%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : GEO626+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 : n016.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 01:18:20 PM UTC 2026
% Result : Theorem 152.34s 25.01s
% Output : Proof 152.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 60
% Number of leaves : 30
% Syntax : Number of formulae : 314 ( 198 unt; 0 def)
% Number of atoms : 514 ( 190 equ)
% Maximal formula atoms : 11 ( 1 avg)
% Number of connectives : 326 ( 126 ~; 120 |; 50 &)
% ( 0 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 3 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-8 aty)
% Number of functors : 15 ( 15 usr; 13 con; 0-4 aty)
% Number of variables : 945 ( 32 sgn 444 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
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(t174,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(t265,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)],[t174]) ).
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(t110,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(t274,plain,
ifeq(perp(X1,X2,X3,X4),true,perp(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t110]) ).
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/sandbox/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(t161,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(t326,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)],[t161]) ).
fof(f68,axiom,
! [A,B,C] :
( midp(A,B,C)
=> cong(A,B,A,C) ),
file('/export/starexec/sandbox/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(t96,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c68]) ).
cnf(t363,plain,
ifeq(midp(X1,X2,X3),true,cong(X1,X2,X1,X3),true) = true,
inference(orient,[status(thm)],[t96]) ).
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/sandbox/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(t222,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(t353,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)],[t222]) ).
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(t145,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(t311,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X3,X4),true,para(X1,X2,X5,X6),true) = true,
inference(orient,[status(thm)],[t145]) ).
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]) ).
cnf(t166,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c18]) ).
cnf(t305,plain,
ifeq(eqangle(X1,X2,X3,X4,X5,X6,X7,X8),true,eqangle(X3,X4,X1,X2,X7,X8,X5,X6),true) = true,
inference(orient,[status(thm)],[t166]) ).
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(t146,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(equality_encoding,[status(esa)],[c39]) ).
cnf(t294,plain,
ifeq(para(X1,X2,X3,X4),true,eqangle(X1,X2,X5,X6,X3,X4,X5,X6),true) = true,
inference(orient,[status(thm)],[t146]) ).
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/sandbox/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(t206,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(t299,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)],[t206]) ).
fof(f86,axiom,
! [A,B,C,O] :
? [P] :
( circle(O,A,B,C)
=> perp(P,A,A,O) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleX11) ).
fof(f86_nnf,plain,
! [A,B,C,O] :
? [P] :
( perp(P,A,A,O)
| ~ circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f86]) ).
fof(f86_sk,plain,
! [O,A,B,C] :
( perp(sk11(A,B,C,O),A,A,O)
| ~ circle(O,A,B,C) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk11])],[f86_nnf]) ).
cnf(c99,plain,
( perp(sk11(X0,X1,X2,X3),X0,X0,X3)
| ~ circle(X3,X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f86_sk]) ).
cnf(hi99,axiom,
ifeq(circle(X0,X1,X2,X3),true,perp(sk11(X1,X2,X3,X0),X1,X1,X0),true) = true,
inference(equality_encoding,[status(esa)],[c99]) ).
fof(f94,conjecture,
! [A,B,C,O,D,G,F,C1,B1,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(B1,D,F)
& circle(O,D,B1,NWPNT3)
& coll(C1,D,G)
& circle(O,D,C1,NWPNT2)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(G,A,B)
& perp(G,D,A,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> para(C1,C,B1,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exemplo6GDDFULL8110990) ).
fof(f94_neg,negated_conjecture,
~ ! [A,B,C,O,D,G,F,C1,B1,NWPNT1,NWPNT2,NWPNT3] :
( ( coll(B1,D,F)
& circle(O,D,B1,NWPNT3)
& coll(C1,D,G)
& circle(O,D,C1,NWPNT2)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(G,A,B)
& perp(G,D,A,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) )
=> para(C1,C,B1,B) ),
inference(negated_conjecture,[status(cth)],[f94]) ).
fof(f94_nnf,plain,
? [A,B,C,O,D,G,F,C1,B1,NWPNT1,NWPNT2,NWPNT3] :
( ~ para(C1,C,B1,B)
& coll(B1,D,F)
& circle(O,D,B1,NWPNT3)
& coll(C1,D,G)
& circle(O,D,C1,NWPNT2)
& coll(F,A,C)
& perp(F,D,A,C)
& coll(G,A,B)
& perp(G,D,A,B)
& circle(O,A,D,NWPNT1)
& circle(O,A,B,C) ),
inference(nnf_transformation,[status(thm)],[f94_neg]) ).
