%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : SEU020+1 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n026.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 02:50:51 PM UTC 2026
% Result : Theorem 59.00s 7.89s
% Output : Proof 59.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 12
% Syntax : Number of formulae : 104 ( 74 unt; 0 def)
% Number of atoms : 190 ( 69 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 161 ( 75 ~; 45 |; 30 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 6 con; 0-4 aty)
% Number of variables : 84 ( 8 sgn 44 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f31,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( ( subset(relation_rng(B),relation_dom(A))
& one_to_one(relation_composition(B,A)) )
=> one_to_one(B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t47_funct_1) ).
fof(f31_nnf,plain,
! [A] :
( ! [B] :
( one_to_one(B)
| ~ subset(relation_rng(B),relation_dom(A))
| ~ one_to_one(relation_composition(B,A))
| ~ function(B)
| ~ relation(B) )
| ~ function(A)
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f31]) ).
fof(f31_sk,plain,
! [A,B] :
( one_to_one(B)
| ~ subset(relation_rng(B),relation_dom(A))
| ~ one_to_one(relation_composition(B,A))
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f31_nnf]) ).
cnf(c47,plain,
( one_to_one(X1)
| ~ subset(relation_rng(X1),relation_dom(X0))
| ~ one_to_one(relation_composition(X1,X0))
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f31_sk]) ).
cnf(t255,plain,
ifeq(relation(X1),true,ifeq(function(X1),true,ifeq(relation(X2),true,ifeq(function(X2),true,ifeq(one_to_one(relation_composition(X2,X1)),true,ifeq(subset(relation_rng(X2),relation_dom(X1)),true,one_to_one(X2),true),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c47]) ).
cnf(t301,plain,
ifeq(relation(X1),true,ifeq(function(X1),true,ifeq(relation(X2),true,ifeq(function(X2),true,ifeq(one_to_one(relation_composition(X2,X1)),true,ifeq(subset(relation_rng(X2),relation_dom(X1)),true,one_to_one(X2),true),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t255]) ).
fof(f28,axiom,
! [A] :
( ( function(A)
& relation(A) )
=> ! [B] :
( ( function(B)
& relation(B) )
=> ( relation_dom(relation_composition(B,A)) = relation_dom(B)
=> subset(relation_rng(B),relation_dom(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t27_funct_1) ).
fof(f28_nnf,plain,
! [A] :
( ! [B] :
( subset(relation_rng(B),relation_dom(A))
| relation_dom(relation_composition(B,A)) != relation_dom(B)
| ~ function(B)
| ~ relation(B) )
| ~ function(A)
| ~ relation(A) ),
inference(nnf_transformation,[status(thm)],[f28]) ).
fof(f28_sk,plain,
! [A,B] :
( subset(relation_rng(B),relation_dom(A))
| relation_dom(relation_composition(B,A)) != relation_dom(B)
| ~ function(B)
| ~ relation(B)
| ~ function(A)
| ~ relation(A) ),
inference(skolemisation,[status(esa)],[f28_nnf]) ).
cnf(c43,plain,
( subset(relation_rng(X1),relation_dom(X0))
| relation_dom(relation_composition(X1,X0)) != relation_dom(X1)
| ~ function(X1)
| ~ relation(X1)
| ~ function(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[status(esa)],[f28_sk]) ).
cnf(t254,plain,
ifeq(relation(X1),true,ifeq(function(X1),true,ifeq(relation(X2),true,ifeq(function(X2),true,ifeq(relation_dom(relation_composition(X2,X1)),relation_dom(X2),subset(relation_rng(X2),relation_dom(X1)),true),true),true),true),true) = true,
inference(equality_encoding,[status(esa)],[c43]) ).
cnf(t297,plain,
ifeq(relation(X1),true,ifeq(function(X1),true,ifeq(relation(X2),true,ifeq(function(X2),true,ifeq(relation_dom(relation_composition(X2,X1)),relation_dom(X2),subset(relation_rng(X2),relation_dom(X1)),true),true),true),true),true) = true,
inference(orient,[status(thm)],[t254]) ).
fof(f37,axiom,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t71_relat_1) ).
fof(f37_nnf,plain,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
inference(nnf_transformation,[status(thm)],[f37]) ).
fof(f37_sk,plain,
! [A] :
( relation_rng(identity_relation(A)) = A
& relation_dom(identity_relation(A)) = A ),
inference(skolemisation,[status(esa)],[f37_nnf]) ).
cnf(c58,plain,
relation_dom(identity_relation(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f37_sk]) ).
cnf(t104,plain,
relation_dom(identity_relation(X1)) = X1,
inference(equality_encoding,[status(esa)],[c58]) ).
