%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO621+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 : n004.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 01:18:19 PM UTC 2026
% Result : Theorem 171.85s 22.15s
% Output : Proof 171.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 72
% Number of leaves : 22
% Syntax : Number of formulae : 257 ( 173 unt; 0 def)
% Number of atoms : 427 ( 169 equ)
% Maximal formula atoms : 9 ( 1 avg)
% Number of connectives : 275 ( 105 ~; 99 |; 49 &)
% ( 0 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 12 ( 12 usr; 10 con; 0-6 aty)
% Number of variables : 785 ( 78 sgn 321 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f12,axiom,
! [A,B,C,D,O] :
( ( cong(O,A,O,D)
& cong(O,A,O,C)
& cong(O,A,O,B) )
=> cyclic(A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD13) ).
fof(f12_nnf,plain,
! [A,B,C,D,O] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(nnf_transformation,[status(thm)],[f12]) ).
fof(f12_sk,plain,
! [O,A,B,C,D] :
( cyclic(A,B,C,D)
| ~ cong(O,A,O,D)
| ~ cong(O,A,O,C)
| ~ cong(O,A,O,B) ),
inference(skolemisation,[status(esa)],[f12_nnf]) ).
cnf(c12,plain,
( cyclic(X0,X1,X2,X3)
| ~ cong(X4,X0,X4,X3)
| ~ cong(X4,X0,X4,X2)
| ~ cong(X4,X0,X4,X1) ),
inference(cnf_transformation,[status(esa)],[f12_sk]) ).
cnf(t234,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t273,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(cong(X1,X2,X1,X4),true,ifeq(cong(X1,X2,X1,X5),true,cyclic(X2,X3,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t234]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD68) ).
fof(f68_nnf,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(nnf_transformation,[status(thm)],[f68]) ).
fof(f68_sk,plain,
! [A,B,C] :
( cong(A,B,A,C)
| ~ midp(A,B,C) ),
inference(skolemisation,[status(esa)],[f68_nnf]) ).
cnf(c68,plain,
( cong(X0,X1,X0,X2)
| ~ midp(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f68_sk]) ).
cnf(t122,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t336,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t122]) ).
fof(f64,axiom,
! [A,B,C,D,M] :
( ( para(A,D,B,C)
& para(A,C,B,D)
& midp(M,A,B) )
=> midp(M,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD64) ).
fof(f64_nnf,plain,
! [A,B,C,D,M] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f64]) ).
fof(f64_sk,plain,
! [M,A,B,C,D] :
( midp(M,C,D)
| ~ para(A,D,B,C)
| ~ para(A,C,B,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa)],[f64_nnf]) ).
cnf(c64,plain,
( midp(X4,X2,X3)
| ~ para(X0,X3,X1,X2)
| ~ para(X0,X2,X1,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f64_sk]) ).
cnf(t226,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c64]) ).
cnf(t333,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X4,X3,X5),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(orient,[status(thm)],[t226]) ).
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/sandbox2/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(t189,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(t285,plain,
ifeq(perp(X1,X2,X3,X4),true,ifeq(perp(X3,X4,X5,X6),true,para(X1,X2,X5,X6),true),true) = true,
inference(orient,[status(thm)],[t189]) ).
fof(f7,axiom,
! [A,B,C,D] :
( perp(A,B,C,D)
=> perp(C,D,A,B) ),
file('/export/starexec/sandbox2/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(t132,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t292,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t132]) ).
fof(f56,axiom,
! [A,B,P,Q] :
( ( cong(A,Q,B,Q)
& cong(A,P,B,P) )
=> perp(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD56) ).
fof(f56_nnf,plain,
! [A,B,P,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(nnf_transformation,[status(thm)],[f56]) ).
fof(f56_sk,plain,
! [A,P,B,Q] :
( perp(A,B,P,Q)
| ~ cong(A,Q,B,Q)
| ~ cong(A,P,B,P) ),
inference(skolemisation,[status(esa)],[f56_nnf]) ).
cnf(c56,plain,
( perp(X0,X1,X2,X3)
| ~ cong(X0,X3,X1,X3)
| ~ cong(X0,X2,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f56_sk]) ).
cnf(t176,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(equality_encoding,[status(esa)],[c56]) ).
cnf(t271,plain,
ifeq(cong(X1,X2,X3,X2),true,ifeq(cong(X1,X4,X3,X4),true,perp(X1,X3,X2,X4),true),true) = true,
inference(orient,[status(thm)],[t176]) ).