fof(f94_sk,plain,
( ~ para(sk27,sk22,sk28,sk21)
& coll(sk28,sk24,sk26)
& circle(sk23,sk24,sk28,sk31)
& coll(sk27,sk24,sk25)
& circle(sk23,sk24,sk27,sk30)
& coll(sk26,sk20,sk22)
& perp(sk26,sk24,sk20,sk22)
& coll(sk25,sk20,sk21)
& perp(sk25,sk24,sk20,sk21)
& circle(sk23,sk20,sk24,sk29)
& circle(sk23,sk20,sk21,sk22) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk20,sk21,sk22,sk23,sk24,sk25,sk26,sk27,sk28,sk29,sk30,sk31])],[f94_nnf]) ).
cnf(c119,plain,
circle(sk23,sk24,sk27,sk30),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi119,negated_conjecture,
circle(sk23,sk24,sk27,sk30) = true,
inference(equality_encoding,[status(esa)],[c119]) ).
cnf(h12,plain,
perp(sk11(sk24,sk27,sk30,sk23),sk24,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi119]) ).
cnf(hi7,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X2,X3,X0,X1),true) = true,
inference(equality_encoding,[status(esa)],[c7]) ).
cnf(h48,plain,
perp(sk24,sk23,sk11(sk24,sk27,sk30,sk23),sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,h12]) ).
cnf(c121,plain,
circle(sk23,sk24,sk28,sk31),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi121,negated_conjecture,
circle(sk23,sk24,sk28,sk31) = true,
inference(equality_encoding,[status(esa)],[c121]) ).
cnf(h16,plain,
perp(sk11(sk24,sk28,sk31,sk23),sk24,sk24,sk23) = true,
inference(hyper_resolution,[status(thm)],[hi99,hi121]) ).
cnf(hi8,axiom,
ifeq(perp(X0,X1,X2,X3),true,ifeq(perp(X2,X3,X4,X5),true,para(X0,X1,X4,X5),true),true) = true,
inference(equality_encoding,[status(esa)],[c8]) ).
cnf(h127,plain,
para(sk11(sk24,sk28,sk31,sk23),sk24,sk11(sk24,sk27,sk30,sk23),sk24) = true,
inference(hyper_resolution,[status(thm)],[hi8,h16,h48]) ).
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(h414,plain,
eqangle(sk11(sk24,sk28,sk31,sk23),sk24,V0,V1,sk11(sk24,sk27,sk30,sk23),sk24,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h127]) ).
cnf(c117,plain,
perp(sk26,sk24,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi117,negated_conjecture,
perp(sk26,sk24,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c117]) ).
cnf(h7,plain,
perp(sk20,sk22,sk26,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi117]) ).
cnf(h36,plain,
para(sk20,sk22,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi8,h7,hi117]) ).
cnf(h102,plain,
eqangle(sk20,sk22,V0,V1,sk20,sk22,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h36]) ).
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/sandbox/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(hi20,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X0,X1,X4,X5,X2,X3,X6,X7),true) = true,
inference(equality_encoding,[status(esa)],[c20]) ).
cnf(h328,plain,
eqangle(sk20,sk22,sk20,sk22,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h102]) ).
fof(f21,axiom,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( ( eqangle(P,Q,U,V,E,F,G,H)
& eqangle(A,B,C,D,P,Q,U,V) )
=> eqangle(A,B,C,D,E,F,G,H) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD22) ).
fof(f21_nnf,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B,C,D,P,Q,U,V,E,F,G,H] :
( eqangle(A,B,C,D,E,F,G,H)
| ~ eqangle(P,Q,U,V,E,F,G,H)
| ~ eqangle(A,B,C,D,P,Q,U,V) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( eqangle(X0,X1,X2,X3,X8,X9,X10,X11)
| ~ eqangle(X4,X5,X6,X7,X8,X9,X10,X11)
| ~ eqangle(X0,X1,X2,X3,X4,X5,X6,X7) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(hi21,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,ifeq(eqangle(X4,X5,X6,X7,X8,X9,X10,X11),true,eqangle(X0,X1,X2,X3,X8,X9,X10,X11),true),true) = true,
inference(equality_encoding,[status(esa)],[c21]) ).
