%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : DAT320^1 : TPTP v9.3.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n019.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 : Wed Sep 30 07:49:11 AM UTC 2026
% Result : Theorem 0.20s 0.28s
% Output : Refutation 0.20s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : DAT320^1 : TPTP v9.3.1. Released v7.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.20 % Computer : n019.cluster.edu
% 0.09/0.20 % Model : x86_64 x86_64
% 0.09/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.20 % Memory : 8046.5625MB
% 0.09/0.20 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 18:27:33 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.21 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.09/0.24 Running first-order model finding
% 0.09/0.24 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.28 % (1177925)Will run a generic schedule for satisfiability detection.
% 0.20/0.28 % (1177933)dis+10_1_sil=32000:sp=arity:random_seed=471620753:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.20/0.28 % (1177931)% WARNING: option uhcvi not known.
% 0.20/0.28 % (1177933) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1177925-1177933"...
% 0.20/0.28 % (1177934)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3414361581:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.20/0.28 % (1177930)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=3137052377_2999 on theBenchmark for (2999ds/0Mi)
% 0.20/0.28 % (1177931)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2718092065:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.20/0.28 % (1177932)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4111983611:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.20/0.28 % (1177933)...printing done.
% 0.20/0.28 % (1177934)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % (1177931)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.20/0.28 % Exception at run slice level
% 0.20/0.28 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.20/0.28 % (1177933)Refutation found. Thanks to Tanya!
% 0.20/0.28 % SZS status Theorem for theBenchmark
% 0.20/0.28 % SZS output start Proof for theBenchmark
% 0.20/0.28 thf(type_def_5, type, 'type/ind_types/list': $tType > $tType).
% 0.20/0.28 thf(type_def_6, type, sTfun: ($tType * $tType) > $tType).
% 0.20/0.28 thf(type_def_7, type, sK0: $tType).
% 0.20/0.28 thf(func_def_0, type, 'const/lists/MEM': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > $o))).
% 0.20/0.28 thf(func_def_1, type, 'const/lists/APPEND': !>[X0: $tType]:(('type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.20/0.28 thf(func_def_2, type, 'const/ind_types/CONS': !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.20/0.28 thf(func_def_4, type, vSIGMA: !>[X0: $tType]:(((X0 > $o) > $o))).
% 0.20/0.28 thf(func_def_5, type, vAND: ($o > $o > $o)).
% 0.20/0.28 thf(func_def_6, type, vNOT: ($o > $o)).
% 0.20/0.28 thf(func_def_7, type, db0: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_8, type, db1: !>[X0: $tType]:(X0)).
% 0.20/0.28 thf(func_def_9, type, vEQ: !>[X0: $tType]:((X0 > X0 > $o))).
% 0.20/0.28 thf(func_def_10, type, vLAM: !>[X0: $tType, X1: $tType]:((X1) > (X0 > X1))).
% 0.20/0.28 thf(func_def_11, type, vOR: ($o > $o > $o)).
% 0.20/0.28 thf(func_def_12, type, sK1: sK0).
% 0.20/0.28 thf(func_def_13, type, sK2: 'type/ind_types/list' @ sK0).
% 0.20/0.28 thf(func_def_16, type, sK3: 'type/ind_types/list' @ sK0).
% 0.20/0.28 thf(func_def_17, type, sK4: 'type/ind_types/list' @ sK0).
% 0.20/0.28 thf(func_def_18, type, sK5: !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.20/0.28 thf(func_def_19, type, sK6: !>[X0: $tType]:((X0 > 'type/ind_types/list' @ X0 > 'type/ind_types/list' @ X0))).
% 0.20/0.28 thf(f1,axiom,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2)) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((X2 = (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)))) & ~('const/lists/MEM' @ X0 @ X1 @ X3)))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_DECOMPOSE_LEFT_')).
% 0.20/0.28 thf(f2,axiom,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3))) = ('const/lists/MEM' @ X0 @ X2 @ X3) | (X2 = X1))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_1')).