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(t208,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)],[t208]) ).
fof(f19,axiom,
! [A,B,C,D,P,Q,U,V] :
( eqangle(A,B,C,D,P,Q,U,V)
=> eqangle(P,Q,U,V,A,B,C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD20) ).
fof(f19_nnf,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B,C,D,P,Q,U,V] :
( eqangle(P,Q,U,V,A,B,C,D)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( eqangle(X4,X5,X6,X7,X0,X1,X2,X3)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(t182,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c19]) ).
cnf(t306,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X5,X6,X7,X8,X1,X2,X3,X4),true) = true,
inference(orient,[status(thm)],[t182]) ).
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(t179,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)],[t179]) ).
fof(f10,axiom,
! [A,B,M] :
( midp(M,B,A)
=> midp(M,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD11) ).
fof(f10_nnf,plain,
! [A,B,M] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [M,B,A] :
( midp(M,A,B)
| ~ midp(M,B,A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( midp(X2,X0,X1)
| ~ midp(X2,X1,X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(hi10,axiom,
ifeq(midp(X0,X1,X2),true,midp(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c10]) ).
fof(f94,conjecture,
! [A,B,C,D,E,F,G,H,I] :
( ( coll(I,A,C)
& coll(I,E,H)
& coll(H,A,B)
& perp(E,G,E,H)
& circle(G,D,E,F)
& midp(F,A,C)
& midp(E,C,B)
& midp(D,B,A) )
=> cyclic(B,H,C,I) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exemplo6GDDFULL8110984) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,D,E,F,G,H,I] :
( ( coll(I,A,C)
& coll(I,E,H)
& coll(H,A,B)
& perp(E,G,E,H)
& circle(G,D,E,F)
& midp(F,A,C)
& midp(E,C,B)
& midp(D,B,A) )
=> cyclic(B,H,C,I) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,D,E,F,G,H,I] :
( ~ cyclic(B,H,C,I)
& coll(I,A,C)
& coll(I,E,H)
& coll(H,A,B)
& perp(E,G,E,H)
& circle(G,D,E,F)
& midp(F,A,C)
& midp(E,C,B)
& midp(D,B,A) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ cyclic(sk21,sk27,sk22,sk28)
& coll(sk28,sk20,sk22)
& coll(sk28,sk24,sk27)
& coll(sk27,sk20,sk21)
& perp(sk24,sk26,sk24,sk27)
& circle(sk26,sk23,sk24,sk25)
& midp(sk25,sk20,sk22)
& midp(sk24,sk22,sk21)
& midp(sk23,sk21,sk20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28])],[f94_nnf]) ).
cnf(c114,plain,
midp(sk24,sk22,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi114,negated_conjecture,
midp(sk24,sk22,sk21) = true,
inference(equality_encoding,[status(esa)],[c114]) ).
cnf(h25,plain,
midp(sk24,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi10,hi114]) ).
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]) ).
cnf(h219,plain,
para(sk21,sk21,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi63,h25,h25]) ).
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(t65,plain,
eqangle(sk21,sk21,X1,X2,sk22,sk22,X1,X2) = true,
inference(hyper_resolution,[status(thm)],[hi39,h219]) ).
cnf(t1961,plain,
eqangle(sk21,sk21,X1,X2,sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t65]) ).
cnf(t1964,plain,
true = ifeq(true,true,eqangle(sk21,sk21,sk22,sk22,X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t312,t1961]) ).
cnf(t45,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t45]) ).
cnf(t30949,plain,
true = eqangle(sk21,sk21,sk22,sk22,X1,X2,X1,X2),
inference(step,[status(thm)],[t1964,t256]) ).
cnf(t9014,plain,
eqangle(sk21,sk21,sk22,sk22,X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t30949]) ).