cnf(t137,plain,
eqangle(sk20,sk22,sk20,sk22,sk11(sk24,sk27,sk30,sk23),sk24,sk11(sk24,sk28,sk31,sk23),sk24) = true,
inference(hyper_resolution,[status(thm)],[hi21,h328,h414]) ).
cnf(t2163,plain,
eqangle(sk20,sk22,sk20,sk22,sk11(sk24,sk27,sk30,sk23),sk24,sk11(sk24,sk28,sk31,sk23),sk24) = true,
inference(orient,[status(thm)],[t137]) ).
cnf(t2175,plain,
true = ifeq(true,true,ifeq(para(sk11(sk24,sk27,sk30,sk23),sk24,sk11(sk24,sk28,sk31,sk23),sk24),true,para(sk20,sk22,sk20,sk22),true),true),
inference(cp,[status(thm)],[t299,t2163]) ).
cnf(t44,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t256,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t44]) ).
cnf(t28795,plain,
true = ifeq(para(sk11(sk24,sk27,sk30,sk23),sk24,sk11(sk24,sk28,sk31,sk23),sk24),true,para(sk20,sk22,sk20,sk22),true),
inference(step,[status(thm)],[t2175,t256]) ).
cnf(h56,plain,
perp(sk24,sk23,sk11(sk24,sk28,sk31,sk23),sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,h16]) ).
cnf(t117,plain,
para(sk11(sk24,sk27,sk30,sk23),sk24,sk11(sk24,sk28,sk31,sk23),sk24) = true,
inference(hyper_resolution,[status(thm)],[hi8,h12,h56]) ).
cnf(t2077,plain,
para(sk11(sk24,sk27,sk30,sk23),sk24,sk11(sk24,sk28,sk31,sk23),sk24) = true,
inference(orient,[status(thm)],[t117]) ).
cnf(t28796,plain,
true = ifeq(true,true,para(sk20,sk22,sk20,sk22),true),
inference(step,[status(thm)],[t28795,t2077]) ).
cnf(t28797,plain,
true = para(sk20,sk22,sk20,sk22),
inference(step,[status(thm)],[t28796,t256]) ).
cnf(t4401,plain,
para(sk20,sk22,sk20,sk22) = true,
inference(orient,[status(thm)],[t28797]) ).
cnf(t4404,plain,
true = ifeq(true,true,eqangle(sk20,sk22,X1,X2,sk20,sk22,X1,X2),true),
inference(cp,[status(thm)],[t294,t4401]) ).
cnf(t29124,plain,
true = eqangle(sk20,sk22,X1,X2,sk20,sk22,X1,X2),
inference(step,[status(thm)],[t4404,t256]) ).
cnf(t9396,plain,
eqangle(sk20,sk22,X1,X2,sk20,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t29124]) ).
cnf(t9402,plain,
true = ifeq(true,true,eqangle(X1,X2,sk20,sk22,X1,X2,sk20,sk22),true),
inference(cp,[status(thm)],[t305,t9396]) ).
cnf(t29507,plain,
true = eqangle(X1,X2,sk20,sk22,X1,X2,sk20,sk22),
inference(step,[status(thm)],[t9402,t256]) ).
cnf(t14723,plain,
eqangle(X1,X2,sk20,sk22,X1,X2,sk20,sk22) = true,
inference(orient,[status(thm)],[t29507]) ).
cnf(t14725,plain,
true = ifeq(true,true,para(X1,X2,X1,X2),true),
inference(cp,[status(thm)],[t311,t14723]) ).
cnf(t29508,plain,
true = para(X1,X2,X1,X2),
inference(step,[status(thm)],[t14725,t256]) ).
cnf(t14747,plain,
para(X1,X2,X1,X2) = true,
inference(orient,[status(thm)],[t29508]) ).
cnf(t14763,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)],[t353,t14747]) ).
cnf(t31140,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)],[t14763,t256]) ).