cnf(t256,plain,
relation_dom(identity_relation(X1)) = X1,
inference(orient,[status(thm)],[t104]) ).
fof(f34,conjecture,
! [A] :
( ( function(A)
& relation(A) )
=> ( ? [B] :
( relation_composition(A,B) = identity_relation(relation_dom(A))
& function(B)
& relation(B) )
=> one_to_one(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t53_funct_1) ).
fof(f34_neg,negated_conjecture,
~ ! [A] :
( ( function(A)
& relation(A) )
=> ( ? [B] :
( relation_composition(A,B) = identity_relation(relation_dom(A))
& function(B)
& relation(B) )
=> one_to_one(A) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
fof(f34_nnf,plain,
? [A] :
( ~ one_to_one(A)
& ? [B] :
( relation_composition(A,B) = identity_relation(relation_dom(A))
& function(B)
& relation(B) )
& function(A)
& relation(A) ),
inference(nnf_transformation,[status(thm)],[f34_neg]) ).
fof(f34_sk,plain,
( ~ one_to_one(sk9)
& relation_composition(sk9,sk10) = identity_relation(relation_dom(sk9))
& function(sk10)
& relation(sk10)
& function(sk9)
& relation(sk9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk9,sk10])],[f34_nnf]) ).
cnf(c54,plain,
relation_composition(sk9,sk10) = identity_relation(relation_dom(sk9)),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(t201,plain,
relation_composition(sk9,sk10) = identity_relation(relation_dom(sk9)),
inference(equality_encoding,[status(esa)],[c54]) ).
cnf(t1600,plain,
identity_relation(relation_dom(sk9)) = relation_composition(sk9,sk10),
inference(orient,[status(thm)],[t201]) ).
cnf(t1601,plain,
relation_dom(sk9) = relation_dom(relation_composition(sk9,sk10)),
inference(cp,[status(thm)],[t256,t1600]) ).
cnf(t1741,plain,
relation_dom(relation_composition(sk9,sk10)) = relation_dom(sk9),
inference(orient,[status(thm)],[t1601]) ).
cnf(t1745,plain,
true = ifeq(relation(sk10),true,ifeq(function(sk10),true,ifeq(relation(sk9),true,ifeq(function(sk9),true,ifeq(relation_dom(sk9),relation_dom(sk9),subset(relation_rng(sk9),relation_dom(sk10)),true),true),true),true),true),
inference(cp,[status(thm)],[t297,t1741]) ).
cnf(c52,plain,
relation(sk10),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(t22,plain,
relation(sk10) = true,
inference(equality_encoding,[status(esa)],[c52]) ).
cnf(t1127,plain,
relation(sk10) = true,
inference(orient,[status(thm)],[t22]) ).
cnf(t1835,plain,
true = ifeq(true,true,ifeq(function(sk10),true,ifeq(relation(sk9),true,ifeq(function(sk9),true,ifeq(relation_dom(sk9),relation_dom(sk9),subset(relation_rng(sk9),relation_dom(sk10)),true),true),true),true),true),
inference(step,[status(thm)],[t1745,t1127]) ).
cnf(t200,plain,
ifeq(X1,X1,X2,X3) = X2,
introduced(definition) ).
cnf(t258,plain,
ifeq(X1,X1,X2,X3) = X2,
inference(orient,[status(thm)],[t200]) ).
cnf(t1836,plain,
true = ifeq(function(sk10),true,ifeq(relation(sk9),true,ifeq(function(sk9),true,ifeq(relation_dom(sk9),relation_dom(sk9),subset(relation_rng(sk9),relation_dom(sk10)),true),true),true),true),
inference(step,[status(thm)],[t1835,t258]) ).
cnf(c53,plain,
function(sk10),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(t12,plain,
function(sk10) = true,
inference(equality_encoding,[status(esa)],[c53]) ).
cnf(t1348,plain,
function(sk10) = true,
inference(orient,[status(thm)],[t12]) ).
cnf(t1837,plain,
true = ifeq(true,true,ifeq(relation(sk9),true,ifeq(function(sk9),true,ifeq(relation_dom(sk9),relation_dom(sk9),subset(relation_rng(sk9),relation_dom(sk10)),true),true),true),true),
inference(step,[status(thm)],[t1836,t1348]) ).
cnf(t1838,plain,
true = ifeq(relation(sk9),true,ifeq(function(sk9),true,ifeq(relation_dom(sk9),relation_dom(sk9),subset(relation_rng(sk9),relation_dom(sk10)),true),true),true),
inference(step,[status(thm)],[t1837,t258]) ).
