A,B,C,D,P,Q,U,V) )
=> para(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD73) ).
fof(f73_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f73]) ).
fof(f73_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( para(A,B,C,D)
| ~ para(P,Q,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f73_nnf]) ).
cnf(c73,plain,
( para(X0,X1,X2,X3)
| ~ para(X4,X5,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f73_sk]) ).
cnf(t209,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c73]) ).
cnf(t305,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,ifeq(para(X5,X6,X7,X8),true,para(X1,X2,X3,X4),true),true) = true,
inference(orient,[status(thm)],[t209]) ).
fof(f20,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(A,B,P,Q,C,D,U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD21) ).
fof(f20_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,P,Q,C,D,U,V)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( eqangle(X0,X1,X4,X5,X2,X3,X6,X7)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(t180,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(t312,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X1,X2,X5,X6,X3,X4,X7,X8),true) = true,
inference(orient,[status(thm)],[t180]) ).
fof(f63,axiom,
! [A,B,C,D,M] :
( ( midp(M,C,D)
& midp(M,A,B) )
=> para(A,C,B,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD63) ).
fof(f63_nnf,plain,
! [A,B,C,D,M] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f63]) ).
fof(f63_sk,plain,
! [M,A,B,C,D] :
( para(A,C,B,D)
| ~ midp(M,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f63_nnf]) ).
cnf(c63,plain,
( para(X0,X2,X1,X3)
| ~ midp(X4,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f63_sk]) ).
cnf(hi63,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X0,X3,X4),true,para(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c63]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,H,I,J,K,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
( ( circle(J,B,K,NWPNT21)
& circle(F,E,K,NWPNT11)
& circle(J,B,NWPNT9,NWPNT01)
& midp(J,B,E)
& circle(G,E,I,NWPNT8)
& coll(I,A,B)
& circle(G,E,H,NWPNT7)
& circle(F,E,H,NWPNT6)
& circle(G,E,NWPNT4,NWPNT5)
& circle(F,E,NWPNT2,NWPNT3)
& midp(G,A,E)
& midp(F,C,E)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) )
=> coll(I,H,K) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL618062) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,I,J,K,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
( ( circle(J,B,K,NWPNT21)
& circle(F,E,K,NWPNT11)
& circle(J,B,NWPNT9,NWPNT01)
& midp(J,B,E)
& circle(G,E,I,NWPNT8)
& coll(I,A,B)
& circle(G,E,H,NWPNT7)
& circle(F,E,H,NWPNT6)
& circle(G,E,NWPNT4,NWPNT5)
& circle(F,E,NWPNT2,NWPNT3)
& midp(G,A,E)
& midp(F,C,E)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) )
=> coll(I,H,K) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,H,I,J,K,NWPNT1,NWPNT2,NWPNT3,NWPNT4,NWPNT5,NWPNT6,NWPNT7,NWPNT8,NWPNT9,NWPNT01,NWPNT11,NWPNT21] :
( ~ coll(I,H,K)
& circle(J,B,K,NWPNT21)
& circle(F,E,K,NWPNT11)
& circle(J,B,NWPNT9,NWPNT01)
& midp(J,B,E)
& circle(G,E,I,NWPNT8)
& coll(I,A,B)
& circle(G,E,H,NWPNT7)
& circle(F,E,H,NWPNT6)
& circle(G,E,NWPNT4,NWPNT5)
& circle(F,E,NWPNT2,NWPNT3)
& midp(G,A,E)
& midp(F,C,E)
& circle(D,A,E,NWPNT1)
& circle(D,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ coll(sk28,sk27,sk30)
& circle(sk29,sk21,sk30,sk42)
& circle(sk25,sk24,sk30,sk41)
& circle(sk29,sk21,sk39,sk40)
& midp(sk29,sk21,sk24)
& circle(sk26,sk24,sk28,sk38)
& coll(sk28,sk20,sk21)
& circle(sk26,sk24,sk27,sk37)
& circle(sk25,sk24,sk27,sk36)
& circle(sk26,sk24,sk34,sk35)
& circle(sk25,sk24,sk32,sk33)
& midp(sk26,sk20,sk24)
& midp(sk25,sk22,sk24)
& circle(sk23,sk20,sk24,sk31)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31,sk32,sk33,sk34,sk35,sk36,sk37,sk38,sk39,sk40,sk41,sk42])],[f94_nnf]) ).
cnf(c115,plain,
midp(sk25,sk22,sk24),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
midp(sk25,sk22,sk24) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h8,plain,
para(sk22,sk22,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi63,hi115,hi115]) ).