cnf(t31141,plain,
true = ifeq(midp(X1,X2,X2),true,ifeq(true,true,midp(X1,X3,X3),true),true),
inference(step,[status(thm)],[t31140,t14747]) ).
cnf(t31142,plain,
true = ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true),
inference(step,[status(thm)],[t31141,t256]) ).
cnf(t28008,plain,
ifeq(midp(X1,X2,X2),true,midp(X1,X3,X3),true) = true,
inference(orient,[status(thm)],[t31142]) ).
fof(f67,axiom,
! [A,B,C] :
( ( coll(A,B,C)
& cong(A,B,A,C) )
=> midp(A,B,C) ),
file('/export/starexec/sandbox/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(t152,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(t327,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)],[t152]) ).
fof(f22,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(A,B,D,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD23) ).
fof(f22_nnf,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
! [A,B,C,D] :
( cong(A,B,D,C)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f22_nnf]) ).
cnf(c22,plain,
( cong(X0,X1,X3,X2)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
cnf(t102,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c22]) ).
cnf(t323,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t102]) ).
fof(f23,axiom,
! [A,B,C,D] :
( cong(A,B,C,D)
=> cong(C,D,A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ruleD24) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( cong(C,D,A,B)
| ~ cong(A,B,C,D) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( cong(X2,X3,X0,X1)
| ~ cong(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(t103,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c23]) ).
cnf(t321,plain,
ifeq(cong(X1,X2,X3,X4),true,cong(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t103]) ).
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/sandbox/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(t341,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/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(t144,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(t343,plain,
ifeq(cyclic(X1,X2,X3,X4),true,eqangle(X3,X1,X3,X2,X4,X1,X4,X2),true) = true,
inference(orient,[status(thm)],[t144]) ).
fof(f1,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(B,A,C) ),
file('/export/starexec/sandbox/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(hi1,axiom,
ifeq(coll(X0,X1,X2),true,coll(X1,X0,X2),true) = true,
inference(equality_encoding,[status(esa)],[c1]) ).
cnf(c116,plain,
coll(sk25,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi116,negated_conjecture,
coll(sk25,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c116]) ).
cnf(h5,plain,
coll(sk20,sk25,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi116]) ).
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(hi2,axiom,
ifeq(coll(X0,X1,X2),true,ifeq(coll(X0,X1,X3),true,coll(X2,X3,X0),true),true) = true,
inference(equality_encoding,[status(esa)],[c2]) ).
cnf(h29,plain,
coll(sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h5,h5]) ).
cnf(h73,plain,
coll(sk20,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h29,h29]) ).
cnf(c118,plain,
coll(sk26,sk20,sk22),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi118,negated_conjecture,
coll(sk26,sk20,sk22) = true,
inference(equality_encoding,[status(esa)],[c118]) ).
cnf(h10,plain,
coll(sk20,sk26,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi1,hi118]) ).
cnf(h42,plain,
coll(sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h10,h10]) ).
cnf(h106,plain,
coll(sk20,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h42,h42]) ).
cnf(h339,plain,
coll(sk22,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h106,h73]) ).
fof(f0,axiom,
! [A,B,C] :
( coll(A,B,C)
=> coll(A,C,B) ),
file('/export/starexec/sandbox/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(hi0,axiom,
ifeq(coll(X0,X1,X2),true,coll(X0,X2,X1),true) = true,
inference(equality_encoding,[status(esa)],[c0]) ).
cnf(h963,plain,
coll(sk22,sk20,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi0,h339]) ).
cnf(h3484,plain,
coll(sk21,sk21,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi2,h963,h963]) ).
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(hi6,axiom,
ifeq(perp(X0,X1,X2,X3),true,perp(X0,X1,X3,X2),true) = true,
inference(equality_encoding,[status(esa)],[c6]) ).
cnf(c115,plain,
perp(sk25,sk24,sk20,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(hi115,negated_conjecture,
perp(sk25,sk24,sk20,sk21) = true,
inference(equality_encoding,[status(esa)],[c115]) ).
cnf(h3,plain,
perp(sk25,sk24,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi115]) ).
cnf(h2,plain,
perp(sk20,sk21,sk25,sk24) = true,
inference(hyper_resolution,[status(thm)],[hi7,hi115]) ).
cnf(h31,plain,
para(sk20,sk21,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h2,h3]) ).
cnf(h90,plain,
eqangle(sk20,sk21,V0,V1,sk21,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h31]) ).