% 0.20/0.28 thf(f3,axiom,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3))) = ('const/lists/MEM' @ X0 @ X1 @ X3) | ('const/lists/MEM' @ X0 @ X1 @ X2))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_')).
% 0.20/0.28 thf(f4,conjecture,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2)) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (X2 = (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)))))),
% 0.20/0.28 file('/export/starexec/sandbox2/benchmark/theBenchmark.p','thm/lists/MEM_APPEND_DECOMPOSE_')).
% 0.20/0.28 thf(f5,negated_conjecture,(
% 0.20/0.28 ~ ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2)) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : (X2 = (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)))))),
% 0.20/0.28 inference(negated_conjecture,[status(cth)],[f4])).
% 0.20/0.28 thf(f6,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2)) = ? [X3 : 'type/ind_types/list' @ X0,X4 : 'type/ind_types/list' @ X0] : ((X2 = (('const/lists/APPEND' @ X0 @ X3 @ ('const/ind_types/CONS' @ X0 @ X1 @ X4)))) & ~('const/lists/MEM' @ X0 @ X1 @ X3)))),
% 0.20/0.28 inference(rectify,[],[f1])).
% 0.20/0.28 thf(f7,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2)) = ((?? @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (?? @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: ((~ ('const/lists/MEM' @ X0 @ X1 @ Y1)) & (('const/lists/APPEND' @ X0 @ Y1 @ ('const/ind_types/CONS' @ X0 @ X1 @ Y0)) = X2))))))))),
% 0.20/0.28 inference(fool_elimination,[],[f6])).
% 0.20/0.28 thf(f8,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3))) = ('const/lists/MEM' @ X0 @ X2 @ X3) | (X2 = X1))),
% 0.20/0.28 inference(rectify,[],[f2])).
% 0.20/0.28 thf(f9,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0,X2 : X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3))) = (((X1 = X2) | ('const/lists/MEM' @ X0 @ X2 @ X3))))),
% 0.20/0.28 inference(fool_elimination,[],[f8])).
% 0.20/0.28 thf(f10,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3))) = ('const/lists/MEM' @ X0 @ X1 @ X3) | ('const/lists/MEM' @ X0 @ X1 @ X2))),
% 0.20/0.28 inference(rectify,[],[f3])).
% 0.20/0.28 thf(f11,plain,(
% 0.20/0.28 ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3))) = ((('const/lists/MEM' @ X0 @ X1 @ X2) | ('const/lists/MEM' @ X0 @ X1 @ X3))))),
% 0.20/0.28 inference(fool_elimination,[],[f10])).
% 0.20/0.28 thf(f12,plain,(
% 0.20/0.28 ~ ! [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2)) = ((?? @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (?? @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (('const/lists/APPEND' @ X0 @ Y1 @ ('const/ind_types/CONS' @ X0 @ X1 @ Y0)) = X2)))))))),
% 0.20/0.28 inference(fool_elimination,[],[f5])).
% 0.20/0.28 thf(f13,plain,(
% 0.20/0.28 ? [X0 : $tType,X1 : X0,X2 : 'type/ind_types/list' @ X0] : ((('const/lists/MEM' @ X0 @ X1 @ X2)) != ((?? @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (?? @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: (('const/lists/APPEND' @ X0 @ Y1 @ ('const/ind_types/CONS' @ X0 @ X1 @ Y0)) = X2)))))))),
% 0.20/0.28 inference(ennf_transformation,[],[f12])).
% 0.20/0.28 thf(f14,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) != ((?? @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (?? @ 'type/ind_types/list' @ sK0 @ (^[Y1 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y1 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ Y0)) = sK2)))))))),
% 0.20/0.28 inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f13])).
% 0.20/0.28 thf(f15,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2)) = ((?? @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (?? @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: ((~ ('const/lists/MEM' @ X0 @ X1 @ Y1)) & (('const/lists/APPEND' @ X0 @ Y1 @ ('const/ind_types/CONS' @ X0 @ X1 @ Y0)) = X2))))))))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f7])).
% 0.20/0.28 thf(f16,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X3 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3))) = (((X1 = X2) | ('const/lists/MEM' @ X0 @ X2 @ X3))))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f9])).