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/sandbox2/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(hi39,axiom,
ifeq(para(X0,X1,X2,X3),true,eqangle(X0,X1,X4,X5,X2,X3,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(h159,plain,
eqangle(sk22,sk22,V0,V1,sk24,sk24,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h8]) ).
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/sandbox2/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]) ).
cnf(hi18,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X2,X3,X0,X1,X6,X7,X4,X5),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t53,plain,
eqangle(X1,X2,sk22,sk22,X1,X2,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi18,h159]) ).
cnf(t1814,plain,
eqangle(X1,X2,sk22,sk22,X1,X2,sk24,sk24) = true,
inference(orient,[status(thm)],[t53]) ).
cnf(t1815,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk22,sk22,sk24,sk24),true),
inference(cp,[status(thm)],[t312,t1814]) ).
cnf(t47,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t47]) ).
cnf(t5994,plain,
true = eqangle(X1,X2,X1,X2,sk22,sk22,sk24,sk24),
inference(step,[status(thm)],[t1815,t256]) ).
cnf(t5712,plain,
eqangle(X1,X2,X1,X2,sk22,sk22,sk24,sk24) = true,
inference(orient,[status(thm)],[t5994]) ).
cnf(t5717,plain,
true = ifeq(true,true,ifeq(para(sk22,sk22,sk24,sk24),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t305,t5712]) ).
cnf(t5995,plain,
true = ifeq(para(sk22,sk22,sk24,sk24),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t5717,t256]) ).
cnf(t49,plain,
para(sk22,sk22,sk24,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi63,hi115,hi115]) ).
cnf(t2528,plain,
para(sk22,sk22,sk24,sk24) = true,
inference(orient,[status(thm)],[t49]) ).
cnf(t5996,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t5995,t2528]) ).
cnf(t5997,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t5996,t256]) ).
cnf(t5723,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t5997]) ).
cnf(t5724,plain,
true = ifeq(true,true,coll(X1,X2,X2),true),
inference(cp,[status(thm)],[t353,t5723]) ).
cnf(t5998,plain,
true = coll(X1,X2,X2),
inference(step,[status(thm)],[t5724,t256]) ).
cnf(t5750,plain,
coll(X1,X2,X2) = true,
inference(orient,[status(thm)],[t5998]) ).
cnf(t5752,plain,
true = ifeq(true,true,coll(X1,X2,X1),true),
inference(cp,[status(thm)],[t261,t5750]) ).
cnf(t5999,plain,
true = coll(X1,X2,X1),
inference(step,[status(thm)],[t5752,t256]) ).
cnf(t5793,plain,
coll(X1,X2,X1) = true,
inference(orient,[status(thm)],[t5999]) ).
cnf(t5796,plain,
true = ifeq(true,true,coll(X1,X1,X2),true),
inference(cp,[status(thm)],[t263,t5793]) ).
cnf(t6000,plain,
true = coll(X1,X1,X2),
inference(step,[status(thm)],[t5796,t256]) ).
cnf(t5825,plain,
coll(X1,X1,X2) = true,
inference(orient,[status(thm)],[t6000]) ).
cnf(t5828,plain,
true = ifeq(true,true,ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),true),
inference(cp,[status(thm)],[t260,t5825]) ).
cnf(t6001,plain,
true = ifeq(coll(X1,X1,X2),true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t5828,t256]) ).
cnf(t6002,plain,
true = ifeq(true,true,coll(X3,X2,X1),true),
inference(step,[status(thm)],[t6001,t5825]) ).
cnf(t6003,plain,
true = coll(X3,X2,X1),
inference(step,[status(thm)],[t6002,t256]) ).
cnf(t5860,plain,
coll(X1,X2,X3) = true,
inference(orient,[status(thm)],[t6003]) ).
cnf(c127,plain,
~ coll(sk28,sk27,sk30),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
coll(sk28,sk27,sk30) != true,
inference(equality_encoding,[status(esa)],[c127]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t5860]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO600+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/5.38 % Computer : n005.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Wed Sep 23 12:30:38 UTC 2026
% 0.10/5.38 % CPUTime :
% 0.10/5.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 70.09/14.45 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 70.09/14.45 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
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