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(hi17,axiom,
ifeq(eqangle(X0,X1,X2,X3,X4,X5,X6,X7),true,eqangle(X1,X0,X2,X3,X4,X5,X6,X7),true) = true,
inference(equality_encoding,[status(esa)],[c17]) ).
cnf(h278,plain,
eqangle(sk21,sk20,V0,V1,sk21,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi17,h90]) ).
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]) ).
cnf(hi42,axiom,
ifeq(eqangle(X0,X1,X0,X2,X3,X1,X3,X2),true,ifeq(coll(X0,X3,X2),true,cyclic(X1,X2,X0,X3),true),true) = true,
inference(equality_encoding,[status(esa)],[c42]) ).
cnf(t29,plain,
cyclic(sk20,sk22,sk21,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi42,h278,h3484]) ).
cnf(t2513,plain,
cyclic(sk20,sk22,sk21,sk21) = true,
inference(orient,[status(thm)],[t29]) ).
cnf(t2518,plain,
true = ifeq(true,true,eqangle(sk21,sk20,sk21,sk22,sk21,sk20,sk21,sk22),true),
inference(cp,[status(thm)],[t343,t2513]) ).
cnf(t28952,plain,
true = eqangle(sk21,sk20,sk21,sk22,sk21,sk20,sk21,sk22),
inference(step,[status(thm)],[t2518,t256]) ).
cnf(t7259,plain,
eqangle(sk21,sk20,sk21,sk22,sk21,sk20,sk21,sk22) = true,
inference(orient,[status(thm)],[t28952]) ).
cnf(t7273,plain,
true = ifeq(cyclic(sk20,sk22,sk21,sk20),true,ifeq(cyclic(sk20,sk22,sk21,sk22),true,ifeq(cyclic(sk20,sk22,sk21,sk21),true,ifeq(true,true,cong(sk20,sk22,sk20,sk22),true),true),true),true),
inference(cp,[status(thm)],[t341,t7259]) ).
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(t106,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(equality_encoding,[status(esa)],[c15]) ).
cnf(t344,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X2,X1,X3,X4),true) = true,
inference(orient,[status(thm)],[t106]) ).
cnf(h324,plain,
cyclic(sk22,sk21,sk20,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi42,h102,h73]) ).
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(hi14,axiom,
ifeq(cyclic(X0,X1,X2,X3),true,cyclic(X0,X2,X1,X3),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t38,plain,
cyclic(sk22,sk20,sk21,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi14,h324]) ).
cnf(t2702,plain,
cyclic(sk22,sk20,sk21,sk20) = true,
inference(orient,[status(thm)],[t38]) ).
cnf(t2707,plain,
true = ifeq(true,true,cyclic(sk20,sk22,sk21,sk20),true),
inference(cp,[status(thm)],[t344,t2702]) ).
cnf(t28827,plain,
true = cyclic(sk20,sk22,sk21,sk20),
inference(step,[status(thm)],[t2707,t256]) ).
cnf(t4922,plain,
cyclic(sk20,sk22,sk21,sk20) = true,
inference(orient,[status(thm)],[t28827]) ).
cnf(t28960,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk22,sk21,sk22),true,ifeq(cyclic(sk20,sk22,sk21,sk21),true,ifeq(true,true,cong(sk20,sk22,sk20,sk22),true),true),true),true),
inference(step,[status(thm)],[t7273,t4922]) ).
cnf(t28961,plain,
true = ifeq(cyclic(sk20,sk22,sk21,sk22),true,ifeq(cyclic(sk20,sk22,sk21,sk21),true,ifeq(true,true,cong(sk20,sk22,sk20,sk22),true),true),true),
inference(step,[status(thm)],[t28960,t256]) ).
cnf(t105,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(equality_encoding,[status(esa)],[c14]) ).
cnf(t346,plain,
ifeq(cyclic(X1,X2,X3,X4),true,cyclic(X1,X3,X2,X4),true) = true,
inference(orient,[status(thm)],[t105]) ).