% 0.20/0.28 thf(f17,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3))) = ((('const/lists/MEM' @ X0 @ X1 @ X2) | ('const/lists/MEM' @ X0 @ X1 @ X3))))) )),
% 0.20/0.28 inference(cnf_transformation,[],[f11])).
% 0.20/0.28 thf(f18,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) != ((?? @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (?? @ 'type/ind_types/list' @ sK0 @ (^[Y1 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y1 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ Y0)) = sK2)))))))),
% 0.20/0.28 inference(cnf_transformation,[],[f14])).
% 0.20/0.28 thf(f21,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $true) | (((?? @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (?? @ 'type/ind_types/list' @ sK0 @ (^[Y1 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y1 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ Y0)) = sK2)))))) = $true)),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f18])).
% 0.20/0.28 thf(f22,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $false) | (((?? @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (?? @ 'type/ind_types/list' @ sK0 @ (^[Y1 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y1 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ Y0)) = sK2)))))) = $false)),
% 0.20/0.28 inference(xor_proxy_clausification,[],[f18])).
% 0.20/0.28 thf(f23,plain,(
% 0.20/0.28 ( ! [X1 : 'type/ind_types/list' @ sK0] : (((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $false) | ($false = (((^[Y0 : 'type/ind_types/list' @ sK0]: (?? @ 'type/ind_types/list' @ sK0 @ (^[Y1 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y1 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ Y0)) = sK2)))) @ X1)))) )),
% 0.20/0.28 inference(pi_proxy_clausification,[],[f22])).
% 0.20/0.28 thf(f24,plain,(
% 0.20/0.28 ( ! [X1 : 'type/ind_types/list' @ sK0] : (((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $false) | ($false = ((?? @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y0 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ X1)) = sK2)))))) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f23])).
% 0.20/0.28 thf(f25,plain,(
% 0.20/0.28 ( ! [X2 : 'type/ind_types/list' @ sK0,X1 : 'type/ind_types/list' @ sK0] : (((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $false) | ($false = (((^[Y0 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y0 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ X1)) = sK2)) @ X2)))) )),
% 0.20/0.28 inference(pi_proxy_clausification,[],[f24])).
% 0.20/0.28 thf(f26,plain,(
% 0.20/0.28 ( ! [X2 : 'type/ind_types/list' @ sK0,X1 : 'type/ind_types/list' @ sK0] : (((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $false) | ($false = ((('const/lists/APPEND' @ sK0 @ X2 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ X1)) = sK2)))) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f25])).
% 0.20/0.28 thf(f27,plain,(
% 0.20/0.28 ( ! [X2 : 'type/ind_types/list' @ sK0,X1 : 'type/ind_types/list' @ sK0] : (((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $false) | (sK2 != (('const/lists/APPEND' @ sK0 @ X2 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ X1))))) )),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f26])).
% 0.20/0.28 thf(f28,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $true) | ($true = (((^[Y0 : 'type/ind_types/list' @ sK0]: (?? @ 'type/ind_types/list' @ sK0 @ (^[Y1 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y1 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ Y0)) = sK2)))) @ sK3)))),
% 0.20/0.28 inference(sigma_proxy_clausification,[],[f21])).
% 0.20/0.28 thf(f29,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $true) | ($true = ((?? @ 'type/ind_types/list' @ sK0 @ (^[Y0 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y0 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ sK3)) = sK2)))))),
% 0.20/0.28 inference(beta-eta_normalization,[],[f28])).
% 0.20/0.28 thf(f30,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $true) | ($true = (((^[Y0 : 'type/ind_types/list' @ sK0]: (('const/lists/APPEND' @ sK0 @ Y0 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ sK3)) = sK2)) @ sK4)))),
% 0.20/0.28 inference(sigma_proxy_clausification,[],[f29])).
% 0.20/0.28 thf(f31,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $true) | ($true = ((('const/lists/APPEND' @ sK0 @ sK4 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ sK3)) = sK2)))),
% 0.20/0.28 inference(beta-eta_normalization,[],[f30])).