cnf(t9017,plain,
true = ifeq(true,true,eqangle(X1,X2,X1,X2,sk21,sk21,sk22,sk22),true),
inference(cp,[status(thm)],[t306,t9014]) ).
cnf(t31159,plain,
true = eqangle(X1,X2,X1,X2,sk21,sk21,sk22,sk22),
inference(step,[status(thm)],[t9017,t256]) ).
cnf(t11860,plain,
eqangle(X1,X2,X1,X2,sk21,sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t31159]) ).
cnf(t11865,plain,
true = ifeq(true,true,ifeq(para(sk21,sk21,sk22,sk22),true,para(X1,X2,X1,X2),true),true),
inference(cp,[status(thm)],[t305,t11860]) ).
cnf(t31160,plain,
true = ifeq(para(sk21,sk21,sk22,sk22),true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t11865,t256]) ).
cnf(t46,plain,
para(sk21,sk21,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi63,h25,h25]) ).
cnf(t2710,plain,
para(sk21,sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t46]) ).
cnf(t31161,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(step,[status(thm)],[t31160,t2710]) ).
cnf(t31162,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t31161,t256]) ).
cnf(t11870,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t31162]) ).
cnf(t11887,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),true),
inference(cp,[status(thm)],[t333,t11870]) ).
cnf(t32879,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(para(X2,X3,X2,X3),true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t11887,t256]) ).
cnf(t32880,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t32879,t11870]) ).
cnf(t32881,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t32880,t256]) ).
cnf(t27671,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t32881]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD67) ).
fof(f67_nnf,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(nnf_transformation,[status(thm)],[f67]) ).
fof(f67_sk,plain,
! [A,B,C] :
( midp(A,B,C)
| ~ coll(A,B,C)
| ~ cong(A,B,A,C) ),
inference(skolemisation,[status(esa)],[f67_nnf]) ).
cnf(c67,plain,
( midp(X0,X1,X2)
| ~ coll(X0,X1,X2)
| ~ cong(X0,X1,X0,X2) ),
inference(cnf_transformation,[status(esa)],[f67_sk]) ).
cnf(t167,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c67]) ).
cnf(t272,plain,
ifeq(cong(X1,X2,X1,X3),true,ifeq(coll(X1,X2,X3),true,midp(X1,X2,X3),true),true) = true,
inference(orient,[status(thm)],[t167]) ).
fof(f43,axiom,
! [A,B,C,P,Q,R] :
( ( eqangle(C,A,C,B,R,P,R,Q)
& cyclic(A,B,C,R)
& cyclic(A,B,C,Q)
& cyclic(A,B,C,P) )
=> cong(A,B,P,Q) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleD43) ).
fof(f43_nnf,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(nnf_transformation,[status(thm)],[f43]) ).
fof(f43_sk,plain,
! [A,B,C,P,Q,R] :
( cong(A,B,P,Q)
| ~ eqangle(C,A,C,B,R,P,R,Q)
| ~ cyclic(A,B,C,R)
| ~ cyclic(A,B,C,Q)
| ~ cyclic(A,B,C,P) ),
inference(skolemisation,[status(esa)],[f43_nnf]) ).
cnf(c43,plain,
( cong(X0,X1,X3,X4)
| ~ eqangle(X2,X0,X2,X1,X5,X3,X5,X4)
| ~ cyclic(X0,X1,X2,X5)
| ~ cyclic(X0,X1,X2,X4)
| ~ cyclic(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f43_sk]) ).
cnf(t253,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t357,plain,
ifeq(cyclic(X1,X2,X3,X4),true,ifeq(cyclic(X1,X2,X3,X5),true,ifeq(cyclic(X1,X2,X3,X6),true,ifeq(eqangle(X3,X1,X3,X2,X6,X4,X6,X5),true,cong(X1,X2,X4,X5),true),true),true),true) = true,
inference(orient,[status(thm)],[t253]) ).