cnf(h337,plain,
coll(sk21,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi2,h73,h106]) ).
cnf(h936,plain,
coll(sk21,sk20,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi0,h337]) ).
cnf(h3304,plain,
coll(sk22,sk22,sk21) = true,
inference(hyper_resolution,[status(thm)],[hi2,h936,h936]) ).
cnf(h8,plain,
perp(sk26,sk24,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi6,hi117]) ).
cnf(h40,plain,
para(sk20,sk22,sk22,sk20) = true,
inference(hyper_resolution,[status(thm)],[hi8,h7,h8]) ).
cnf(h111,plain,
eqangle(sk20,sk22,V0,V1,sk22,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi39,h40]) ).
cnf(h376,plain,
eqangle(sk22,sk20,V0,V1,sk22,sk20,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi17,h111]) ).
cnf(t28,plain,
cyclic(sk20,sk21,sk22,sk22) = true,
inference(hyper_resolution,[status(thm)],[hi42,h376,h3304]) ).
cnf(t2494,plain,
cyclic(sk20,sk21,sk22,sk22) = true,
inference(orient,[status(thm)],[t28]) ).
cnf(t2495,plain,
true = ifeq(true,true,cyclic(sk20,sk22,sk21,sk22),true),
inference(cp,[status(thm)],[t346,t2494]) ).
cnf(t28808,plain,
true = cyclic(sk20,sk22,sk21,sk22),
inference(step,[status(thm)],[t2495,t256]) ).
cnf(t4586,plain,
cyclic(sk20,sk22,sk21,sk22) = true,
inference(orient,[status(thm)],[t28808]) ).
cnf(t28962,plain,
true = ifeq(true,true,ifeq(cyclic(sk20,sk22,sk21,sk21),true,ifeq(true,true,cong(sk20,sk22,sk20,sk22),true),true),true),
inference(step,[status(thm)],[t28961,t4586]) ).
cnf(t28963,plain,
true = ifeq(cyclic(sk20,sk22,sk21,sk21),true,ifeq(true,true,cong(sk20,sk22,sk20,sk22),true),true),
inference(step,[status(thm)],[t28962,t256]) ).
cnf(t28964,plain,
true = ifeq(true,true,ifeq(true,true,cong(sk20,sk22,sk20,sk22),true),true),
inference(step,[status(thm)],[t28963,t2513]) ).
cnf(t28965,plain,
true = ifeq(true,true,cong(sk20,sk22,sk20,sk22),true),
inference(step,[status(thm)],[t28964,t256]) ).
cnf(t28966,plain,
true = cong(sk20,sk22,sk20,sk22),
inference(step,[status(thm)],[t28965,t256]) ).
cnf(t7417,plain,
cong(sk20,sk22,sk20,sk22) = true,
inference(orient,[status(thm)],[t28966]) ).
cnf(t7420,plain,
true = ifeq(true,true,cong(sk20,sk22,sk22,sk20),true),
inference(cp,[status(thm)],[t323,t7417]) ).
cnf(t28971,plain,
true = cong(sk20,sk22,sk22,sk20),
inference(step,[status(thm)],[t7420,t256]) ).
cnf(t7509,plain,
cong(sk20,sk22,sk22,sk20) = true,
inference(orient,[status(thm)],[t28971]) ).
cnf(t7511,plain,
true = ifeq(true,true,cong(sk22,sk20,sk20,sk22),true),
inference(cp,[status(thm)],[t321,t7509]) ).
cnf(t28973,plain,
true = cong(sk22,sk20,sk20,sk22),
inference(step,[status(thm)],[t7511,t256]) ).
cnf(t7542,plain,
cong(sk22,sk20,sk20,sk22) = true,
inference(orient,[status(thm)],[t28973]) ).
cnf(t7544,plain,
true = ifeq(true,true,cong(sk22,sk20,sk22,sk20),true),
inference(cp,[status(thm)],[t323,t7542]) ).
cnf(t28981,plain,
true = cong(sk22,sk20,sk22,sk20),
inference(step,[status(thm)],[t7544,t256]) ).
cnf(t7692,plain,
cong(sk22,sk20,sk22,sk20) = true,
inference(orient,[status(thm)],[t28981]) ).
cnf(t7701,plain,
true = ifeq(true,true,ifeq(coll(sk22,sk20,sk20),true,midp(sk22,sk20,sk20),true),true),
inference(cp,[status(thm)],[t327,t7692]) ).
cnf(t28982,plain,
true = ifeq(coll(sk22,sk20,sk20),true,midp(sk22,sk20,sk20),true),
inference(step,[status(thm)],[t7701,t256]) ).