% 0.20/0.28 thf(f32,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $true) | (sK2 = (('const/lists/APPEND' @ sK0 @ sK4 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ sK3))))),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f31])).
% 0.20/0.28 thf(f33,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3))) = $true) | (((('const/lists/MEM' @ X0 @ X1 @ X2) | ('const/lists/MEM' @ X0 @ X1 @ X3))) = $false)) )),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f17])).
% 0.20/0.28 thf(f36,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X3 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X1 @ ('const/lists/APPEND' @ X0 @ X2 @ X3))) = $true) | ((('const/lists/MEM' @ X0 @ X1 @ X3)) = $false)) )),
% 0.20/0.28 inference(or_proxy_clausification,[],[f33])).
% 0.20/0.28 thf(f38,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X3 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3))) = $true) | ((((X1 = X2) | ('const/lists/MEM' @ X0 @ X2 @ X3))) = $false)) )),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f16])).
% 0.20/0.28 thf(f43,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X3 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3))) = $true) | (((X1 = X2)) = $false)) )),
% 0.20/0.28 inference(or_proxy_clausification,[],[f38])).
% 0.20/0.28 thf(f44,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : X0,X3 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X2 @ ('const/ind_types/CONS' @ X0 @ X1 @ X3))) = $true) | (X1 != X2)) )),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f43])).
% 0.20/0.28 thf(f46,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2)) = $false) | (((?? @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: (?? @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: ((~ ('const/lists/MEM' @ X0 @ X1 @ Y1)) & (('const/lists/APPEND' @ X0 @ Y1 @ ('const/ind_types/CONS' @ X0 @ X1 @ Y0)) = X2))))))) = $true)) )),
% 0.20/0.28 inference(iff_proxy_clausification,[],[f15])).
% 0.20/0.28 thf(f47,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2)) = $false) | ($true = (((^[Y0 : 'type/ind_types/list' @ X0]: (?? @ 'type/ind_types/list' @ X0 @ (^[Y1 : 'type/ind_types/list' @ X0]: ((~ ('const/lists/MEM' @ X0 @ X1 @ Y1)) & (('const/lists/APPEND' @ X0 @ Y1 @ ('const/ind_types/CONS' @ X0 @ X1 @ Y0)) = X2))))) @ (sK5 @ X0 @ X1 @ X2))))) )),
% 0.20/0.28 inference(sigma_proxy_clausification,[],[f46])).
% 0.20/0.28 thf(f48,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2)) = $false) | ($true = ((?? @ 'type/ind_types/list' @ X0 @ (^[Y0 : 'type/ind_types/list' @ X0]: ((~ ('const/lists/MEM' @ X0 @ X1 @ Y0)) & (('const/lists/APPEND' @ X0 @ Y0 @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK5 @ X0 @ X1 @ X2))) = X2))))))) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f47])).
% 0.20/0.28 thf(f49,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2)) = $false) | ($true = (((^[Y0 : 'type/ind_types/list' @ X0]: ((~ ('const/lists/MEM' @ X0 @ X1 @ Y0)) & (('const/lists/APPEND' @ X0 @ Y0 @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK5 @ X0 @ X1 @ X2))) = X2))) @ (sK6 @ X0 @ X1 @ X2))))) )),
% 0.20/0.28 inference(sigma_proxy_clausification,[],[f48])).
% 0.20/0.28 thf(f50,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2)) = $false) | ($true = (((~ ('const/lists/MEM' @ X0 @ X1 @ (sK6 @ X0 @ X1 @ X2))) & (('const/lists/APPEND' @ X0 @ (sK6 @ X0 @ X1 @ X2) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK5 @ X0 @ X1 @ X2))) = X2))))) )),
% 0.20/0.28 inference(beta-eta_normalization,[],[f49])).
% 0.20/0.28 thf(f51,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/MEM' @ X0 @ X1 @ X2)) = $false) | ($true = ((('const/lists/APPEND' @ X0 @ (sK6 @ X0 @ X1 @ X2) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK5 @ X0 @ X1 @ X2))) = X2)))) )),
% 0.20/0.28 inference(and_proxy_clausification,[],[f50])).