fof(f40,axiom,
! [A,B,P,Q] :
( cyclic(A,B,P,Q)
=> eqangle(P,A,P,B,Q,A,Q,B) ),
file('/export/starexec/sandbox2/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(t159,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(equality_encoding,[status(esa)],[c40]) ).
cnf(t359,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t159]) ).
fof(f14,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(A,C,B,D) ),
file('/export/starexec/sandbox2/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(t127,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t362,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t127]) ).
fof(f15,axiom,
! [A,B,C,D] :
( cyclic(A,B,C,D)
=> cyclic(B,A,C,D) ),
file('/export/starexec/sandbox2/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(t128,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t360,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t128]) ).
cnf(hi68,axiom,
ifeq(midp(X0,X1,X2),true,cong(X0,X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(h218,plain,
cong(sk24,sk21,sk24,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi68,h25]) ).
cnf(hi12,axiom,
ifeq(cong(X0,X1,X0,X2),true,ifeq(cong(X0,X1,X0,X3),true,ifeq(cong(X0,X1,X0,X4),true,cyclic(X1,X2,X3,X4),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c12]) ).
cnf(t41,plain,
cyclic(sk21,sk22,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi12,h218,h218,h218]) ).
cnf(t3097,plain,
cyclic(sk21,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t41]) ).
cnf(t3098,plain,
true = ifeq(true,true,cyclic(sk22,sk21,sk22,sk22),true),
inference(cp,[status(thm)],[t360,t3097]) ).
cnf(t30789,plain,
true = cyclic(sk22,sk21,sk22,sk22),
inference(step,[status(thm)],[t3098,t256]) ).
cnf(t5438,plain,
cyclic(sk22,sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t30789]) ).
cnf(t5439,plain,
true = ifeq(true,true,cyclic(sk22,sk22,sk21,sk22),true),
inference(cp,[status(thm)],[t362,t5438]) ).
cnf(t30803,plain,
true = cyclic(sk22,sk22,sk21,sk22),
inference(step,[status(thm)],[t5439,t256]) ).
cnf(t5721,plain,
cyclic(sk22,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t30803]) ).
cnf(t5724,plain,
true = ifeq(true,true,eqangle(sk21,sk22,sk21,sk22,sk22,sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t359,t5721]) ).
cnf(t31124,plain,
true = eqangle(sk21,sk22,sk21,sk22,sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t5724,t256]) ).
cnf(t11431,plain,
eqangle(sk21,sk22,sk21,sk22,sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t31124]) ).
cnf(t11441,plain,
true = ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),true),
inference(cp,[status(thm)],[t357,t11431]) ).
cnf(t31125,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),true),
inference(step,[status(thm)],[t11441,t5721]) ).
cnf(t31126,plain,
true = ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),
inference(step,[status(thm)],[t31125,t256]) ).
cnf(t31127,plain,
true = ifeq(true,true,ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),true),
inference(step,[status(thm)],[t31126,t5721]) ).
cnf(t31128,plain,
true = ifeq(cyclic(sk22,sk22,sk21,sk22),true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),
inference(step,[status(thm)],[t31127,t256]) ).
cnf(t31129,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),true),
inference(step,[status(thm)],[t31128,t5721]) ).
cnf(t31130,plain,
true = ifeq(true,true,cong(sk22,sk22,sk22,sk22),true),
inference(step,[status(thm)],[t31129,t256]) ).
cnf(t31131,plain,
true = cong(sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t31130,t256]) ).
cnf(t11442,plain,
cong(sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t31131]) ).
cnf(t11452,plain,
true = ifeq(true,true,ifeq(coll(sk22,sk22,sk22),true,midp(sk22,sk22,sk22),true),true),
inference(cp,[status(thm)],[t272,t11442]) ).
cnf(t31132,plain,
true = ifeq(coll(sk22,sk22,sk22),true,midp(sk22,sk22,sk22),true),
inference(step,[status(thm)],[t11452,t256]) ).
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(t123,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)],[t123]) ).