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(t97,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(equality_encoding,[status(esa)],[c66]) ).
cnf(t295,plain,
ifeq(para(X1,X2,X1,X3),true,coll(X1,X2,X3),true) = true,
inference(orient,[status(thm)],[t97]) ).
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(t107,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(equality_encoding,[status(esa)],[c3]) ).
cnf(t292,plain,
ifeq(para(X1,X2,X3,X4),true,para(X1,X2,X4,X3),true) = true,
inference(orient,[status(thm)],[t107]) ).
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(t108,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(equality_encoding,[status(esa)],[c4]) ).
cnf(t290,plain,
ifeq(para(X1,X2,X3,X4),true,para(X3,X4,X1,X2),true) = true,
inference(orient,[status(thm)],[t108]) ).
cnf(h374,plain,
eqangle(sk20,sk22,sk22,sk20,V0,V1,V0,V1) = true,
inference(hyper_resolution,[status(thm)],[hi20,h111]) ).
cnf(t138,plain,
eqangle(sk20,sk22,sk22,sk20,sk11(sk24,sk27,sk30,sk23),sk24,sk11(sk24,sk28,sk31,sk23),sk24) = true,
inference(hyper_resolution,[status(thm)],[hi21,h374,h414]) ).
cnf(t2178,plain,
eqangle(sk20,sk22,sk22,sk20,sk11(sk24,sk27,sk30,sk23),sk24,sk11(sk24,sk28,sk31,sk23),sk24) = true,
inference(orient,[status(thm)],[t138]) ).
cnf(t2190,plain,
true = ifeq(true,true,ifeq(para(sk11(sk24,sk27,sk30,sk23),sk24,sk11(sk24,sk28,sk31,sk23),sk24),true,para(sk20,sk22,sk22,sk20),true),true),
inference(cp,[status(thm)],[t299,t2178]) ).
cnf(t28801,plain,
true = ifeq(para(sk11(sk24,sk27,sk30,sk23),sk24,sk11(sk24,sk28,sk31,sk23),sk24),true,para(sk20,sk22,sk22,sk20),true),
inference(step,[status(thm)],[t2190,t256]) ).
cnf(t28802,plain,
true = ifeq(true,true,para(sk20,sk22,sk22,sk20),true),
inference(step,[status(thm)],[t28801,t2077]) ).
cnf(t28803,plain,
true = para(sk20,sk22,sk22,sk20),
inference(step,[status(thm)],[t28802,t256]) ).
cnf(t4523,plain,
para(sk20,sk22,sk22,sk20) = true,
inference(orient,[status(thm)],[t28803]) ).
cnf(t4526,plain,
true = ifeq(true,true,para(sk22,sk20,sk20,sk22),true),
inference(cp,[status(thm)],[t290,t4523]) ).
cnf(t28840,plain,
true = para(sk22,sk20,sk20,sk22),
inference(step,[status(thm)],[t4526,t256]) ).
cnf(t5181,plain,
para(sk22,sk20,sk20,sk22) = true,
inference(orient,[status(thm)],[t28840]) ).
cnf(t5184,plain,
true = ifeq(true,true,para(sk22,sk20,sk22,sk20),true),
inference(cp,[status(thm)],[t292,t5181]) ).
cnf(t28875,plain,
true = para(sk22,sk20,sk22,sk20),
inference(step,[status(thm)],[t5184,t256]) ).
cnf(t5826,plain,
para(sk22,sk20,sk22,sk20) = true,
inference(orient,[status(thm)],[t28875]) ).
cnf(t5828,plain,
true = ifeq(true,true,coll(sk22,sk20,sk20),true),
inference(cp,[status(thm)],[t295,t5826]) ).
cnf(t28876,plain,
true = coll(sk22,sk20,sk20),
inference(step,[status(thm)],[t5828,t256]) ).