cnf(c50,plain,
relation(sk9),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(t27,plain,
relation(sk9) = true,
inference(equality_encoding,[status(esa)],[c50]) ).
cnf(t1091,plain,
relation(sk9) = true,
inference(orient,[status(thm)],[t27]) ).
cnf(t1839,plain,
true = ifeq(true,true,ifeq(function(sk9),true,ifeq(relation_dom(sk9),relation_dom(sk9),subset(relation_rng(sk9),relation_dom(sk10)),true),true),true),
inference(step,[status(thm)],[t1838,t1091]) ).
cnf(t1840,plain,
true = ifeq(function(sk9),true,ifeq(relation_dom(sk9),relation_dom(sk9),subset(relation_rng(sk9),relation_dom(sk10)),true),true),
inference(step,[status(thm)],[t1839,t258]) ).
cnf(c51,plain,
function(sk9),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(t15,plain,
function(sk9) = true,
inference(equality_encoding,[status(esa)],[c51]) ).
cnf(t1328,plain,
function(sk9) = true,
inference(orient,[status(thm)],[t15]) ).
cnf(t1841,plain,
true = ifeq(true,true,ifeq(relation_dom(sk9),relation_dom(sk9),subset(relation_rng(sk9),relation_dom(sk10)),true),true),
inference(step,[status(thm)],[t1840,t1328]) ).
cnf(t1842,plain,
true = ifeq(relation_dom(sk9),relation_dom(sk9),subset(relation_rng(sk9),relation_dom(sk10)),true),
inference(step,[status(thm)],[t1841,t258]) ).
cnf(t1843,plain,
true = subset(relation_rng(sk9),relation_dom(sk10)),
inference(step,[status(thm)],[t1842,t258]) ).
cnf(t1760,plain,
subset(relation_rng(sk9),relation_dom(sk10)) = true,
inference(orient,[status(thm)],[t1843]) ).
cnf(t1763,plain,
true = ifeq(relation(sk10),true,ifeq(function(sk10),true,ifeq(relation(sk9),true,ifeq(function(sk9),true,ifeq(one_to_one(relation_composition(sk9,sk10)),true,ifeq(true,true,one_to_one(sk9),true),true),true),true),true),true),
inference(cp,[status(thm)],[t301,t1760]) ).
cnf(t1844,plain,
true = ifeq(true,true,ifeq(function(sk10),true,ifeq(relation(sk9),true,ifeq(function(sk9),true,ifeq(one_to_one(relation_composition(sk9,sk10)),true,ifeq(true,true,one_to_one(sk9),true),true),true),true),true),true),
inference(step,[status(thm)],[t1763,t1127]) ).
cnf(t1845,plain,
true = ifeq(function(sk10),true,ifeq(relation(sk9),true,ifeq(function(sk9),true,ifeq(one_to_one(relation_composition(sk9,sk10)),true,ifeq(true,true,one_to_one(sk9),true),true),true),true),true),
inference(step,[status(thm)],[t1844,t258]) ).
cnf(t1846,plain,
true = ifeq(true,true,ifeq(relation(sk9),true,ifeq(function(sk9),true,ifeq(one_to_one(relation_composition(sk9,sk10)),true,ifeq(true,true,one_to_one(sk9),true),true),true),true),true),
inference(step,[status(thm)],[t1845,t1348]) ).
cnf(t1847,plain,
true = ifeq(relation(sk9),true,ifeq(function(sk9),true,ifeq(one_to_one(relation_composition(sk9,sk10)),true,ifeq(true,true,one_to_one(sk9),true),true),true),true),
inference(step,[status(thm)],[t1846,t258]) ).
cnf(t1848,plain,
true = ifeq(true,true,ifeq(function(sk9),true,ifeq(one_to_one(relation_composition(sk9,sk10)),true,ifeq(true,true,one_to_one(sk9),true),true),true),true),
inference(step,[status(thm)],[t1847,t1091]) ).
cnf(t1849,plain,
true = ifeq(function(sk9),true,ifeq(one_to_one(relation_composition(sk9,sk10)),true,ifeq(true,true,one_to_one(sk9),true),true),true),
inference(step,[status(thm)],[t1848,t258]) ).
cnf(t1850,plain,
true = ifeq(true,true,ifeq(one_to_one(relation_composition(sk9,sk10)),true,ifeq(true,true,one_to_one(sk9),true),true),true),
inference(step,[status(thm)],[t1849,t1328]) ).
cnf(t1851,plain,
true = ifeq(one_to_one(relation_composition(sk9,sk10)),true,ifeq(true,true,one_to_one(sk9),true),true),
inference(step,[status(thm)],[t1850,t258]) ).