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/sandbox2/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(t160,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c38]) ).
cnf(t314,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t160]) ).
cnf(t5441,plain,
true = ifeq(true,true,eqangle(sk22,sk22,sk22,sk21,sk22,sk22,sk22,sk21),true),
inference(cp,[status(thm)],[t359,t5438]) ).
cnf(t31096,plain,
true = eqangle(sk22,sk22,sk22,sk21,sk22,sk22,sk22,sk21),
inference(step,[status(thm)],[t5441,t256]) ).
cnf(t11131,plain,
eqangle(sk22,sk22,sk22,sk21,sk22,sk22,sk22,sk21) = true,
inference(orient,[status(thm)],[t31096]) ).
cnf(t11133,plain,
true = ifeq(true,true,para(sk22,sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t314,t11131]) ).
cnf(t31097,plain,
true = para(sk22,sk22,sk22,sk22),
inference(step,[status(thm)],[t11133,t256]) ).
cnf(t11145,plain,
para(sk22,sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t31097]) ).
cnf(t11146,plain,
true = ifeq(true,true,coll(sk22,sk22,sk22),true),
inference(cp,[status(thm)],[t353,t11145]) ).
cnf(t31098,plain,
true = coll(sk22,sk22,sk22),
inference(step,[status(thm)],[t11146,t256]) ).
cnf(t11165,plain,
coll(sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t31098]) ).
cnf(t31133,plain,
true = ifeq(true,true,midp(sk22,sk22,sk22),true),
inference(step,[status(thm)],[t31132,t11165]) ).
cnf(t31134,plain,
true = midp(sk22,sk22,sk22),
inference(step,[status(thm)],[t31133,t256]) ).
cnf(t11480,plain,
midp(sk22,sk22,sk22) = true,
inference(orient,[status(thm)],[t31134]) ).
cnf(t27672,plain,
true = ifeq(true,true,midp(sk22,X1,X1),true),
inference(cp,[status(thm)],[t27671,t11480]) ).
cnf(t32882,plain,
true = midp(sk22,X1,X1),
inference(step,[status(thm)],[t27672,t256]) ).
cnf(t27678,plain,
midp(sk22,X1,X1) = true,
inference(orient,[status(thm)],[t32882]) ).
cnf(t27679,plain,
true = ifeq(true,true,cong(sk22,X1,sk22,X1),true),
inference(cp,[status(thm)],[t336,t27678]) ).
cnf(t32885,plain,
true = cong(sk22,X1,sk22,X1),
inference(step,[status(thm)],[t27679,t256]) ).
cnf(t27738,plain,
cong(sk22,X1,sk22,X1) = true,
inference(orient,[status(thm)],[t32885]) ).
cnf(t27753,plain,
true = ifeq(true,true,ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),true),
inference(cp,[status(thm)],[t271,t27738]) ).
cnf(t32889,plain,
true = ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t27753,t256]) ).
cnf(t32890,plain,
true = ifeq(true,true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t32889,t27738]) ).
cnf(t32891,plain,
true = perp(sk22,sk22,X2,X1),
inference(step,[status(thm)],[t32890,t256]) ).
cnf(t27872,plain,
perp(sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t32891]) ).
cnf(t27873,plain,
true = ifeq(true,true,perp(X1,X2,sk22,sk22),true),
inference(cp,[status(thm)],[t292,t27872]) ).
cnf(t32902,plain,
true = perp(X1,X2,sk22,sk22),
inference(step,[status(thm)],[t27873,t256]) ).
cnf(t28055,plain,
perp(X1,X2,sk22,sk22) = true,
inference(orient,[status(thm)],[t32902]) ).
cnf(t28062,plain,
true = ifeq(true,true,ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t285,t28055]) ).
cnf(t32908,plain,
true = ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t28062,t256]) ).
cnf(t32909,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t32908,t27872]) ).
cnf(t32910,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t32909,t256]) ).
cnf(t28215,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t32910]) ).
cnf(t32922,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true),true) = true,
inference(step,[status(thm)],[t333,t28215]) ).
cnf(t32923,plain,
ifeq(midp(X1,X2,X3),true,ifeq(para(X2,X5,X3,X4),true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t32922,t256]) ).
cnf(t32924,plain,
ifeq(midp(X1,X2,X3),true,ifeq(true,true,midp(X1,X4,X5),true),true) = true,
inference(step,[status(thm)],[t32923,t28215]) ).