% 0.20/0.28 thf(f54,plain,(
% 0.20/0.28 ( ! [X0 : $tType,X2 : 'type/ind_types/list' @ X0,X1 : X0] : (((('const/lists/APPEND' @ X0 @ (sK6 @ X0 @ X1 @ X2) @ ('const/ind_types/CONS' @ X0 @ X1 @ (sK5 @ X0 @ X1 @ X2)))) = X2) | ((('const/lists/MEM' @ X0 @ X1 @ X2)) = $false)) )),
% 0.20/0.28 inference(equality_proxy_clausification,[],[f51])).
% 0.20/0.28 thf(f63,definition,(
% 0.20/0.28 spl7_1 <=> ! [X2 : 'type/ind_types/list' @ sK0,X1 : 'type/ind_types/list' @ sK0] : (sK2 != (('const/lists/APPEND' @ sK0 @ X2 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ X1))))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl7_1])],[avatar_definition])).
% 0.20/0.28 thf(f64,plain,(
% 0.20/0.28 ( ! [X2 : 'type/ind_types/list' @ sK0,X1 : 'type/ind_types/list' @ sK0] : ((sK2 != (('const/lists/APPEND' @ sK0 @ X2 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ X1))))) ) | ~spl7_1),
% 0.20/0.28 inference(avatar_component_clause,[],[f63])).
% 0.20/0.28 thf(f66,definition,(
% 0.20/0.28 spl7_2 <=> ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $false)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl7_2])],[avatar_definition])).
% 0.20/0.28 thf(f68,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $false) | ~spl7_2),
% 0.20/0.28 inference(avatar_component_clause,[],[f66])).
% 0.20/0.28 thf(f69,plain,(
% 0.20/0.28 spl7_1 | spl7_2),
% 0.20/0.28 inference(avatar_split_clause,[],[f27,f66,f63])).
% 0.20/0.28 thf(f71,definition,(
% 0.20/0.28 spl7_3 <=> (sK2 = (('const/lists/APPEND' @ sK0 @ sK4 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ sK3))))),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl7_3])],[avatar_definition])).
% 0.20/0.28 thf(f73,plain,(
% 0.20/0.28 (sK2 = (('const/lists/APPEND' @ sK0 @ sK4 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ sK3)))) | ~spl7_3),
% 0.20/0.28 inference(avatar_component_clause,[],[f71])).
% 0.20/0.28 thf(f75,definition,(
% 0.20/0.28 spl7_4 <=> ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $true)),
% 0.20/0.28 introduced(definition,[new_symbols(definition,[spl7_4])],[avatar_definition])).
% 0.20/0.28 thf(f77,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $true) | ~spl7_4),
% 0.20/0.28 inference(avatar_component_clause,[],[f75])).
% 0.20/0.28 thf(f78,plain,(
% 0.20/0.28 spl7_3 | spl7_4),
% 0.20/0.28 inference(avatar_split_clause,[],[f32,f75,f71])).
% 0.20/0.28 thf(f115,plain,(
% 0.20/0.28 ( ! [X0 : sK0] : (($false = (('const/lists/MEM' @ sK0 @ X0 @ ('const/ind_types/CONS' @ sK0 @ sK1 @ sK3)))) | ($true = (('const/lists/MEM' @ sK0 @ X0 @ sK2)))) ) | ~spl7_3),
% 0.20/0.28 inference(constrained_superposition,[],[f36,f73])).
% 0.20/0.28 thf(f126,plain,(
% 0.20/0.28 ( ! [X0 : sK0] : (($true = $false) | (sK1 != X0) | ($true = (('const/lists/MEM' @ sK0 @ X0 @ sK2)))) ) | ~spl7_3),
% 0.20/0.28 inference(constrained_superposition,[],[f44,f115])).
% 0.20/0.28 thf(f127,plain,(
% 0.20/0.28 ( ! [X0 : sK0] : ((sK1 != X0) | ($true = (('const/lists/MEM' @ sK0 @ X0 @ sK2)))) ) | ~spl7_3),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f126])).