cnf(t5851,plain,
coll(sk22,sk20,sk20) = true,
inference(orient,[status(thm)],[t28876]) ).
cnf(t28983,plain,
true = ifeq(true,true,midp(sk22,sk20,sk20),true),
inference(step,[status(thm)],[t28982,t5851]) ).
cnf(t28984,plain,
true = midp(sk22,sk20,sk20),
inference(step,[status(thm)],[t28983,t256]) ).
cnf(t7731,plain,
midp(sk22,sk20,sk20) = true,
inference(orient,[status(thm)],[t28984]) ).
cnf(t28009,plain,
true = ifeq(true,true,midp(sk22,X1,X1),true),
inference(cp,[status(thm)],[t28008,t7731]) ).
cnf(t31143,plain,
true = midp(sk22,X1,X1),
inference(step,[status(thm)],[t28009,t256]) ).
cnf(t28016,plain,
midp(sk22,X1,X1) = true,
inference(orient,[status(thm)],[t31143]) ).
cnf(t28017,plain,
true = ifeq(true,true,cong(sk22,X1,sk22,X1),true),
inference(cp,[status(thm)],[t363,t28016]) ).
cnf(t31147,plain,
true = cong(sk22,X1,sk22,X1),
inference(step,[status(thm)],[t28017,t256]) ).
cnf(t28104,plain,
cong(sk22,X1,sk22,X1) = true,
inference(orient,[status(thm)],[t31147]) ).
cnf(t28115,plain,
true = ifeq(true,true,ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),true),
inference(cp,[status(thm)],[t326,t28104]) ).
cnf(t31152,plain,
true = ifeq(cong(sk22,X1,sk22,X1),true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t28115,t256]) ).
cnf(t31153,plain,
true = ifeq(true,true,perp(sk22,sk22,X2,X1),true),
inference(step,[status(thm)],[t31152,t28104]) ).
cnf(t31154,plain,
true = perp(sk22,sk22,X2,X1),
inference(step,[status(thm)],[t31153,t256]) ).
cnf(t28252,plain,
perp(sk22,sk22,X1,X2) = true,
inference(orient,[status(thm)],[t31154]) ).
cnf(t28253,plain,
true = ifeq(true,true,perp(X1,X2,sk22,sk22),true),
inference(cp,[status(thm)],[t274,t28252]) ).
cnf(t31168,plain,
true = perp(X1,X2,sk22,sk22),
inference(step,[status(thm)],[t28253,t256]) ).
cnf(t28484,plain,
perp(X1,X2,sk22,sk22) = true,
inference(orient,[status(thm)],[t31168]) ).
cnf(t28501,plain,
true = ifeq(true,true,ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),true),
inference(cp,[status(thm)],[t265,t28484]) ).
cnf(t31181,plain,
true = ifeq(perp(sk22,sk22,X1,X2),true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t28501,t256]) ).
cnf(t31182,plain,
true = ifeq(true,true,para(X3,X4,X1,X2),true),
inference(step,[status(thm)],[t31181,t28252]) ).
cnf(t31183,plain,
true = para(X3,X4,X1,X2),
inference(step,[status(thm)],[t31182,t256]) ).
cnf(t28731,plain,
para(X1,X2,X3,X4) = true,
inference(orient,[status(thm)],[t31183]) ).
cnf(c123,plain,
~ para(sk27,sk22,sk28,sk21),
inference(cnf_transformation,[status(esa)],[f94_sk]) ).
cnf(goal_0,negated_conjecture,
para(sk27,sk22,sk28,sk21) != true,
inference(equality_encoding,[status(esa)],[c123]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t28731]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO626+1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/5.37 % Computer : n016.cluster.edu
% 0.11/5.37 % Model : x86_64 x86_64
% 0.11/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.37 % Memory : 8046.5625MB
% 0.11/5.37 % OS : Linux 6.8.0-71-generic
% 0.11/5.37 % CPULimit : 300
% 0.11/5.37 % WCLimit : 300
% 0.11/5.37 % DateTime : Wed Sep 23 12:40:16 UTC 2026
% 0.11/5.38 % CPUTime :
% 0.11/5.38 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 152.34/25.01 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 152.34/25.01 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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