cnf(t32925,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(step,[status(thm)],[t32924,t256]) ).
cnf(t28222,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(rw,[status(thm)],[t32925]) ).
cnf(t30392,plain,
ifeq(midp(X1,X2,X3),true,midp(X1,X4,X5),true) = true,
inference(orient,[status(thm)],[t28222]) ).
fof(f81,axiom,
! [A,B,C,D,M,N] :
? [P] :
( ( midp(N,C,D)
& midp(M,A,B) )
=> ( para(P,N,A,C)
& para(P,M,B,D)
& midp(P,A,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ruleX6) ).
fof(f81_nnf,plain,
! [A,B,C,D,M,N] :
? [P] :
( ( para(P,N,A,C)
& para(P,M,B,D)
& midp(P,A,D) )
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(nnf_transformation,[status(thm)],[f81]) ).
fof(f81_sk,plain,
! [M,A,B,N,C,D] :
( ( para(sk5(A,B,C,D,M,N),N,A,C)
& para(sk5(A,B,C,D,M,N),M,B,D)
& midp(sk5(A,B,C,D,M,N),A,D) )
| ~ midp(N,C,D)
| ~ midp(M,A,B) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f81_nnf]) ).
cnf(c86,plain,
( midp(sk5(X0,X1,X2,X3,X4,X5),X0,X3)
| ~ midp(X5,X2,X3)
| ~ midp(X4,X0,X1) ),
inference(cnf_transformation,[status(esa)],[f81_sk]) ).
cnf(hi86,axiom,
ifeq(midp(X0,X1,X2),true,ifeq(midp(X3,X4,X5),true,midp(sk5(X1,X2,X4,X5,X0,X3),X1,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c86]) ).
cnf(c113,plain,
midp(sk23,sk21,sk20),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi113,negated_conjecture,
midp(sk23,sk21,sk20) = true,
inference(equality_encoding,[status(esa)],[c113]) ).
cnf(h16,plain,
midp(sk5(sk21,sk20,sk22,sk21,sk23,sk24),sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi86,hi113,hi114]) ).
cnf(h353,plain,
cong(sk5(sk21,sk20,sk22,sk21,sk23,sk24),sk21,sk5(sk21,sk20,sk22,sk21,sk23,sk24),sk21) = true,
inference(hyper_resolution,[status(thm)],[hi68,h16]) ).
cnf(t40,plain,
cyclic(sk21,sk21,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi12,h353,h353,h353]) ).
cnf(t3086,plain,
cyclic(sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t40]) ).
cnf(t3087,plain,
true = ifeq(true,true,eqangle(sk21,sk21,sk21,sk21,sk21,sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t359,t3086]) ).
cnf(t30973,plain,
true = eqangle(sk21,sk21,sk21,sk21,sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t3087,t256]) ).
cnf(t9301,plain,
eqangle(sk21,sk21,sk21,sk21,sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t30973]) ).
cnf(t9323,plain,
true = ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),true),
inference(cp,[status(thm)],[t357,t9301]) ).
cnf(t30976,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),true),
inference(step,[status(thm)],[t9323,t3086]) ).
cnf(t30977,plain,
true = ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),
inference(step,[status(thm)],[t30976,t256]) ).
cnf(t30978,plain,
true = ifeq(true,true,ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),true),
inference(step,[status(thm)],[t30977,t3086]) ).
cnf(t30979,plain,
true = ifeq(cyclic(sk21,sk21,sk21,sk21),true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),
inference(step,[status(thm)],[t30978,t256]) ).
cnf(t30980,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),true),
inference(step,[status(thm)],[t30979,t3086]) ).
cnf(t30981,plain,
true = ifeq(true,true,cong(sk21,sk21,sk21,sk21),true),
inference(step,[status(thm)],[t30980,t256]) ).
cnf(t30982,plain,
true = cong(sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t30981,t256]) ).
cnf(t9370,plain,
cong(sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t30982]) ).