% 0.20/0.28 thf(f139,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $true) | ~spl7_3),
% 0.20/0.28 inference(equality_resolution,[],[f127])).
% 0.20/0.28 thf(f140,plain,(
% 0.20/0.28 ($true = $false) | (~spl7_2 | ~spl7_3)),
% 0.20/0.28 inference(forward_demodulation,[],[f139,f68])).
% 0.20/0.28 thf(f141,plain,(
% 0.20/0.28 $false | (~spl7_2 | ~spl7_3)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f140])).
% 0.20/0.28 thf(f142,plain,(
% 0.20/0.28 ~spl7_2 | ~spl7_3),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f141])).
% 0.20/0.28 thf(f149,plain,(
% 0.20/0.28 ($true = $false) | (~spl7_2 | ~spl7_4)),
% 0.20/0.28 inference(constrained_superposition,[],[f68,f77])).
% 0.20/0.28 thf(f155,plain,(
% 0.20/0.28 $false | (~spl7_2 | ~spl7_4)),
% 0.20/0.28 inference(trivial_inequality_removal,[],[f149])).
% 0.20/0.28 thf(f156,plain,(
% 0.20/0.28 ~spl7_2 | ~spl7_4),
% 0.20/0.28 inference(avatar_contradiction_clause,[],[f155])).
% 0.20/0.28 thf(f180,plain,(
% 0.20/0.28 ( ! [X0 : 'type/ind_types/list' @ sK0] : ((sK2 != X0) | ($false = (('const/lists/MEM' @ sK0 @ sK1 @ X0)))) ) | ~spl7_1),
% 0.20/0.28 inference(constrained_superposition,[],[f64,f54])).
% 0.20/0.28 thf(f186,plain,(
% 0.20/0.28 ((('const/lists/MEM' @ sK0 @ sK1 @ sK2)) = $false) | ~spl7_1),
% 0.20/0.28 inference(equality_resolution,[],[f180])).
% 0.20/0.28 thf(f187,plain,(
% 0.20/0.28 spl7_2 | ~spl7_1),
% 0.20/0.28 inference(avatar_split_clause,[],[f186,f63,f66])).
% 0.20/0.28 cnf(s1, plain, spl7_1 | spl7_2, inference(sat_conversion,[],[f69])).
% 0.20/0.28 cnf(s2, plain, spl7_3 | spl7_4, inference(sat_conversion,[],[f78])).
% 0.20/0.28 cnf(s4, plain, ~spl7_2 | ~spl7_3, inference(sat_conversion,[],[f142])).
% 0.20/0.28 cnf(s8, plain, ~spl7_2 | ~spl7_4, inference(sat_conversion,[],[f156])).
% 0.20/0.28 cnf(s9, plain, ~spl7_1 | spl7_2, inference(sat_conversion,[],[f187])).
% 0.20/0.28 cnf(s10, plain, ~spl7_2, inference(rat,[],[s2,s4,s8])).
% 0.20/0.28 cnf(s11, plain, ~spl7_1, inference(rat,[],[s9,s10])).
% 0.20/0.28 cnf(s12, plain, $false, inference(rat,[],[s1,s10,s11])).
% 0.20/0.28 thf(f188,plain,(
% 0.20/0.28 $false),
% 0.20/0.28 inference(avatar_sat_refutation,[],[s12])).
% 0.20/0.28 % SZS output end Proof for theBenchmark
% 0.20/0.28 % (1177933)------------------------------
% 0.20/0.28 % (1177933)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.28 % (1177933)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.28 % (1177933)CaDiCaL version: 2.1.3
% 0.20/0.28 % (1177933)Termination reason: Refutation
% 0.20/0.28 % (1177933)Time elapsed: 0.007 s
% 0.20/0.28 % (1177933)Peak memory usage: 12 MB
% 0.20/0.28 % (1177933)Instructions burned: 21 (million)
% 0.20/0.28 % (1177925)Success in time 0.036 s
% 0.20/0.28 % Vampire exiting
%------------------------------------------------------------------------------