fof(f33,axiom,
! [A] : one_to_one(identity_relation(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t52_funct_1) ).
fof(f33_nnf,plain,
! [A] : one_to_one(identity_relation(A)),
inference(nnf_transformation,[status(thm)],[f33]) ).
fof(f33_sk,plain,
! [A] : one_to_one(identity_relation(A)),
inference(skolemisation,[status(esa)],[f33_nnf]) ).
cnf(c49,plain,
one_to_one(identity_relation(X0)),
inference(cnf_transformation,[status(esa)],[f33_sk]) ).
cnf(t64,plain,
one_to_one(identity_relation(X1)) = true,
inference(equality_encoding,[status(esa)],[c49]) ).
cnf(t1532,plain,
one_to_one(identity_relation(X1)) = true,
inference(orient,[status(thm)],[t64]) ).
cnf(t1602,plain,
true = one_to_one(relation_composition(sk9,sk10)),
inference(cp,[status(thm)],[t1532,t1600]) ).
cnf(t1708,plain,
one_to_one(relation_composition(sk9,sk10)) = true,
inference(orient,[status(thm)],[t1602]) ).
cnf(t1852,plain,
true = ifeq(true,true,ifeq(true,true,one_to_one(sk9),true),true),
inference(step,[status(thm)],[t1851,t1708]) ).
cnf(t1853,plain,
true = ifeq(true,true,one_to_one(sk9),true),
inference(step,[status(thm)],[t1852,t258]) ).
cnf(t1854,plain,
true = one_to_one(sk9),
inference(step,[status(thm)],[t1853,t258]) ).
cnf(c55,plain,
~ one_to_one(sk9),
inference(cnf_transformation,[status(esa)],[f34_sk]) ).
cnf(t18,plain,
one_to_one(sk9) = false,
inference(equality_encoding,[status(esa)],[c55]) ).
cnf(t1680,plain,
one_to_one(sk9) = false,
inference(orient,[status(thm)],[t18]) ).
cnf(t1855,plain,
true = false,
inference(step,[status(thm)],[t1854,t1680]) ).
cnf(t1764,plain,
false = true,
inference(orient,[status(thm)],[t1855]) ).
fof(f0,axiom,
! [A,B] :
( in(A,B)
=> ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f0_nnf,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B] :
( ~ in(B,A)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
fof(f9,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f9_nnf,plain,
! [A] : ~ empty(powerset(A)),
inference(nnf_transformation,[status(thm)],[f9]) ).
fof(f9_sk,plain,
! [A] : ~ empty(powerset(A)),
inference(skolemisation,[status(esa)],[f9_nnf]) ).
cnf(c13,plain,
~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f9_sk]) ).
fof(f22,axiom,
? [A] :
( relation(A)
& ~ empty(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_relat_1) ).
fof(f22_nnf,plain,
? [A] :
( relation(A)
& ~ empty(A) ),
inference(nnf_transformation,[status(thm)],[f22]) ).
fof(f22_sk,plain,
( relation(sk5)
& ~ empty(sk5) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk5])],[f22_nnf]) ).
cnf(c34,plain,
~ empty(sk5),
inference(cnf_transformation,[status(esa)],[f22_sk]) ).
fof(f24,axiom,
? [A] : ~ empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f24_nnf,plain,
? [A] : ~ empty(A),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
~ empty(sk7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sk7])],[f24_nnf]) ).
cnf(c38,plain,
~ empty(sk7),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
fof(f35,axiom,
! [A,B,C] :
~ ( empty(C)
& element(B,powerset(C))
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f35_nnf,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f35]) ).
fof(f35_sk,plain,
! [A,B,C] :
( ~ empty(C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f35_nnf]) ).
cnf(c56,plain,
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f35_sk]) ).
fof(f38,axiom,
! [A,B] :
~ ( empty(B)
& in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f38_nnf,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(nnf_transformation,[status(thm)],[f38]) ).
fof(f38_sk,plain,
! [A,B] :
( ~ empty(B)
| ~ in(A,B) ),
inference(skolemisation,[status(esa)],[f38_nnf]) ).
cnf(c60,plain,
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f38_sk]) ).
cnf(goal_0,negated_conjecture,
true != false,
inference(equality_encoding,[status(esa)],[c0,c13,c34,c38,c55,c56,c60]) ).
cnf(g0_0,plain,
true != true,
inference(rw,[status(thm)],[goal_0,t1764]) ).
cnf(contradiction_0,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[g0_0]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU020+1 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Thu Sep 24 12:38:24 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.35 Running run_findproof /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 59.00/7.89 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 59.00/7.89 % SZS output start Proof for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
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