cnf(t9380,plain,
true = ifeq(true,true,ifeq(coll(sk21,sk21,sk21),true,midp(sk21,sk21,sk21),true),true),
inference(cp,[status(thm)],[t272,t9370]) ).
cnf(t30983,plain,
true = ifeq(coll(sk21,sk21,sk21),true,midp(sk21,sk21,sk21),true),
inference(step,[status(thm)],[t9380,t256]) ).
cnf(t9303,plain,
true = ifeq(true,true,para(sk21,sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t314,t9301]) ).
cnf(t30974,plain,
true = para(sk21,sk21,sk21,sk21),
inference(step,[status(thm)],[t9303,t256]) ).
cnf(t9324,plain,
para(sk21,sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t30974]) ).
cnf(t9325,plain,
true = ifeq(true,true,coll(sk21,sk21,sk21),true),
inference(cp,[status(thm)],[t353,t9324]) ).
cnf(t30975,plain,
true = coll(sk21,sk21,sk21),
inference(step,[status(thm)],[t9325,t256]) ).
cnf(t9344,plain,
coll(sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t30975]) ).
cnf(t30984,plain,
true = ifeq(true,true,midp(sk21,sk21,sk21),true),
inference(step,[status(thm)],[t30983,t9344]) ).
cnf(t30985,plain,
true = midp(sk21,sk21,sk21),
inference(step,[status(thm)],[t30984,t256]) ).
cnf(t9408,plain,
midp(sk21,sk21,sk21) = true,
inference(orient,[status(thm)],[t30985]) ).
cnf(t27674,plain,
true = ifeq(true,true,midp(sk21,X1,X1),true),
inference(cp,[status(thm)],[t27671,t9408]) ).
cnf(t32884,plain,
true = midp(sk21,X1,X1),
inference(step,[status(thm)],[t27674,t256]) ).
cnf(t27718,plain,
midp(sk21,X1,X1) = true,
inference(orient,[status(thm)],[t32884]) ).
cnf(t30396,plain,
true = ifeq(true,true,midp(sk21,X1,X2),true),
inference(cp,[status(thm)],[t30392,t27718]) ).
cnf(t33095,plain,
true = midp(sk21,X1,X2),
inference(step,[status(thm)],[t30396,t256]) ).
cnf(t30425,plain,
midp(sk21,X1,X2) = true,
inference(orient,[status(thm)],[t33095]) ).
cnf(t30426,plain,
true = ifeq(true,true,cong(sk21,X1,sk21,X2),true),
inference(cp,[status(thm)],[t336,t30425]) ).
cnf(t33101,plain,
true = cong(sk21,X1,sk21,X2),
inference(step,[status(thm)],[t30426,t256]) ).
cnf(t30483,plain,
cong(sk21,X1,sk21,X2) = true,
inference(orient,[status(thm)],[t33101]) ).
cnf(t30503,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X2),true,ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),true),true),
inference(cp,[status(thm)],[t273,t30483]) ).
cnf(t33127,plain,
true = ifeq(cong(sk21,X1,sk21,X2),true,ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),true),
inference(step,[status(thm)],[t30503,t256]) ).
cnf(t33128,plain,
true = ifeq(true,true,ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),true),
inference(step,[status(thm)],[t33127,t30483]) ).
cnf(t33129,plain,
true = ifeq(cong(sk21,X1,sk21,X3),true,cyclic(X1,X4,X2,X3),true),
inference(step,[status(thm)],[t33128,t256]) ).
cnf(t33130,plain,
true = ifeq(true,true,cyclic(X1,X4,X2,X3),true),
inference(step,[status(thm)],[t33129,t30483]) ).
cnf(t33131,plain,
true = cyclic(X1,X4,X2,X3),
inference(step,[status(thm)],[t33130,t256]) ).
cnf(t30721,plain,
cyclic(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t33131]) ).
cnf(c121,plain,
~ cyclic(sk21,sk27,sk22,sk28),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
cyclic(sk21,sk27,sk22,sk28) != true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t30721]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO621+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.37 % Computer : n004.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
% 0.10/0.38 % DateTime : Wed Sep 23 12:34:35 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 171.85/22.15 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 171.85/22.15 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------